Digital methods and project MEP - 4PMMPNU

Goal(s)

Numerical Methods and Project (20 hours of lectures, 10 hours of tutorials, 30 hours of practical work):

Understand the theoretical foundations of fine difference and finite volume methods for solving ordinary differential equations (ODEs) and partial differential equations (PDEs):
Local and integral conservation of physical quantities.
Implement methods for:
The steady-state heat equation (pure diffusion problem).
The time-dependent diffusion-advection equation.

Master the discretization steps:
Mesh construction and definition of control volumes.
Approximation of diffusive fluxes, advective terms, and time discretization.

Numerically implement the schemes:
Construction of the associated linear system.
Treatment of boundary conditions (Dirichlet, Neumann).
Numerical resolution.

Validate numerical results by comparison with analytical or reference solutions.

Content(s)

Numerical Methods and Projects (20 hours of lectures, 10 hours of tutorials, 30 hours of practical work)

Numerical Methods Lectures and Tutorials (see Objectives for details):
Numerical Methods projects typically involve the simulation of conduction and convection heat transfer problems.

Digital Methods and Projects (20 hours of lectures, 10 hours of tutorials, 30 hours of practical work):
Basic concepts of Python programming

Test

Numerical methods and project: 100% CC assessment (session reports and project presentation)

Additional Information