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

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vadim Lisitsa & Galina Reshetova & Vladimir Tcheverda, 2010. "Local Time-Space Mesh Refinement for Finite Difference Simulation of Waves," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 609-616, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_65
    DOI: 10.1007/978-3-642-11795-4_65
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