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Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving SourceWe propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.
Document ID
Acquisition Source
Langley Research Center
Document Type
Preprint (Draft being sent to journal)
Ryabenkii, V. S.
(Academy of Sciences (USSR) Moscow, USSR)
Turchaninov, V. I.
(Academy of Sciences (USSR) Moscow, USSR)
Tsynkov, S. V.
(Institute for Computer Applications in Science and Engineering Hampton, VA United States)
Date Acquired
September 6, 2013
Publication Date
June 1, 1999
Subject Category
Numerical Analysis
Report/Patent Number
NAS 1.26:209350
Funding Number(s)
PROJECT: RTOP 505-90-52-01
Distribution Limits
Work of the US Gov. Public Use Permitted.
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