Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

O'Reilly, Ossian; Petersson, N. Anders

doi:10.1016/j.jcp.2020.109386

Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

Journal Article · Fri Mar 06 00:00:00 EST 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109386· OSTI ID:1755849

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Univ. of Southern California, Los Angeles, CA (United States). Southern California Earthquake Center
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing

In this work, we develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that outperforms a Cartesian basis decomposition on rotated grids. The discretization is based on high order Summation-By-Parts (SBP) operators and preserves both symmetry and positive definiteness of the contravariant metric tensor. To improve accuracy and decrease computational cost, we also derive a modified discretization of the metric tensor that leads to a conditionally stable discretization. Bounds are derived that yield a point-wise condition that can be evaluated to check for stability of the modified discretization. This condition shows that the interpolation operators should be constructed such that their norm is close to one.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); US Geological Survey (USGS); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1755849

Report Number(s):: LLNL-JRNL--780017; 974832

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: na Vol. 411; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

97 MATHEMATICS AND COMPUTING
Summation-by-parts
acoustic wave equation
covariant formulation
curvilinear coordinates
high order accuracy
staggered grids

Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

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