Practical Course SC & V Discretization II AVS Dr. Miriam Mehl Institut für Informatik Schwerpunkt Wissenschaftliches Rechnen Practical Course SC & V Discretization II AVS Dr. Miriam Mehl

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

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

Boundaries continuous boundary conditions discrete boundary conditions modified discrete operators

Boundaries discrete momentum equations discrete boundary conditions for pressure

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

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

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

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

Result

AVS

AVS

AVS

AVS

AVS

AVS