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Title: Discretizing singular point sources in hyperbolic wave propagation problems

Journal Article · · Journal of Computational Physics
 [1];  [2];  [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Stanford Univ., Stanford, CA (United States)
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Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.

Research Organization:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344; LLNL-JRNL-679293
OSTI ID:
1343000
Alternate ID(s):
OSTI ID: 1329335
Report Number(s):
LLNL-JRNL-679293
Journal Information:
Journal of Computational Physics, Vol. 321, Issue C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 21 works
Citation information provided by
Web of Science

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Cited By (2)

High-fidelity Sound Propagation in a Varying 3D Atmosphere journal June 2018
Numerical noise suppression for wave propagation with finite elements in first-order form by an extended source term journal August 2018

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Related Subjects

58 GEOSCIENCES
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
singular sources
hyperbolic wave propagation
moment conditions
smoothness conditions
summation by parts