Local Time-Space Mesh Refinement for Finite Difference Simulation of Waves

Vadim Lisitsa (), Galina Reshetova () and Vladimir Tcheverda ()
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Vadim Lisitsa: Institute of Petroleum Geology and Geophysics of SB RAS
Galina Reshetova: Institute of Computational Mathematics and Mathematical Geophysics of SB RAS
Vladimir Tcheverda: Institute of Petroleum Geology and Geophysics of SB RAS

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 609-616 from Springer

Abstract: Abstract This paper presents a new approach to a local time-space mesh refinement for a finite difference simulation of waves. The approach is based on the approximation of wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used the finite difference scheme preserves second order of convergence. We proved that this approach is low-reflecting and the artificial reflections are about 10−4 of incident wave. We also proved that if successive refinement is applied, i.e., temporal and spatial steps are refined at a different interfaces, the approach is stable.

Keywords: Wave Equation; Difference Scheme; Incident Wave; Coarse Grid; Order Equation (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_65

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DOI: 10.1007/978-3-642-11795-4_65

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