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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:411

Article

O'Reilly, Ossian¹  Petersson, N. Anders² 

[1] Univ Southern Calif, Southern Calif Earthquake Ctr, Los Angeles, CA 90089 USA

[2] Lawrence Livermore Natl Lab, Ctr Appl Sci Comp, L-561,POB 808, Livermore, CA 94551 USA

关键词: Summation-by-parts;    High order accuracy;    Staggered grids;    Curvilinear coordinates;    Covariant formulation;    Acoustic wave equation;   

DOI  :  10.1016/j.jcp.2020.109386

来源: Elsevier

【 摘 要 】

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. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free