期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 372, 期 -, 页码 972-995出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2017.10.026
关键词
Embedded methods; Immersed boundary method; Small cut-cell problem; Approximate domain boundaries; Weak boundary conditions; Finite element method
资金
- U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research under Early Career Research Program Grant [SC0012169]
- U.S. Office of Naval Research [N00014-14-1-0311]
- ExxonMobil Upstream Research Company (Houston, TX)
We propose a new finite element method for embedded domain computations, which falls in the category of surrogate/approximate boundary algorithms. The key feature of the proposed approach is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary, and to appropriately modify the shifted boundary conditions, enforced weakly, in order to preserve optimal convergence rates of the numerical solution. This process yields a method which, in our view, is simple, efficient, and also robust, since it is not affected by the small-cut-cell problem. Although general in nature, here we apply this new concept to the Poisson and Stokes problems. We present in particular the full analysis of stability and convergence for the case of the Poisson operator, and numerical tests for both the Poisson and Stokes equations, for geometries of progressively higher complexity. (C) 2017 Elsevier Inc. All rights reserved.
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