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Scholars Day 2008, Wednesday, April 9

Numerical Solution of the Lid-Driven Cavity Problem and Applications to Meteorology

The Navier-Stokes equations are the fundamental partial differential equations that describe the flow of fluids. These differential equations, like many differential equations, have no known analytical solution. However, high speed computers can be used to solve approximations to these equations using a variety of techniques like finite difference and finite element methods. In this case, the Navier-Stokes equations, using the Streamline-vorticity formulation, is applied to a lid driven cavity problem. The lid driven cavity problem historically has been used to test new solution methods; the problem geometry, as well as the initial and boundary conditions, allow the problem to be relatively simple. A forward time, center space finite difference approximation scheme is implemented to approximate the flow inside the lid driven cavity based on Navier-Stokes equations. The model is run with differing Reynolds numbers, time steps and grid spacings to determine how the differencing scheme works.

Presenter: Jeffrey Curtis (Graduate Student)
Topic: Computational Science
Location: 102 Edwards
Time: 3:10 pm (Session IV)

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