Servizi per la didattica

PORTALE DELLA DIDATTICA

01NMFQD

A.A. 2020/21

2020/21

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

The subject consists of two parts: the first one discusses some advanced topics in the field of engineering thermodynamics, the second one discusses the use of numerical methods for solving engineering problems. In particular, the modeling and numerical methods are applied to meaningful test cases relevant for engineering thermodynamics. The module of Advanced Engineering Thermodynamics is designed to complete the student's preparation in the field of engineering thermodynamics, whose basics were provided in previous subjects. This teaching module completes the theoretical background required by the design of devices with regards to the specific problems involving heat transfer. In particular, the subject discusses the thermal performance of energy components and mechanical systems and it provides some basic concepts about numerical fluid dynamics, including modeling of heat transfer systems. Finally, the basic concepts of environmental acoustics and lighting are provided in order to characterize the interaction of the devices with the end users. The module of Numerical Modelling is intended to provide the tools for the systematic and critical study of the main numerical models involving partial derivatives and used in various fields of engineering, which can be solved by appropriate numerical discretization methods. In particular, the module aims to provide the essential features for evaluating a numerical method in terms of the quality and the reliability of the numerical solution. Some test cases will be discussed in the field of advanced engineering thermodynamics.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

The subject consists of two parts: the first one discusses some advanced topics in the field of engineering thermodynamics, the second one discusses the use of numerical methods for solving engineering problems. In particular, the modeling and numerical methods are applied to meaningful test cases relevant for engineering thermodynamics. The module of Advanced Engineering Thermodynamics is designed to complete the student's preparation in the field of engineering thermodynamics, whose basics were provided in previous subjects. This teaching module completes the theoretical background required by the design of devices with regards to the specific problems involving heat transfer. In particular, the subject discusses the thermal performance of energy components and mechanical systems and it provides some basic concepts about numerical fluid dynamics, including modeling of heat transfer systems. Finally, the basic concepts of environmental acoustics and lighting are provided in order to characterize the interaction of the devices with the end users. The module of Numerical Modelling is intended to provide the tools for the systematic and critical study of the main numerical models involving partial derivatives and used in various fields of engineering, which can be solved by appropriate numerical discretization methods. In particular, the module aims to provide the essential features for evaluating a numerical method in terms of the quality and the reliability of the numerical solution. Some test cases will be discussed in the field of advanced engineering thermodynamics.

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

The subject consists of two parts: the first one discusses some advanced topics in the field of engineering thermodynamics, the second one discusses the use of numerical methods for solving engineering problems. In particular, the modeling and numerical methods are applied to meaningful test cases relevant for engineering thermodynamics. The module of Advanced Engineering Thermodynamics is designed to complete the student's preparation in the field of engineering thermodynamics, whose basics were provided in previous subjects. This teaching module completes the theoretical background required by the design of devices with regards to the specific problems involving heat transfer. In particular, the subject discusses the thermal performance of energy components and mechanical systems and it provides some basic concepts about numerical fluid dynamics, including modeling of heat transfer systems. Finally, the basic concepts of environmental acoustics and lighting are provided in order to characterize the interaction of the devices with the end users. The module of Numerical Modelling is intended to provide the tools for the systematic and critical study of the main numerical models involving partial derivatives and used in various fields of engineering, which can be solved by appropriate numerical discretization methods. In particular, the module aims to provide the essential features for evaluating a numerical method in terms of the quality and the reliability of the numerical solution. Some test cases will be discussed in the field of advanced engineering thermodynamics.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

The objective is to convey to the student in-depth knowledge of thermomechanical continuous media, thermodynamics and fluid dynamics, with particular emphasis on the concept of exergy, and, as regards the interaction with the end user, the basic elements of environmental acoustics and lighting. Additionally, the student should acquire the basic knowledge about the discretization methods for initial and boundary value problems involving elliptic, parabolic and hyperbolic partial differential equations (PDEs). Some emphasis is put on the basic mathematical properties (such as consistency, stability and convergence) of numerical methods. Students should become able to transform numerical models into systems of algebraic equations, and to solve these systems. The student is expected to learn how to use theoretical tools for studying heat transfer and energy balance of real systems, performing energy and exergy analysis of complex real systems (including using appropriate mathematical models) and managing complex energy conversion systems. Another objective is to convey to the student the ability to understand the regulations about environmental acoustics and lighting and to perform basic design calculations. Finally, the student is expected to learn the ability to implement in the MATLAB(r) software, or similar ones, some numerical models that describe engineering problems (particularly those relevant to engineering thermodynamics) and to relate their performances to the theoretical context. The student should also develop the ability of applying the numerical tools to the simulation of the behaviour of simple yet significant problems in applied thermodynamics.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

The objective is to convey to the student in-depth knowledge of thermomechanical continuous media, thermodynamics and fluid dynamics, with particular emphasis on the concept of exergy, and, as regards the interaction with the end user, the basic elements of environmental acoustics and lighting. Additionally, the student should acquire the basic knowledge about the discretization methods for initial and boundary value problems involving elliptic, parabolic and hyperbolic partial differential equations (PDEs). Some emphasis is put on the basic mathematical properties (such as consistency, stability and convergence) of numerical methods. Students should become able to transform numerical models into systems of algebraic equations, and to solve these systems. The student is expected to learn how to use theoretical tools for studying heat transfer and energy balance of real systems, performing energy and exergy analysis of complex real systems (including using appropriate mathematical models) and managing complex energy conversion systems. Another objective is to convey to the student the ability to understand the regulations about environmental acoustics and lighting and to perform basic design calculations. Finally, the student is expected to learn the ability to implement in the MATLAB(r) software, or similar ones, some numerical models that describe engineering problems (particularly those relevant to engineering thermodynamics) and to relate their performances to the theoretical context. The student should also develop the ability of applying the numerical tools to the simulation of the behaviour of simple yet significant problems in applied thermodynamics.

The objective is to convey to the student in-depth knowledge of thermomechanical continuous media, thermodynamics and fluid dynamics, with particular emphasis on the concept of exergy, and, as regards the interaction with the end user, the basic elements of environmental acoustics and lighting. Additionally, the student should acquire the basic knowledge about the discretization methods for initial and boundary value problems involving elliptic, parabolic and hyperbolic partial differential equations (PDEs). Some emphasis is put on the basic mathematical properties (such as consistency, stability and convergence) of numerical methods. Students should become able to transform numerical models into systems of algebraic equations, and to solve these systems. The student is expected to learn how to use theoretical tools for studying heat transfer and energy balance of real systems, performing energy and exergy analysis of complex real systems (including using appropriate mathematical models) and managing complex energy conversion systems. Another objective is to convey to the student the ability to understand the regulations about environmental acoustics and lighting and to perform basic design calculations. Finally, the student is expected to learn the ability to implement in the MATLAB(r) software, or similar ones, some numerical models that describe engineering problems (particularly those relevant to engineering thermodynamics) and to relate their performances to the theoretical context. The student should also develop the ability of applying the numerical tools to the simulation of the behaviour of simple yet significant problems in applied thermodynamics.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Thermodynamics and heat transfer basics. Calculus, linear algebra and geometry basics. Basic knowledge of computer programming techniques and coding in programming languages as C, C++, MATLAB(r) o Python.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Thermodynamics and heat transfer basics. Calculus, linear algebra and geometry basics. Basic knowledge of computer programming techniques and coding in programming languages as C, C++, MATLAB(r) o Python.

Thermodynamics and heat transfer basics. Calculus, linear algebra and geometry basics. Basic knowledge of computer programming techniques and coding in programming languages as C, C++, MATLAB(r) o Python.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Concerning the first part, about advanced engineering thermodynamics, further details about the program are provided. There are essentially 5 chapters. CLASSICAL MOLECULAR DYNAMICS and KINETIC THEORY. Introduction to classical molecular dynamics. Bond and non-bond interactions. Force fields. Elementary numerical schemes (Verlet integration). Elementary statistical ensembles: Thermostats and barostats. Practical examples. Large systems approaching the local equilibrium: Maxwellian distribution function. The distribution function dynamics. Linear relaxation towards the local equilibrium: Bhatnagar–Gross–Krook (BGK) model. Practical examples. CONTINUUM THERMO-MECHANICS. Deduction of the equation of mass and momentum conservation by both kinetic local equilibrium and by elementary control volume. Deduction of the wave equation. Small deviations from the conditions of local equilibrium. Phenomenological relations in Navier-Stokes-Fourier equations: Stress tensor and thermal flux. Generalization of the results obtained by the ideal gas to other types of fluids. Dimensionless equations. Meaning of dimensionless numbers. Incompressible limit. Equation for kinetic energy and enthalpy. First principle of thermodynamics. Generalization of entropy for continuous body. Generalization of Gibbs’s correlation. The second principle of thermodynamics for a continuous body. Work, heat and the thermodynamics of irreversible processes. THERMAL DESIGN. Deduction of the integral equations for closed systems and open systems. Technical formulation of integral equations. Physical meaning of irreversibility. Correct calculation of irreversibility by practical formulas. Turbulence and turbulent flows. Characteristic scales of the phenomenon, deduction of the equations for the average quantities and the closure problem. Artificial viscosity induced by turbulence and modeling. Exergy balance in a reversible system. Exergy and internal exergy for an ideal gas. The theorem of Guy-Stodola. Physical meaning of exergy. Efficiency according to the second principle. Examples of exergy analysis. Exergy diagrams. Thermodynamic diagrams. ACOUSTICS. Deduction of the wave equation. Introduction, elastic, plane, longitudinal and progressive waves. Propagation speed of elastic waves; sound speed of air. Mechanical power transported by sound wave, wave intensity, resistance and effective pressure. Acoustic intensity and acoustic feeling: Law of Weber-Fechner. Diagram of the normal acoustic response. Acoustic field, feeling and the intensity level, decibels. Iso-phon curves. Frequency bands, level of pressure, interpolating weight curve A. Interaction between elastic waves and materials, factors of reflection, transmission, absorption, apparent absorption. Effect of frequency. Apparent absorption factor of several walls. Acoustics in open environments. Open field. Sound tail. Acoustic energy balance and reverberation, reverberation time by conventional formula of Sabine. Sound insulation; sound proofing; plain wall and law of mass and frequency; case study for a pipe. LIGHTING. Deduction of the radiative transfer equation (RTE) from kinetic theory. The light, electromagnetic radiation, main features, diffuse radiation. Visual perception and photometric system. Definition of physical units of measured quantities. Point source. Light intensity. Indicator of emission. Light flux emitted from a point source with a given indicator of emission. The first formula of Lambert. Linear source, linear luminance, and lighting calculations on surface. Surface source, luminance, and lighting calculation on a surface. The second law of Lambert. Lambert emitter. Efficiency of a light bulb. Concerning the model of numerical modelling, the program of class lessons is provided below. INTRODUCTORY PART. General concepts about partial differential equations; boundary and initial conditions; properties of solutions. Basic concepts of numerical methods. STEADY-STATE PROBLEMS. Elliptic problems; the steady diffusion and the membrane equilibrium examples; discretization by centered finite differences; variational formulation; discretization by finite elements. Implementation of Dirichlet, Neumann and Robin boundary conditions. Reduction of the discrete problem to an algebraic problem; properties of the corresponding matrices; techniques for solving large systems of algebraic equations. Mathematical properties of consistency, stability and convergence of the numerical schemes. Modal analysis; the free vibration of a membrane; discretization of eigenvalue problems. TIME-DEPENDENT PROBLEMS. Formulation and discretization of evolutionary problems; parabolic and hyperbolic equations; the heat equation, the wave equation; mass lumping; time advancing techniques; asymptotic stability and choice of the time step; rate of convergence in space and time. Convection-diffusion problems; mesh Peclet number; centered versus upwind discretizations. Conservation and balance laws; characteristics; integral formulation; discretization by finite volumes; cell averages and numerical fluxes; review of the main classical methods; relation with finite differences; Courant number and CFL condition; numerical diffusion and dispersion; stability and convergence.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Concerning the first part, about advanced engineering thermodynamics, further details about the program are provided. There are essentially 5 chapters. CLASSICAL MOLECULAR DYNAMICS and KINETIC THEORY. Introduction to classical molecular dynamics. Bond and non-bond interactions. Force fields. Elementary numerical schemes (Verlet integration). Elementary statistical ensembles: Thermostats and barostats. Practical examples. Large systems approaching the local equilibrium: Maxwellian distribution function. The distribution function dynamics. Linear relaxation towards the local equilibrium: Bhatnagar–Gross–Krook (BGK) model. Practical examples. CONTINUUM THERMO-MECHANICS. Deduction of the equation of mass and momentum conservation by both kinetic local equilibrium and by elementary control volume. Deduction of the wave equation. Small deviations from the conditions of local equilibrium. Phenomenological relations in Navier-Stokes-Fourier equations: Stress tensor and thermal flux. Generalization of the results obtained by the ideal gas to other types of fluids. Dimensionless equations. Meaning of dimensionless numbers. Incompressible limit. Equation for kinetic energy and enthalpy. First principle of thermodynamics. Generalization of entropy for continuous body. Generalization of Gibbs’s correlation. The second principle of thermodynamics for a continuous body. Work, heat and the thermodynamics of irreversible processes. THERMAL DESIGN. Deduction of the integral equations for closed systems and open systems. Technical formulation of integral equations. Physical meaning of irreversibility. Correct calculation of irreversibility by practical formulas. Turbulence and turbulent flows. Characteristic scales of the phenomenon, deduction of the equations for the average quantities and the closure problem. Artificial viscosity induced by turbulence and modeling. Exergy balance in a reversible system. Exergy and internal exergy for an ideal gas. The theorem of Guy-Stodola. Physical meaning of exergy. Efficiency according to the second principle. Examples of exergy analysis. Exergy diagrams. Thermodynamic diagrams. ACOUSTICS. Deduction of the wave equation. Introduction, elastic, plane, longitudinal and progressive waves. Propagation speed of elastic waves; sound speed of air. Mechanical power transported by sound wave, wave intensity, resistance and effective pressure. Acoustic intensity and acoustic feeling: Law of Weber-Fechner. Diagram of the normal acoustic response. Acoustic field, feeling and the intensity level, decibels. Iso-phon curves. Frequency bands, level of pressure, interpolating weight curve A. Interaction between elastic waves and materials, factors of reflection, transmission, absorption, apparent absorption. Effect of frequency. Apparent absorption factor of several walls. Acoustics in open environments. Open field. Sound tail. Acoustic energy balance and reverberation, reverberation time by conventional formula of Sabine. Sound insulation; sound proofing; plain wall and law of mass and frequency; case study for a pipe. LIGHTING. Deduction of the radiative transfer equation (RTE) from kinetic theory. The light, electromagnetic radiation, main features, diffuse radiation. Visual perception and photometric system. Definition of physical units of measured quantities. Point source. Light intensity. Indicator of emission. Light flux emitted from a point source with a given indicator of emission. The first formula of Lambert. Linear source, linear luminance, and lighting calculations on surface. Surface source, luminance, and lighting calculation on a surface. The second law of Lambert. Lambert emitter. Efficiency of a light bulb. Concerning the model of numerical modelling, the program of class lessons is provided below. INTRODUCTORY PART. General concepts about partial differential equations; boundary and initial conditions; properties of solutions. Basic concepts of numerical methods. STEADY-STATE PROBLEMS. Elliptic problems; the steady diffusion and the membrane equilibrium examples; discretization by centered finite differences; variational formulation; discretization by finite elements. Implementation of Dirichlet, Neumann and Robin boundary conditions. Reduction of the discrete problem to an algebraic problem; properties of the corresponding matrices; techniques for solving large systems of algebraic equations. Mathematical properties of consistency, stability and convergence of the numerical schemes. Modal analysis; the free vibration of a membrane; discretization of eigenvalue problems. TIME-DEPENDENT PROBLEMS. Formulation and discretization of evolutionary problems; parabolic and hyperbolic equations; the heat equation, the wave equation; mass lumping; time advancing techniques; asymptotic stability and choice of the time step; rate of convergence in space and time. Convection-diffusion problems; mesh Peclet number; centered versus upwind discretizations. Conservation and balance laws; characteristics; integral formulation; discretization by finite volumes; cell averages and numerical fluxes; review of the main classical methods; relation with finite differences; Courant number and CFL condition; numerical diffusion and dispersion; stability and convergence.

Concerning the first part, about advanced engineering thermodynamics, further details about the program are provided. There are essentially 5 chapters. CLASSICAL MOLECULAR DYNAMICS and KINETIC THEORY. Introduction to classical molecular dynamics. Bond and non-bond interactions. Force fields. Elementary numerical schemes (Verlet integration). Elementary statistical ensembles: Thermostats and barostats. Practical examples. Large systems approaching the local equilibrium: Maxwellian distribution function. The distribution function dynamics. Linear relaxation towards the local equilibrium: Bhatnagar–Gross–Krook (BGK) model. Practical examples. CONTINUUM THERMO-MECHANICS. Deduction of the equation of mass and momentum conservation by both kinetic local equilibrium and by elementary control volume. Deduction of the wave equation. Small deviations from the conditions of local equilibrium. Phenomenological relations in Navier-Stokes-Fourier equations: Stress tensor and thermal flux. Generalization of the results obtained by the ideal gas to other types of fluids. Dimensionless equations. Meaning of dimensionless numbers. Incompressible limit. Equation for kinetic energy and enthalpy. First principle of thermodynamics. Generalization of entropy for continuous body. Generalization of Gibbs’s correlation. The second principle of thermodynamics for a continuous body. Work, heat and the thermodynamics of irreversible processes. THERMAL DESIGN. Deduction of the integral equations for closed systems and open systems. Technical formulation of integral equations. Physical meaning of irreversibility. Correct calculation of irreversibility by practical formulas. Turbulence and turbulent flows. Characteristic scales of the phenomenon, deduction of the equations for the average quantities and the closure problem. Artificial viscosity induced by turbulence and modeling. Exergy balance in a reversible system. Exergy and internal exergy for an ideal gas. The theorem of Guy-Stodola. Physical meaning of exergy. Efficiency according to the second principle. Examples of exergy analysis. Exergy diagrams. Thermodynamic diagrams. ACOUSTICS. Deduction of the wave equation. Introduction, elastic, plane, longitudinal and progressive waves. Propagation speed of elastic waves; sound speed of air. Mechanical power transported by sound wave, wave intensity, resistance and effective pressure. Acoustic intensity and acoustic feeling: Law of Weber-Fechner. Diagram of the normal acoustic response. Acoustic field, feeling and the intensity level, decibels. Iso-phon curves. Frequency bands, level of pressure, interpolating weight curve A. Interaction between elastic waves and materials, factors of reflection, transmission, absorption, apparent absorption. Effect of frequency. Apparent absorption factor of several walls. Acoustics in open environments. Open field. Sound tail. Acoustic energy balance and reverberation, reverberation time by conventional formula of Sabine. Sound insulation; sound proofing; plain wall and law of mass and frequency; case study for a pipe. LIGHTING. Deduction of the radiative transfer equation (RTE) from kinetic theory. The light, electromagnetic radiation, main features, diffuse radiation. Visual perception and photometric system. Definition of physical units of measured quantities. Point source. Light intensity. Indicator of emission. Light flux emitted from a point source with a given indicator of emission. The first formula of Lambert. Linear source, linear luminance, and lighting calculations on surface. Surface source, luminance, and lighting calculation on a surface. The second law of Lambert. Lambert emitter. Efficiency of a light bulb. Concerning the model of numerical modelling, the program of class lessons is provided below. INTRODUCTORY PART. General concepts about partial differential equations; boundary and initial conditions; properties of solutions. Basic concepts of numerical methods. STEADY-STATE PROBLEMS. Elliptic problems; the steady diffusion and the membrane equilibrium examples; discretization by centered finite differences; variational formulation; discretization by finite elements. Implementation of Dirichlet, Neumann and Robin boundary conditions. Reduction of the discrete problem to an algebraic problem; properties of the corresponding matrices; techniques for solving large systems of algebraic equations. Mathematical properties of consistency, stability and convergence of the numerical schemes. Modal analysis; the free vibration of a membrane; discretization of eigenvalue problems. TIME-DEPENDENT PROBLEMS. Formulation and discretization of evolutionary problems; parabolic and hyperbolic equations; the heat equation, the wave equation; mass lumping; time advancing techniques; asymptotic stability and choice of the time step; rate of convergence in space and time. Convection-diffusion problems; mesh Peclet number; centered versus upwind discretizations. Conservation and balance laws; characteristics; integral formulation; discretization by finite volumes; cell averages and numerical fluxes; review of the main classical methods; relation with finite differences; Courant number and CFL condition; numerical diffusion and dispersion; stability and convergence.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

In addition to lessons, the following activities are provided. Concerning the first part of applied engineering thermodynamics, students are expected to develop a project. Students are divided into 5 teams, as many as the number of applications. For each theme, they must provide (a) calculation of an off-design condition, (b) exergetic analysis and (c) all the technical details related to the design performed. To develop the project, specific notes are made available on the “Portale della Didattica”. In addition, some lectures are focused on the presentation of the guidelines for the project developments and practical examples. Concerning the part on applied acoustics, a practical application in class is developed, aiming at the evaluation of acoustic behavior of the room. In particular, three different analyses are performed: evaluation of the acoustic field, measurement of the reverberation time and measurements of the acoustic pressure. Concerning the part on numerical modeling, the following exercises and laboratory activity is developed: Mesh generation; construction of mass and stiffness matrices in various situations; iterative solution of large algebraic systems with sparse matrices; computation of the equilibrium configuration of several physical problems; analysis of the behavior of the spatial discretization error. Implementation of eigenvalue problems and modal analysis. Implementation of time advancing techniques; investigation on the stability of the schemes and the behavior of the temporal error; computation of the evolution of the temperature of a conducting body, and of the propagation of waves in an elastic body. Implementation of numerical schemes for scalar conservation laws and experimental investigation on their behavior.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

In addition to lessons, the following activities are provided. Concerning the first part of applied engineering thermodynamics, students are expected to develop a project. Students are divided into 5 teams, as many as the number of applications. For each theme, they must provide (a) calculation of an off-design condition, (b) exergetic analysis and (c) all the technical details related to the design performed. To develop the project, specific notes are made available on the “Portale della Didattica”. In addition, some lectures are focused on the presentation of the guidelines for the project developments and practical examples. Concerning the part on applied acoustics, a practical application in class is developed, aiming at the evaluation of acoustic behavior of the room. In particular, three different analyses are performed: evaluation of the acoustic field, measurement of the reverberation time and measurements of the acoustic pressure. Concerning the part on numerical modeling, the following exercises and laboratory activity is developed: Mesh generation; construction of mass and stiffness matrices in various situations; iterative solution of large algebraic systems with sparse matrices; computation of the equilibrium configuration of several physical problems; analysis of the behavior of the spatial discretization error. Implementation of eigenvalue problems and modal analysis. Implementation of time advancing techniques; investigation on the stability of the schemes and the behavior of the temporal error; computation of the evolution of the temperature of a conducting body, and of the propagation of waves in an elastic body. Implementation of numerical schemes for scalar conservation laws and experimental investigation on their behavior.

In addition to lessons, the following activities are provided. Concerning the first part of applied engineering thermodynamics, students are expected to develop a project. Students are divided into 5 teams, as many as the number of applications. For each theme, they must provide (a) calculation of an off-design condition, (b) exergetic analysis and (c) all the technical details related to the design performed. To develop the project, specific notes are made available on the “Portale della Didattica”. In addition, some lectures are focused on the presentation of the guidelines for the project developments and practical examples. Concerning the part on applied acoustics, a practical application in class is developed, aiming at the evaluation of acoustic behavior of the room. In particular, three different analyses are performed: evaluation of the acoustic field, measurement of the reverberation time and measurements of the acoustic pressure. Concerning the part on numerical modeling, the following exercises and laboratory activity is developed: Mesh generation; construction of mass and stiffness matrices in various situations; iterative solution of large algebraic systems with sparse matrices; computation of the equilibrium configuration of several physical problems; analysis of the behavior of the spatial discretization error. Implementation of eigenvalue problems and modal analysis. Implementation of time advancing techniques; investigation on the stability of the schemes and the behavior of the temporal error; computation of the evolution of the temperature of a conducting body, and of the propagation of waves in an elastic body. Implementation of numerical schemes for scalar conservation laws and experimental investigation on their behavior.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

- P. Asinari, E. Chiavazzo, An Introduction to Multiscale Modeling with Applications, Società Editrice Esculapio, Bologna 2013. - M. Calì, P. Gregorio, "Termodinamica" Esculapio, Bologna 1997. - A. Bejan, "Advanced Engineering Thermodynamic" John Wiley & Sons 1997. - G. Guglielmini, C. Pisoni, Introduzione alla trasmissione del calore, Casa Editrice Ambrosiana, 2002. - G. Comini, G. Cortella, Fondamenti di trasmissione del calore, Servizi Grafici Editoriali, 2001. - C. Canuto, "Metodi e Modelli Numerici ", note delle lezioni con esercizi, disponibile online sul Portale della Didattica. - A. Quarteroni, "Numerical Models for Differential Problems", Springer 2014.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

- P. Asinari, E. Chiavazzo, An Introduction to Multiscale Modeling with Applications, Società Editrice Esculapio, Bologna 2013. - M. Calì, P. Gregorio, "Termodinamica" Esculapio, Bologna 1997. - A. Bejan, "Advanced Engineering Thermodynamic" John Wiley & Sons 1997. - G. Guglielmini, C. Pisoni, Introduzione alla trasmissione del calore, Casa Editrice Ambrosiana, 2002. - G. Comini, G. Cortella, Fondamenti di trasmissione del calore, Servizi Grafici Editoriali, 2001. - C. Canuto, "Metodi e Modelli Numerici ", note delle lezioni con esercizi, disponibile online sul Portale della Didattica. - A. Quarteroni, "Numerical Models for Differential Problems", Springer 2014.

- P. Asinari, E. Chiavazzo, An Introduction to Multiscale Modeling with Applications, Società Editrice Esculapio, Bologna 2013. - M. Calì, P. Gregorio, "Termodinamica" Esculapio, Bologna 1997. - A. Bejan, "Advanced Engineering Thermodynamic" John Wiley & Sons 1997. - G. Guglielmini, C. Pisoni, Introduzione alla trasmissione del calore, Casa Editrice Ambrosiana, 2002. - G. Comini, G. Cortella, Fondamenti di trasmissione del calore, Servizi Grafici Editoriali, 2001. - C. Canuto, "Metodi e Modelli Numerici ", note delle lezioni con esercizi, disponibile online sul Portale della Didattica. - A. Quarteroni, "Numerical Models for Differential Problems", Springer 2014.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

**Modalità di esame:** Prova scritta su carta con videosorveglianza dei docenti; Prova scritta a risposta aperta o chiusa tramite PC con l'utilizzo della piattaforma di ateneo Exam integrata con strumenti di proctoring (Respondus); Elaborato progettuale in gruppo;

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

**Modalità di esame:**

Module of Advanced Engineering Thermodynamics. Each student will be given an online test sub-divided in two parts on her/his computer via the Exam+Respondus platform. Each test includes a number of both open-ended and closed-ended questions and the navigation through questions is free. In addition, each student will also be assessed on the result of the group's project and the applied acoustics report. It is permitted to have and use only a few blank A4 papers, a pen (black or blue) and if needed a physical calculator as a possible support during the answers (provided that during the environmental recording and the subsequent use they are all clearly showed in the webcam). It will be possible to close the exam and finish only if at least 90% of the total time has elapsed. The Virtual Classroom integrated in the Exam platform will be also enabled to allow possible interaction with the lecturers. More specifically, the exam of this module is structured in three parts as follows: 1.The first part will include a maximum of 15 open- and/or closed-ended questions that will focus on the fundamental parts of the course, and which aim to assess that the student has correctly understood the theoretical foundations underlying the continuum thermo-mechanics, thermodynamics, heat transfer, applied acoustics and lighting technology discussed during both theoretical and practise lectures. During this first part, using support materials of any kind is strictly forbidden. The maximum time available to complete this part will be at least 40 minutes. The final result of this part will be evaluated up to a max of 15 points. 2. In the second part of the online test, the student must demonstrate that she/he has actively contributed to the group project as well as to the implementation of the applied acoustic report. To this end, a maximum of 12 open- and/or closed-ended questions will be given to each student. The questions will be focused on the design aspects addressed in the specific group work and will aim to assess that the student has understood the use of the tools illustrated in the course for thermal analysis, energy and exergy analysis of processes/systems, as well as the most important aspects of the applied acoustics report. During this part, the support of the group project and the applied acoustic report is allowed. The maximum time available to complete this part will be at least 40 minutes. The final result of this part will be evaluated up to a max of 12 points. 3. Each team must deliver a pdf copy of both the group’s project and the applied acoustics report at least one week before the exam date. Pdf upload must occur through the Teaching Portal, uploading a single PDF file (which contains both the files) in the section "Elaborati". The upload of the file should be performed only by one representative for each group, taking care to report the names, surnames of each group member on the first page of the report. The reports will be evaluated at most 6 points, and the score will be applied to each of the group members. The final mark of the Advanced topics of Engineering Thermodynamics module will be calculated for each student by summing up the scores of the first online part, the second online part and the evaluation of the project reports. The maximum score will be 30 (possibly cum laude if a total grade exceeding 30 points is achieved). Whenever needed, the upper-rounded rule will be used. The Advanced topics of Engineering Thermodynamics module is considered passed if the final score is at least 18 and both reports have been delivered by the group. The final mark will be communicated by the lecturer a week after the exam date, specifying the contribution to the final score of each part of the exam (online part and report evaluation). Consistently with the expected learning outcomes, the exam aims at assessing the achievement of the following objectives: 1. In-depth knowledge of the theoretical notions on thermo-mechanics, continuum theory and thermodynamic. This is accomplished by the first set of online questions; 2. Ability to use the theoretical tools provided in the subject energy and exergetic design and analysis to study real/complex systems involving energy transformation processes. This is established both through the second set of theoretical questions and through the implementation of the group project; 3. Ability to properly interpret the regulations and to perform estimates in the field of lighting and applied acoustic. This is mainly determined by the implementation of the group project and the report on applied acoustic. This is accomplished by the implementation of the group reports. Module of Numerical Modelling. The exam is based on the following tests: a) solving some exercises on the main topics covered in the module (duration 35 minutes); b) answering, using MATLAB(r), a series of multiple choice questions (Duration 40 minutes). It is not allowed the use of any support materials during these tests. In the formulation of the mark, possibly we will take into account also the: c) optional preparation of a computational project during the semester, carried out by small groups of students on a numerical problem linked to an applied project of the module of Advanced Engineering Thermodynamics, and evaluated on the basis of the individual contribution of each student. Tests a) and b) have a relative weight of 2/3 and 1/3 and are provided to reach up to 28 points, while test c) enables to go beyond 28, including “cum laude”. The marks obtained in the written tests will be communicated to the students through the Teaching Portal, together with an indication of when and where the students can view their tests. In the fully remote mode, tests a) and b) are carried out through video surveillance by the teachers: students enter small groups in a certain number of Virtual Classroom activating microphone and webcam, and are followed by a teacher during the exam. At the end of the test a), students upload the written paper on the University platform intended for this purpose. To perform the test b), the students carry out the necessary calculations with Matlab on their computer, by accessing the Exam platform to receive the questions and enter the answers. Finally, test c) is carried out by uploading a paper containing the results of the project and the corresponding teacher-student discussion held on Virtual Classroom. Consistent with the declared learning outcomes, the written part aims at assessing the achievement of the following objectives: 1. Knowledge of the main discretization methodologies of mathematical models and their translation into algebraic equation systems. This is established through test a). 2. Ability to implement the studied numerical models in the MATLAB environment. This is established mainly through test b), but also through test c). 3. Ability to apply the numerical tools studied to the simulation of the problem of engineering thermodynamics problems. This is established through test c). Finally, it should be noted that the mark obtained in the Advanced topics of Engineering Thermodynamics module shall be averaged with the mark obtained in the Numerical modelling module. The upper rounded arithmetic mean of the two modules will be officially recorded as a final grade.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

**Exam:** Paper-based written test with video surveillance of the teaching staff; Computer-based written test with open-ended questions or multiple-choice questions using the Exam platform and proctoring tools (Respondus); Group project;

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

**Exam:**

Module of Advanced Engineering Thermodynamics. Each student will be given an online test sub-divided in two parts on her/his computer via the Exam+Respondus platform. Each test includes a number of both open-ended and closed-ended questions and the navigation through questions is free. In addition, each student will also be assessed on the result of the group's project and the applied acoustics report. It is permitted to have and use only a few blank A4 papers, a pen (black or blue) and if needed a physical calculator as a possible support during the answers (provided that during the environmental recording and the subsequent use they are all clearly showed in the webcam). It will be possible to close the exam and finish only if at least 90% of the total time has elapsed. The Virtual Classroom integrated in the Exam platform will be also enabled to allow possible interaction with the lecturers. More specifically, the exam of this module is structured in three parts as follows: 1.The first part will include a maximum of 15 open- and/or closed-ended questions that will focus on the fundamental parts of the course, and which aim to assess that the student has correctly understood the theoretical foundations underlying the continuum thermo-mechanics, thermodynamics, heat transfer, applied acoustics and lighting technology discussed during both theoretical and practise lectures. During this first part, using support materials of any kind is strictly forbidden. The maximum time available to complete this part will be at least 40 minutes. The final result of this part will be evaluated up to a max of 15 points. 2. In the second part of the online test, the student must demonstrate that she/he has actively contributed to the group project as well as to the implementation of the applied acoustic report. To this end, a maximum of 12 open- and/or closed-ended questions will be given to each student. The questions will be focused on the design aspects addressed in the specific group work and will aim to assess that the student has understood the use of the tools illustrated in the course for thermal analysis, energy and exergy analysis of processes/systems, as well as the most important aspects of the applied acoustics report. During this part, the support of the group project and the applied acoustic report is allowed. The maximum time available to complete this part will be at least 40 minutes. The final result of this part will be evaluated up to a max of 12 points. 3. Each team must deliver a pdf copy of both the group’s project and the applied acoustics report at least one week before the exam date. Pdf upload must occur through the Teaching Portal, uploading a single PDF file (which contains both the files) in the section "Elaborati". The upload of the file should be performed only by one representative for each group, taking care to report the names, surnames of each group member on the first page of the report. The reports will be evaluated at most 6 points, and the score will be applied to each of the group members. The final mark of the Advanced topics of Engineering Thermodynamics module will be calculated for each student by summing up the scores of the first online part, the second online part and the evaluation of the project reports. The maximum score will be 30 (possibly cum laude if a total grade exceeding 30 points is achieved). Whenever needed, the upper-rounded rule will be used. The Advanced topics of Engineering Thermodynamics module is considered passed if the final score is at least 18 and both reports have been delivered by the group. The final mark will be communicated by the lecturer a week after the exam date, specifying the contribution to the final score of each part of the exam (online part and report evaluation). Consistently with the expected learning outcomes, the exam aims at assessing the achievement of the following objectives: 1. In-depth knowledge of the theoretical notions on thermo-mechanics, continuum theory and thermodynamic. This is accomplished by the first set of online questions; 2. Ability to use the theoretical tools provided in the subject energy and exergetic design and analysis to study real/complex systems involving energy transformation processes. This is established both through the second set of theoretical questions and through the implementation of the group project; 3. Ability to properly interpret the regulations and to perform estimates in the field of lighting and applied acoustic. This is mainly determined by the implementation of the group project and the report on applied acoustic. This is accomplished by the implementation of the group reports. Module of Numerical Modelling. The exam is based on the following tests: a) solving some exercises on the main topics covered in the module (duration 35 minutes); b) answering, using MATLAB(r), a series of multiple choice questions (Duration 40 minutes). It is not allowed the use of any support materials during these tests. In the formulation of the mark, possibly we will take into account also the: c) optional preparation of a computational project during the semester, carried out by small groups of students on a numerical problem linked to an applied project of the module of Advanced Engineering Thermodynamics, and evaluated on the basis of the individual contribution of each student. Tests a) and b) have a relative weight of 2/3 and 1/3 and are provided to reach up to 28 points, while test c) enables to go beyond 28, including “cum laude”. The marks obtained in the written tests will be communicated to the students through the Teaching Portal, together with an indication of when and where the students can view their tests. In the fully remote mode, tests a) and b) are carried out through video surveillance by the teachers: students enter small groups in a certain number of Virtual Classroom activating microphone and webcam, and are followed by a teacher during the exam. At the end of the test a), students upload the written paper on the University platform intended for this purpose. To perform the test b), the students carry out the necessary calculations with Matlab on their computer, by accessing the Exam platform to receive the questions and enter the answers. Finally, test c) is carried out by uploading a paper containing the results of the project and the corresponding teacher-student discussion held on Virtual Classroom. Consistent with the declared learning outcomes, the written part aims at assessing the achievement of the following objectives: 1. Knowledge of the main discretization methodologies of mathematical models and their translation into algebraic equation systems. This is established through test a). 2. Ability to implement the studied numerical models in the MATLAB environment. This is established mainly through test b), but also through test c). 3. Ability to apply the numerical tools studied to the simulation of the problem of engineering thermodynamics problems. This is established through test c). Finally, it should be noted that the mark obtained in the Advanced topics of Engineering Thermodynamics module shall be averaged with the mark obtained in the Numerical modelling module. The upper rounded arithmetic mean of the two modules will be officially recorded as a final grade.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

**Modalità di esame:** Prova scritta (in aula); Prova orale obbligatoria; Prova scritta a risposta aperta o chiusa tramite PC con l'utilizzo della piattaforma di ateneo Exam integrata con strumenti di proctoring (Respondus); Elaborato progettuale in gruppo;

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

**Modalità di esame:**

Module of Advanced Engineering Thermodynamics. Each student will be given an online test on her/his computer via the Exam+Respondus platform. The online test includes a number of both open-ended and closed-ended questions and the navigation through questions is free. In addition, each student will also be assessed on the result of the group's project and the applied acoustics report as reported below. During the online test, it is permitted to have a few blank A4 papers, a pen (black or blue) and if needed a physical calculator as a possible support during the answers (provided that during the environmental recording and the subsequent use they be all clearly showed in the webcam). It will be possible to close the exam and finish only if at least 90% of the total time has elapsed. The Virtual Classroom integrated in the Exam platform will be also enabled to allow possible interaction with the lecturers. More specifically, the exam of this module is structured in three parts as follows: 1. The first part will make use of the “Exam” platform with proctoring tools (Respondus) and includes a maximum of 15 open- and/or closed-ended questions that will focus on the fundamental parts of the course, and which aim to assess that the student has correctly understood the theoretical foundations underlying the continuum thermo-mechanics, thermodynamics, heat transfer, applied acoustics and lighting technology discussed during both theoretical and practise lectures. During this first part, using support materials of any kind is strictly forbidden. The maximum time available to complete this part will be at least 40 minutes. The final result of this part will be evaluated up to a max of 15 points. Whenever needed, the upper-rounded rule will be used. 2. A second part will follow where the student has to demonstrate that he/she has actively contributed to the group project, answering a second oral question by the examiner. Here, by focussing on a realistic energy conversion system, it is possible to assess if the student correctly developed sufficient skills for thermal, energy, exergy analysis of energy conversion devices. Alternatively, at the choice of the examiner, this second question may possibly focus on the applied acoustics part. About thirty minutes will be given to reply to the second question. The maximum score for this second part will be 18 points. During this part, it is allowed the use of educational material. This second part might be carried out either remotely or onsite. 3. Each team must deliver a pdf copy of both the group’s project and the applied acoustics report at least one week before the exam date. Pdf upload must occur through the Teaching Portal, uploading a single PDF file (which contains both the files) in the section "Elaborati". The upload of the file should be performed only by one representative for each group, taking care to report the names, surnames of each group member on the first page of the report. The final mark of the Advanced topics of Engineering Thermodynamics module will be calculated for each student by summing up the scores of the first online part and the second part. The maximum score will be 30 (possibly cum laude if a total grade exceeding 30 points is achieved). The Advanced topics of Engineering Thermodynamics module is considered passed if the final score is at least 18 and both reports have been delivered by the group. The final mark will be communicated by the lecturer a week after the exam date, specifying the contribution to the final score of each part of the exam (online part and report evaluation). Consistently with the expected learning outcomes, the exam aims at assessing the achievement of the following objectives: 1. In-depth knowledge of the theoretical notions on thermo-mechanics, continuum theory and thermodynamic. This is accomplished by the online questions; 2. Ability to use the theoretical tools provided in the subject energy and exergetic design and analysis to study real/complex systems involving energy transformation processes. This is established both through the second part and the implementation of the group project; 3. Ability to properly interpret the regulations and to perform estimates in the field of lighting and applied acoustic. This is mainly determined by the implementation of the group project and the report on applied acoustic. This is mainly accomplished by the implementation of the two group reports. Module of Numerical Modelling. The exam is based on the following tests: a) solving some exercises on the main topics covered in the module (duration 35 minutes); b) answering, using MATLAB, a series of multiple choice questions (Duration 40 minutes). It is not allowed the use of any support materials during these tests. In the formulation of the mark, possibly we will take into account also the: c) optional preparation of a computational project during the semester, carried out by small groups of students on a numerical problem linked to an applied project of the module of Advanced Engineering Thermodynamics, and evaluated on the basis of the individual contribution of each student. Tests a) and b) have a relative weight of 2/3 and 1/3 and are provided to reach up to 28 points, while test c) enables to go beyond 28, including “cum laude”. The marks obtained in the written tests will be communicated to the students through the Teaching Portal, together with an indication of when and where the students can view their tests. In the fully remote mode, tests a) and b) are carried out through video surveillance by the teachers: students enter small groups in a certain number of Virtual Classroom activating microphone and webcam, and are followed by a teacher during the exam. At the end of the test a), students upload the written paper on the University platform intended for this purpose. To perform the test b), the students carry out the necessary calculations with Matlab on their computer, by accessing the Exam platform to receive the questions and enter the answers. Finally, test c) is carried out by uploading a paper containing the results of the project and the corresponding teacher-student discussion held on Virtual Classroom. In the blended mode, the written test a) is carried out in a classroom, the computer test b) is carried out in a computer lab, while the test c) is carried out by uploading a paper containing the results of the project with teacher discussion-student created in a classroom. Consistent with the declared learning outcomes, the written part aims at assessing the achievement of the following objectives: 1. Knowledge of the main discretization methodologies of mathematical models and their translation into algebraic equation systems. This is established through test a). 2. Ability to implement the studied numerical models in the MATLAB environment. This is established mainly through test b), but also through test c). 3. Ability to apply the numerical tools studied to the simulation of the problem of engineering thermodynamics problems. This is established through test c). Finally, it should be noted that the mark obtained in the Advanced topics of Engineering Thermodynamics module shall be averaged with the mark obtained in the Numerical Modelling module. The upper rounded arithmetic mean of the two modules will be officially recorded as a final grade.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

**Exam:** Written test; Compulsory oral exam; Computer-based written test with open-ended questions or multiple-choice questions using the Exam platform and proctoring tools (Respondus); Group project;

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

**Exam:**

Module of Advanced Engineering Thermodynamics. Each student will be given an online test on her/his computer via the Exam+Respondus platform. The online test includes a number of both open-ended and closed-ended questions and the navigation through questions is free. In addition, each student will also be assessed on the result of the group's project and the applied acoustics report as reported below. During the online test, it is permitted to have a few blank A4 papers, a pen (black or blue) and if needed a physical calculator as a possible support during the answers (provided that during the environmental recording and the subsequent use they be all clearly showed in the webcam). It will be possible to close the exam and finish only if at least 90% of the total time has elapsed. The Virtual Classroom integrated in the Exam platform will be also enabled to allow possible interaction with the lecturers. More specifically, the exam of this module is structured in three parts as follows: 1. The first part will make use of the “Exam” platform with proctoring tools (Respondus) and includes a maximum of 15 open- and/or closed-ended questions that will focus on the fundamental parts of the course, and which aim to assess that the student has correctly understood the theoretical foundations underlying the continuum thermo-mechanics, thermodynamics, heat transfer, applied acoustics and lighting technology discussed during both theoretical and practise lectures. During this first part, using support materials of any kind is strictly forbidden. The maximum time available to complete this part will be at least 40 minutes. The final result of this part will be evaluated up to a max of 15 points. Whenever needed, the upper-rounded rule will be used. 2. A second part will follow where the student has to demonstrate that he/she has actively contributed to the group project, answering a second oral question by the examiner. Here, by focussing on a realistic energy conversion system, it is possible to assess if the student correctly developed sufficient skills for thermal, energy, exergy analysis of energy conversion devices. Alternatively, at the choice of the examiner, this second question may possibly focus on the applied acoustics part. About thirty minutes will be given to reply to the second question. The maximum score for this second part will be 18 points. During this part, it is allowed the use of educational material. This second part might be carried out either remotely or onsite. 3. Each team must deliver a pdf copy of both the group’s project and the applied acoustics report at least one week before the exam date. Pdf upload must occur through the Teaching Portal, uploading a single PDF file (which contains both the files) in the section "Elaborati". The upload of the file should be performed only by one representative for each group, taking care to report the names, surnames of each group member on the first page of the report. The final mark of the Advanced topics of Engineering Thermodynamics module will be calculated for each student by summing up the scores of the first online part and the second part. The maximum score will be 30 (possibly cum laude if a total grade exceeding 30 points is achieved). The Advanced topics of Engineering Thermodynamics module is considered passed if the final score is at least 18 and both reports have been delivered by the group. The final mark will be communicated by the lecturer a week after the exam date, specifying the contribution to the final score of each part of the exam (online part and report evaluation). Consistently with the expected learning outcomes, the exam aims at assessing the achievement of the following objectives: 1. In-depth knowledge of the theoretical notions on thermo-mechanics, continuum theory and thermodynamic. This is accomplished by the online questions; 2. Ability to use the theoretical tools provided in the subject energy and exergetic design and analysis to study real/complex systems involving energy transformation processes. This is established both through the second part and the implementation of the group project; 3. Ability to properly interpret the regulations and to perform estimates in the field of lighting and applied acoustic. This is mainly determined by the implementation of the group project and the report on applied acoustic. This is mainly accomplished by the implementation of the two group reports. Module of Numerical Modelling. The exam is based on the following tests: a) solving some exercises on the main topics covered in the module (duration 35 minutes); b) answering, using MATLAB, a series of multiple choice questions (Duration 40 minutes). It is not allowed the use of any support materials during these tests. In the formulation of the mark, possibly we will take into account also the: c) optional preparation of a computational project during the semester, carried out by small groups of students on a numerical problem linked to an applied project of the module of Advanced Engineering Thermodynamics, and evaluated on the basis of the individual contribution of each student. Tests a) and b) have a relative weight of 2/3 and 1/3 and are provided to reach up to 28 points, while test c) enables to go beyond 28, including “cum laude”. The marks obtained in the written tests will be communicated to the students through the Teaching Portal, together with an indication of when and where the students can view their tests. In the fully remote mode, tests a) and b) are carried out through video surveillance by the teachers: students enter small groups in a certain number of Virtual Classroom activating microphone and webcam, and are followed by a teacher during the exam. At the end of the test a), students upload the written paper on the University platform intended for this purpose. To perform the test b), the students carry out the necessary calculations with Matlab on their computer, by accessing the Exam platform to receive the questions and enter the answers. Finally, test c) is carried out by uploading a paper containing the results of the project and the corresponding teacher-student discussion held on Virtual Classroom. In the blended mode, the written test a) is carried out in a classroom, the computer test b) is carried out in a computer lab, while the test c) is carried out by uploading a paper containing the results of the project with teacher discussion-student created in a classroom. Consistent with the declared learning outcomes, the written part aims at assessing the achievement of the following objectives: 1. Knowledge of the main discretization methodologies of mathematical models and their translation into algebraic equation systems. This is established through test a). 2. Ability to implement the studied numerical models in the MATLAB environment. This is established mainly through test b), but also through test c). 3. Ability to apply the numerical tools studied to the simulation of the problem of engineering thermodynamics problems. This is established through test c). Finally, it should be noted that the mark obtained in the Advanced topics of Engineering Thermodynamics module shall be averaged with the mark obtained in the Numerical Modelling module. The upper rounded arithmetic mean of the two modules will be officially recorded as a final grade.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

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