EU Numerical Methods 2 - 4PUGNME2

Goal(s)

Understand the theoretical foundations of the finite volume method applied to partial differential equations (PDEs):
Local and integral conservation of physical quantities.
Weak formulation suitable for general meshes.
Apply the finite volume method to:
The steady-state heat equation (pure diffusion problem).
The time-dependent advection-diffusion equation.
Master the discretization steps:
Mesh construction and definition of control volumes.
Approximation of diffusive fluxes (central scheme).
Treatment of advective terms (upwind, central, and stabilized schemes).
Semi-implicit time discretization.
Implement the numerical schemes:
Assembly of the associated linear system.
Treatment of boundary conditions (Dirichlet, Neumann).
Numerical solution (direct or iterative methods).
Analyze the properties of the schemes:
Consistency, stability, convergence.
Influence of mesh quality and boundary conditions.
Validate numerical results by comparison with analytical solutions or reference benchmarks.

Content(s)

Numerical Methods 2
Numerical Method projects

EU Engineering sciences 1