Abigail Wacher
Remeshing and Refining with Moving Finite Elements. Application to Nonlinear Wave Problems
Wacher, Abigail; Givoli, Dan
Authors
Dan Givoli
Abstract
The recently proposed String Gradient Weighted Moving Finite Element (SGWMFE) method is extended to include remeshing and refining. The method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to the nonlinear time-dependent two-dimensional shallow water equations, under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation. Such effects are of major importance in geophysical fluid dynamics applications. Two deficiencies of the original SGWMFE method are (1) possible tangling of the mesh which causes the method's failure, and (2) no mechanism for global refinement when necessary due to the constant number of degrees of freedom. Here the method is extended in order to continue computing solutions when the meshes become too distorted, which happens quickly when the flow is rotationally dominant. Optimal rates of convergence are obtained when remeshing is applied. The method is also extended to include refinement to enable handling of new physical phenomena of a smaller scale which may appear during the solution process. It is shown that the errors in time are kept under control when refinement is necessary. Results of the extended method for some example problems of water hump release are presented.
Citation
Wacher, A., & Givoli, D. (2006). Remeshing and Refining with Moving Finite Elements. Application to Nonlinear Wave Problems. Computer Modeling in Engineering & Sciences, 15(3), 147-164. https://doi.org/10.3970/cmes.2006.015.147
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2006 |
Deposit Date | Jan 26, 2011 |
Publicly Available Date | Feb 11, 2011 |
Journal | Computer modeling in engineering & sciences : CMES. |
Print ISSN | 1526-1492 |
Electronic ISSN | 1526-1506 |
Publisher | Tech Science Press |
Peer Reviewed | Peer Reviewed |
Volume | 15 |
Issue | 3 |
Pages | 147-164 |
DOI | https://doi.org/10.3970/cmes.2006.015.147 |
Keywords | Moving finite elements, Remeshing, global mesh refinement, Shallow water equations, Coriolis, Wave dispersion, Nonlinear waves. |
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