Content of Learning Activity

Part 1 : Introduction
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
Simulation process and 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
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 :  Electromagnetic Modelling and Numerical Methods for CEM
Formulations and modelling : Fields, differential operators and PDEs, electromagnetic modelling and related formulations, local and global quantities 
The FEM for CEM: Domain decomposition, nodal approximation and application to magnetostatic problems, Variational formulation and FEM: The Rayleigh‐Ritz method, Nonlinear problems, Transient problems, FEM and multiphysics
Integral equations and related numerical methods: Dirac delta " function " and Green’s functions, The Boundary Element Method, Dirac and FEM
Solutions of simultaneous set of linear equations: Direct & Iterative Methods
Weak formulation and FEM
Whitney elements

Part 3 : Flow and Heat Transfer Modelling with FVM for CFD and CHT
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

Required Learning Resources/Tools

Not applicable

Recommended Learning Resources/Tools

Not applicable

Other Recommended Reading

Not applicable

Mode of delivery

• Face-to-face

Type of Teaching Activity/Activities

• Cours magistraux
• Ateliers et projets encadrés au sein de l'établissement

Evaluations

The assessment methods of the Learning Activity (AA) are specified in the course description of the corresponding Educational Component (UE)