Stability analysis of unstructured finite volume methods for linear shallow water flows using pseudospectra and singular value decomposition
Author | Beljadid, Abdelaziz |
Author | Mohammadian, Abdolmajid |
Author | Qiblawey, Hazim |
Available date | 2021-06-07T09:59:14Z |
Publication Date | 2016 |
Publication Name | Advances in Water Resources |
Resource | Scopus |
Abstract | The discretization of the shallow water system on unstructured grids can lead to spurious modes which usually can affect accuracy and/or cause stability problems. This paper introduces a new approach for stability analysis of unstructured linear finite volume schemes for linear shallow water equations with the Coriolis Effect using spectra, pseudospectra, and singular value decomposition. The discrete operator of the scheme is the principal parameter used in the analysis. It is shown that unstructured grids have a large influence on operator normality. In some cases the eigenvectors of the operator can be far from orthogonal, which leads to amplification of solutions and/or stability problems. Large amplifications of the solution can be observed, even for discrete operators which respect the condition of asymptotic stability, and in some cases even for Lax-Richtmyer stable methods. The pseudospectra are shown to be efficient for the verification of stability of finite volume methods for linear shallow water equations. In some cases, the singular value decomposition is employed for further analysis in order to provide more information about the existence of unstable modes. The results of the analysis can be helpful in choosing the type of mesh, the appropriate placements of the variables of the system on the grid, and the suitable discretization method which is stable for a wide range of modes. |
Sponsor | The authors thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. This publication was made possible by NPRP Grant 4-935-2-354 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors. Appendix A |
Language | en |
Publisher | Elsevier Ltd |
Subject | Amplification Asymptotic stability Discrete event simulation Equations of motion Finite volume method Mesh generation Stability Discrete operators Discretization method Finite volume schemes Linear shallow water equations Pseudospectra Shallow-water systems Unstructured finite volume methods Unstructured meshes Singular value decomposition Coriolis force decomposition analysis eigenvalue finite volume method linearity shallow-water equation stability analysis water flow |
Type | Article |
Pagination | 127-144 |
Volume Number | 96 |
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