Mass Residuals as a Criterion for Mesh Refinement in Continuous Galerkin Shallow Water Models
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 5
Abstract
Mass balance error has been computed traditionally by using conventional fluxes derived from the conservation of mass equation, but recent literature supports a method based on fluxes that are consistent with the discretization of the governing equations. By comparing the mass residuals from these two methods to the truncation errors produced by the discretization of the governing equations, we show that the conventional fluxes produce mass residuals that are more descriptive of the overall behavior of the model, i.e., they are better correlated with truncation error. Then we demonstrate that these mass residuals can be used as a criterion for mesh refinement. In an example using a one-dimensional shallow water model, we demonstrate that, by moving nodes from regions with large mass residuals to regions with small mass residuals, a mesh can be developed that shows less truncation error than a mesh developed by using localized truncation error analysis. And, in an example using a two-dimensional shallow water model, we demonstrate that the computed solution can be improved in regions with large mass residuals through mesh refinement.
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Acknowledgments
The writers would like to thank Evan Tromble and Ian Toohey of the University of Oklahoma for their help in the completion of the mesh refinement example in two dimensions. The authors would also like to thank Dr. Joannes Westerink of the University of Notre Dame for his help in the completion of the convergence study in one dimension. The authors acknowledge funding from the National Defense Science and Engineering Graduate Fellowship from the Department of Defense, the Office of Naval Research under Grant No. N00014-02-1-0651, and the Department of Education through the GAANN Program. Any opinions, findings, conclusions, and recommendations expressed in this material are those of the authors and do not necessarily reflect those of the funding agencies.
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Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 5 • May 2008
Pages: 520 - 532
Copyright
© 2008 ASCE.
History
Received: Sep 13, 2005
Accepted: Sep 14, 2007
Published online: May 1, 2008
Published in print: May 2008
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