Lab Course CFD

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Lab Course CFD

• Pressure Poisson Equation

Dr. Miriam Mehl
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Algorithm (One Time Step)

1. compute time step dt
2. set boundary values
3. compute preliminary velocities
4. solve pressure equation
5. compute final velocities

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Discretisation

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

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Geometry Discretisation
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Function Discretisation
pi,j
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Discretisation Laplace Operator

• finite differences
• homogeneous Neumann boundaries

pi,j
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Gauss-Seidel Principle

• point by point
• eliminate local residual

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Gauss-Seidel Convergence

• 2D Poisson, 5-point-stencil
• homogeneous Dirichlet boundary conditions
• convergence rate

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Improving Gauss-Seidel SOR

• scale correction term
• optimal w
• convergence rate