1. Practical Course SC & V Discretization II AVS Dr. Miriam Mehl
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Practical Course SC & V
Discretization II
AVS
Dr. Miriam Mehl

2. What We Know Euler step for momentum equations
pressure ensures mass conservation
poisson equation
correction of velocities

3. Time Step – Stability small reynolds number: dt < dx2
high reynolds number: dt < dx

4. Boundaries continuous boundary conditions discrete boundary conditions
modified discrete operators

5. Boundaries discrete momentum equations
discrete boundary conditions for pressure

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

7. Discretization II Re >> 1 oscillations!!!
reason: discrete convection terms
remedy: Donor cell scheme
stable
lower order of accuracy

8. Debugging simple setup: one(!!!) time step external forces zero
test preliminary velocities at boundaries
test residual of the pressure equation

9. Debugging enhanced setup:
initialize velocities constant but with nonzero boundary values
test preliminary velocities
finally: simulate driven cavity

10. Result

11. AVS

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