The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows

Published

Journal Article

© 2018 Elsevier Inc. 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.

Full Text

Duke Authors

Cited Authors

  • Song, T; Main, A; Scovazzi, G; Ricchiuto, M

Published Date

  • September 15, 2018

Published In

Volume / Issue

  • 369 /

Start / End Page

  • 45 - 79

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/j.jcp.2018.04.052

Citation Source

  • Scopus