Pressure Poisson Equation Lab Course CFD Pressure Poisson Equation Dr. Miriam Mehl

Algorithm (One Time Step) compute time step dt set boundary values compute preliminary velocities solve pressure equation compute final velocities

Discretisation continuous (analytical) representation discrete (computer) representation 1) geometry 2) functions 3) operators

Geometry Discretisation

Function Discretisation pi,j

Discretisation Laplace Operator finite differences homogeneous Neumann boundaries pi,j

Gauss-Seidel – Principle point by point eliminate local residual

Gauss-Seidel – Convergence 2D Poisson, 5-point-stencil homogeneous Dirichlet boundary conditions convergence rate:

Improving Gauss-Seidel – SOR scale correction term: optimal w: convergence rate: