Elastic Wave Propagation in Curvilinear Coordinates with Mesh Refinement Interfaces by a Fourth Order Finite Difference Method

Zhang, Lu; Wang, Siyang; Petersson, N. Anders

doi:10.1137/20m1339702

Elastic Wave Propagation in Curvilinear Coordinates with Mesh Refinement Interfaces by a Fourth Order Finite Difference Method

Journal Article · Tue Apr 27 00:00:00 EDT 2021 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/20m1339702· OSTI ID:1810668

Zhang, Lu ^[1]; Wang, Siyang ^[2]; Petersson, N. Anders ^[3]

Columbia Univ., New York, NY (United States)
Malardalen Univ., Vasteras (Sweden)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing

In this work, we develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved interfaces. The governing equations are discretized in second order form on curvilinear meshes by using a fourth order finite difference operator satisfying a summation-by-parts property. The method is energy stable and high order accurate. The highlight is that mesh sizes can be chosen according to the velocity structure of the material so that computational efficiency is improved. At the mesh refinement interfaces with hanging nodes, physical interface conditions are imposed by using ghost points and interpolation. With a fourth order predictor-corrector time integrator, the fully discrete scheme is energy conserving. Numerical experiments are presented to verify the fourth order convergence rate and the energy conserving property.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1810668

Report Number(s):: LLNL-JRNL--810518; 1017177

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 2 Vol. 43; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
elastic wave equations
finite difference methods
non-conforming mesh refinement
summation-by-parts
three space dimension

Elastic Wave Propagation in Curvilinear Coordinates with Mesh Refinement Interfaces by a Fourth Order Finite Difference Method

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