A Two-Dimensional Mesh Moving Technique for Time Dependent Partial Differential Equations.
RENSSELAER POLYTECHNIC INST TROY NY DEPT OF MATHEMATICAL SCIENCES
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This document discusses an adaptive mesh moving technique that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of partial differential equations in two space dimensions. The mesh moving technique is based on an algebraic node movement function determined from the geometry and propagations of regions having significant discretization error indicators. This procedure is designed to be flexible, so that it can be used with many existing finite difference and finite element methods. To test the mesh moving algorithm, it was implemented in a system code with and initial mesh generator and a MacCormack finite difference scheme on quadrilateral cells for hyperbolic vector systems of conservation laws. Results are presented for several computational examples. The moving mesh scheme reduces dispersive errors near shocks and wave fronts and thereby reduces the grid requirements necessary to compute accurate solutions while incereasing computational efficiency. Additional keywords Error clustering. Author
- Theoretical Mathematics