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Time Discretisation in Scientific Computing | Practical Course at Computer Science Institute

This practical course at the Institute of Computer Science covers time discretisation methods for momentum equations, mass conservation, the Poisson equation, and velocity corrections. Learn about stability criteria, the algorithm for one time step, and debugging strategies for velocity calculations and pressure equations.

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Time Discretisation in Scientific Computing | Practical Course at Computer Science Institute

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  1. Scientific Computing in Computer Science Institut für Informatik Practical Course SC & V Time Discretisation Dr. Miriam Mehl

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

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

  6. Debugging • enhanced setup: • initialize velocities constant butwith nonzero boundary values • test preliminary velocities

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