期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 369, 期 -, 页码 45-79出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.04.052
关键词
Embedded boundary conditions; Wave equation; Shallow water flows; Finite elements; Approximate boundary methods
资金
- U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research under Early Career Research Program [SC0012169]
- Army Research Office (ARO) [W911NF-13-1-0452]
- TANDEM of the French Programme Investissements d'Avenir [ANR-11-RSNR-0023-01]
- Duke University
- CARDAMOM INRIA
- Agence Nationale de la Recherche (ANR) [ANR-11-RSNR-0023] Funding Source: Agence Nationale de la Recherche (ANR)
We propose a new computational approach for embedded boundary simulations of hyperbolic systems and, in particular, the linear wave equations and the nonlinear shallow water equations. The proposed approach belongs to the class of surrogate/approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary. Accordingly, boundary conditions, enforced weakly, are appropriately modified to preserve optimal error convergence rates. This framework is applied here in the setting of a stabilized finite element method, even though other spatial discretization techniques could have been employed. Accuracy, stability and robustness of the proposed method are tested by means of an extensive set of computational experiments for the acoustic wave propagation equations and shallow water equations. Comparisons with standard weak boundary conditions imposed on body-fitted grids, which conform to the geometry of the computational domain boundaries, are also presented. (C) 2018 Elsevier Inc. All rights reserved.
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