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

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

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

4. Geometry Discretisation

5. Function Discretisation
pi,j

6. Discretisation Laplace Operator
finite differences
homogeneous Neumann boundaries
pi,j

7. Gauss-Seidel – Principle
point by point
eliminate local residual

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

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