Objectives of Programme's Learning Outcomes

• Imagine, design, build and operate machines, equipment and processes to provide a solution to a complex problem of energy production, conversion and transmission by integrating the needs, constraints, context and technical, economic, societal, ethical and environmental issues.
• Identify the complex problem to be solved and develop the specifications by integrating the needs, constraints, context and technical, economic, societal, ethical and environmental issues.
• Implement a chosen solution in the form of a drawing, schematic, diagram or plan that conforms to standards, a model, a prototype, software and/or a digital model.
• Evaluate the approach and results in order to adapt or optimize the proposed solution.
• Mobilize a structured set of scientific knowledge and skills and specialized techniques to meet, with expertise and adaptability, the missions of the civil engineer in energy engineering.
• Master and appropriately mobilize knowledge, models, methods and techniques related to solid and fluid mechanics, energy exchange, dynamic and vibratory behavior of systems, mechanical manufacturing and production, machine operation, physical phenomena, machines, equipment and processes related to the production, conversion and transmission of energy
• Assess the validity of models and results given the state of the science and the characteristics of the problem.
• Work effectively in a team, develop leadership, make decisions in multidisciplinary, multicultural and international contexts.
• Interact effectively with other actors to carry out joint projects in various contexts (multidisciplinary, multicultural and international).
• Communicate and exchange information in a structured manner - orally, graphically and in writing, in French and in one or more other languages - at the scientific, cultural, technical and interpersonal levels, adapting to the goal pursued and the audience concerned.
• Argue and convince, both orally and in writing, in front of a client, a colleague, teachers and juries.
• Use and produce scientific and technical documents (report, plan, specifications, ...) adapted to the goal and the public concerned.
• Act as a responsible, open-minded, and critical professional in an autonomous professional development process.
• Demonstrate openness and critical thinking by comparing the technical and non-technical aspects of the problems analyzed and the solutions proposed.
• Make critical use of the various means available for independent research and training.
• Contribute through research to the innovative solution of a problem in engineering sciences.
• Interpret results appropriately, taking into account the frame of reference within which the research was developed.
• Communicate, in writing and orally, on the process and its results by highlighting the scientific quality criteria of the research carried out, as well as the potential for theoretical or technical innovation and the possible non-technical issues.

Learning Outcomes of UE

Introduction to numerical methods in the world of virtual prototyping in the energy fields of fluid flow, heat transfer and electromagnetism simulations.
For analysis or design problems involving flows, heat transfer and electromagnetic fields, the course objective is to acquire a critical mind in the field of Computational ElectroMagnetism (CEM), Computational Fluid Dynamics (CFD) and Computational Heat Transfer (CHT) in order to be able :
• To describe the concepts of Finite Difference (FDM), Finite Element (FEM) and Finite Volume (FVM) Methods their potential and their limitations 
• To summarize the different steps and the most common simulation methods 
• To understand what is implemented in existing codes and commercial software
• To contribute to the development of CFD, CHT & CEM software
• To make a judicious use of numerical simulations and commercial software
• To know how to judge the quality of simulation results
• To be able to read and understand the literature on this subjects
• To be able to solve a simplified 1D, 2D or 3D problems
• To use these knowledges as a basis for a possible Master Thesis Work

UE Content: description and pedagogical relevance

Part 1  Introduction
-  Course objective: Introduction to CFD, CHT and CEM
- Numerical simulation in the world of virtual prototyping et place and interest of CFD (Computational Fluid Dynamics), CHT (Computational Heat transfer) and CEM (Computational ElectroMagnetics) for digital twins
- Requirements for CHT, CEM and CFD simulations
- Reminder on the Navier-Stokes PDEs (Partial Differential Equations) for flows, Fourier-Kirchhoff equation for heat transfer, Maxwell PDEs for electromagnetism
- Simulation process and notion of mesh
- Mathematical nature of PDEs and influence on the numerical method
- Well-posed problem, boundary conditions and initial conditions
- Discrete approximation of the solution: Issue on time scale (time refinement) and space scale (space refinement)
- Finite Difference Method (FDM): Notion of truncation error and accuracy and link with polynomial interpolation 
Part 2  Computational Electromagnetics (CEM) - Formulations and modelling 
- Numerical methods for CEM 
- Solutions of simultaneous set of linear equations
- Weak formulation and FEM
- Whitney elements
Part 3 : Computational Fluid Dynamics (CFD) and Numerical Heat Transfer (NHT)- Finite volume methodology
- Basic numerical schemes: Time explicit and time implicit schemes
- Resulting ODEs (Ordinary Differential Equations) of the FVM formulation
- Spatial and temporal discretisation: Convective flux discretisation with central and upwind schemes, diffusive flux discretisation, temporal discretisation (implicit schemes, explicit and Runge-Kutta schemes, implicit dual time-stepping approach)
- Acceleration techniques 
- Density-based and pressure-based schemes for incompressible flows 
- Some specificities for NHT 
- Consistency, stability, and convergence 
- Boundary conditions treatments for compressible flows
Part 4  Project

Prior Experience

Not applicable