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Numerical Solutions of Cauchy Riemann Equations for Two Dimensional Flows
Student-Run Research| Speaker: | Jeff Housman, UC Davis Math Dept. |
| Location: | 693 Kerr |
| Start time: | Wed, Jun 6 2001, 1:10PM |
Description
For two dimensional flows, the conservation of mass and the definition of
vorticity comprise a generalized Cauchy Riemann system for the velocity
components assuming the vorticity is given. Introducing artificial time, a
symmetric hyperbolic system can be easily constructed. Artificial
viscosity is needed for numerical stability and is obtained from a
least-squares formulation. The augmented system is solved explicitly with
a standard point relaxation algorithm which is highly parallelizable.
Second order accurate results are compared with exact solutions for
steady, incompressible, irrotational, inviscid, two dimensional flows
around a cylinder.