Poisson

Verification of the solution of the Poisson equation (Laplacian operator) More...

Topics
	1D Poisson equation with Dirichlet boundary conditions
	1D Poisson test cases with Dirichlet boundary conditions
	1D Poisson equation with Robin boundary conditions
	1D Poisson test cases with Robin boundary conditions
	2D/3D Poisson equation with Robin boundary conditions
	2D/3D Poisson test cases with Robin boundary conditions
	2D/3D Poisson equation with Neumann boundary conditions
	2D/3D Poisson test cases with Neumann boundary conditions
	2D-AS Poisson equation with Dirichlet boundary conditions
	2D axisymmetric Poisson test cases with Dirichlet boundary conditions
	2D/3D Poisson equation with immersed boundaries
	This test case suite focuses on the immersed boundary applied to the Poisson equation.

Detailed Description

Verification of the solution of the Poisson equation (Laplacian operator)

The Poisson equation:

\[ - \Delta T = f \]

is a key equation to solve as it is the stationary heat equation with a source term. It permits us to test the Laplacian operator \( \Delta \equiv \sum_{i=1}^{i=dim} \partial_{x_i x_i} \) schemes as well as the boundary condition schemes. The equation is solved on various geometries (1D, 2D, 3D and immersed boundaries).

Herein, we propose verification, convergence tests as well as some numerical analysis of the available schemes.