Upwind Summation By Parts Finite Difference Methods for Large Scale Elastic Wave Simulations In Complex Geometries
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High-order accurate summation-by-parts (SBP) finite difference (FD) methods constitute efficient numerical methods for simulating large-scale hyperbolic wave propagation problems. Traditional SBP FD operators that approximate first-order spatial derivatives with central-difference stencils often have spurious unresolved wave-modes in their numerical solutions. On marginally resolved computational grids, these spurious wave-modes have the potential to destroy the accuracy of numerical solutions for a first-order hyperbolic partial differential equation, such as the elastic wave equation. To ensure the accuracy of numerical solutions of the three space dimensional (3D) elastic wave equation in complex geometries, we discretise the 3D elastic wave equation with a pair of non-central (upwind) finite-difference stencils, on boundary-conforming curvilinear meshes. Using the energy method we prove that the numerical method is numerically stable, and energy conserving. Furthermore, computational results show the robustness of the scheme. We present numerical simulations of the 3D elastic wave equation in heterogeneous media with complex non-planar free surface topography, including numerical simulations of community developed seismological benchmark problems. Our results show that the upwind SBP operators are more robust and less prone to numerical dispersion errors on marginally resolved meshes when compared to traditional SBP operators, thereby increasing efficiency.
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