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Remeshing and refining with moving finite elements : application to nonlinear wave problems.

By Abigail Wacher and 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

Topics: Moving finite elements, Remeshing, global mesh refinement, Shallow water equations, Coriolis, Wave dispersion, Nonlinear waves.
Publisher: Tech Science Press
Year: 2006
DOI identifier: 10.3970/cmes.2006.015.147
OAI identifier: oai:dro.dur.ac.uk.OAI2:7908
Journal:

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Citations

  1. (1997). A geometrical-mechanical interpretation of gradient-weighted moving finite elements.
  2. (1998). A New Meshless Local Petrov-Galerkin (MLPG) doi
  3. (1987). An adaptive finite element scheme for transient problems in CFD.
  4. (2000). Arbitrary placement of secondary nodes, and error control,
  5. (1984). Computational Solid Mechanics (Finite Elements and Boundary Elements): -Present Status and Future Directions.
  6. (1992). Creation And Annihilation Of Nodes For The Moving Finite Element Method, PhD thesis.
  7. (1998). Design and application of a gradient-weighted moving finite element code II: in two dimensions. doi
  8. (1998). Design and application of a gradient-weightedmoving finite element code I: in one dimension. doi
  9. (1987). Geophysical Fluid Dynamics. doi
  10. (2003). High-order non-reflecting boundary conditions for dispersivewaves. doi
  11. (2006). Maturity of operational numerical weather prediction: Medium range. doi
  12. (1981). Moving Finite Elements I.
  13. (1981). Moving Finite Elements II.
  14. (1994). Moving Finite Elements. doi
  15. (2004). Moving mesh method with error-estimator-based monitor and its applications to static obstacle problem.
  16. (2004). Moving mesh methods with locally varying time steps. doi
  17. (1980). Numerical Modeling of Dynamic Crack Propagation in Finite Bodies, by Moving Singular Elements, Part 1: Formulation.
  18. (1980). Numerical Modeling of Dynamic Crack Propagation in Finite Bodies, by Moving Singular Elements, Part 2: Results.
  19. (1980). Numerical Prediction and Dynamic Meteorology. doi
  20. (2005). Precise computations of chemotactic collapse usingmovingmesh methods. doi
  21. (2005). Recent Advances in Numerical Simulation Technologies for Various Dynamic Fracture Phenomena.
  22. (2003). Review of numerical methods for nonhydrostatic weather prediction models. doi
  23. (1995). Time Dependent Problems and Difference Methods.
  24. (1992). Water Waves: The Mathematical Theory with Applications.

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