Local uniform mesh refinement with moving grids

Local Uniform Mesh Refinement (LUMR) is a powerful technique for solving hyperbolic partial differential equations. However, many problems contain regions where numerical dispersion is very large, such as steep fronts. In these regions, mesh refinement is not very efficient. A better approach in the...

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Bibliographic Details
Published inSIAM journal on scientific and statistical computing Vol. 8; no. 3; pp. 292 - 304
Main Author GROPP, W. D
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.05.1987
Subjects
Algorithms
Coordinate transformations
Cost control
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, miscellaneous problems
Sciences and techniques of general use
Velocity
Transformation of coordinates
Discretization
Multistep method
Partial differential equation
Hyperbolic equation
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Summary:Local Uniform Mesh Refinement (LUMR) is a powerful technique for solving hyperbolic partial differential equations. However, many problems contain regions where numerical dispersion is very large, such as steep fronts. In these regions, mesh refinement is not very efficient. A better approach in these regions is to locally transform the coordinate system to move with the front. We show how to combine these two approaches in a way that maintains the advantages of LUMR and the effectiveness of moving grids. Experiments with 2-D scalar problems are presented.
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0908036