Accession Number : ADA268425


Title :   An Adaptive Mesh-Moving and Local Refinement Method for Time-Dependent Partial Differential Equations


Corporate Author : RENSSELAER POLYTECHNIC INST TROY NY


Personal Author(s) : Arney, David C ; Flaherty, Joseph E


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a268425.pdf


Report Date : 01 Mar 1990


Pagination or Media Count : 26


Abstract : We discuss mesh-moving, static mesh-regeneration, and local mesh- refinement algorithms that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse based mesh of quadrilateral cells is moved by an algebraic mesh- movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied The static mesh-regeneration procedure is used to create a new base mesh when the existing ones becomes to distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.


Descriptors :   *ALGORITHMS , *TIME DEPENDENCE , *PARTIAL DIFFERENTIAL EQUATIONS , *MESH , FUNCTIONS , TIME , BOUNDARY VALUE PROBLEMS , VALUE , INDICATORS , EXTRAPOLATION , STATICS , TOLERANCE , ERRORS , BOUNDARIES , ESTIMATES , REGIONS , REPRINTS


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE