Interface error analysis for numerical wave propagation

The numerical error associated with finite-difference simulation of wave propagation in discontinuous media consists of two components. The first component is a higher-order error that leads to grid dispersion; it can be controlled by higher-order methods. The second component results from misalignm...

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Bibliographic Details
Published in:Computational geosciences 2009-09, Vol.13 (3), p.363-371
Main Authors: Symes, William W., Vdovina, Tetyana
Format: Article
Language:English
Subjects:
Earth and Environmental Science
Earth Sciences
Error analysis
Geophysics
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Interfaces
Mathematical Modeling and Industrial Mathematics
Mathematics
Original Paper
Simulation
Soil Science & Conservation
Wave propagation
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Summary:The numerical error associated with finite-difference simulation of wave propagation in discontinuous media consists of two components. The first component is a higher-order error that leads to grid dispersion; it can be controlled by higher-order methods. The second component results from misalignment between numerical grids and material interfaces. We provide an explicit estimate of the interface misalignment error for the second order in time and space staggered finite-difference scheme applied to the acoustic wave equation. Our analysis, confirmed by numerical experiments, demonstrates that the interface error results in a first-order time shift proportional to the distance between the interface and computational grids. A 2D experiment shows that the interface error cannot be suppressed by higher-order methods and indicates that our 1D analysis gives a good prediction about the behavior of the numerical solution in higher dimensions.
ISSN:1420-0597
1573-1499
DOI:10.1007/s10596-008-9124-8