Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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A new approach for the generation of flow-adaptive grids for numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numerical evaluation of any partial differential equation. The dynamic coupling of the grid with the flow solution is accomplished through a grid-optimization technique. The optimization is based on the minimization of the finite difference truncation error in the transformed plane. The method is tested on the one-dimensional Burgers equation which is representative of typical fluid dynamics problems. Burgers equation is solved with an optimized SOR Successive Over Relaxation method using upwind difference for the convective term. Results are presented for various Reynolds numbers and are compared to results from a similar adaptive grid method and to results for a static grid. They show the ability of the method to concentrate grid points high in gradient regions where large truncation errors occur. Author
- Numerical Mathematics
- Fluid Mechanics