A Schwarz-Christoffel method for generating two-dimensional flow grids
Abstract
A new coordinate generation technique, developed by Davis for external flows, is extended to allow for accurate grid generation for a variety of complex internal flow configurations. The approach is based on numerical integration of the Schwarz-Christoffel transformation for polygonal surfaces. It is shown to be second-order accurate with mesh size due to analytic treatment of boundary singularities. The method is flexible enough to allow for treatment of severe internal geometries, for a high degree of control of mesh spacing, and for generation of either orthogonal or nonorthogonal grids. In addition, this technique directly provides the two-dimensional incompressible potential flow solution for internal flows, as well as a simple expression for calculating the grid metric coefficients. Sample cases include symmetric and asymmetric channel, diffuser, and cascade flows.
- Publication:
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ASME Journal of Fluids Engineering
- Pub Date:
- September 1985
- Bibcode:
- 1985ATJFE.107..330S
- Keywords:
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- Computational Fluid Dynamics;
- Computational Grids;
- Grid Generation (Mathematics);
- Numerical Integration;
- Schwarz-Christoffel Transformation;
- Two Dimensional Flow;
- Cascade Flow;
- Channel Flow;
- Flow Geometry;
- Incompressible Flow;
- Potential Flow;
- Fluid Mechanics and Heat Transfer