Institut fürInformatik

Scientific Computing in Computer Science

Practical Course SC & VTime Discretisation

Dr. Miriam Mehl

Time Discretisation

• 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

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

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 butwith nonzero boundary values

• test preliminary velocities