A survey of dynamically-adaptive grids in the numerical solution of partial differential equations
Abstract
The construction of dynamically-adaptive curvilinear coordinate systems based on numerical grid generation and the use thereof in the numerical solution of partial differential equations is surveyed, and correlations are made among the various approaches. These adaptive grids are coupled with the physical solution being done on the grid so that the grid points continually move in the course of the solution in order to resolve developing gradients, or higher variations, in the solution. Particular attention is given to systems using elliptic grid generation based on variational principles. It is noted that dynamic grid adaption can remove the oscillations common when strong gradients occur on fixed grids, and that it appears that when the grid adapts to the solution most numerical solution algorithms work well. Particular applications in computational fluid dynamics and heat transfer are noted.
- Publication:
-
17th Fluid Dynamics, Plasma Dynamics, and Lasers Conference
- Pub Date:
- June 1984
- Bibcode:
- 1984fdpd.confQ....T
- Keywords:
-
- Computational Fluid Dynamics;
- Computational Grids;
- Grid Generation (Mathematics);
- Heat Transfer;
- Partial Differential Equations;
- Spherical Coordinates;
- Algorithms;
- Finite Element Method;
- Galerkin Method;
- High Reynolds Number;
- Jacobi Matrix Method;
- Lagrange Coordinates;
- Variational Principles;
- Fluid Mechanics and Heat Transfer