Non-stiff narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids

Abstract

The Laplacian appears in several partial differential equations used to model wave propagation. Summation-by-parts--simultaneous approximation term (SBP-SAT) finite difference methods are often used for such equations, as they combine computational efficiency with provable stability on curvilinear multiblock grids. However, the existing SBP-SAT discretization of the Laplacian quickly becomes prohibitively stiff as grid skewness increases. The stiffness stems from the SATs that impose inter-block couplings and Dirichlet boundary conditions. We resolve this issue by deriving stable SATs whose stiffness is almost insensitive to grid skewness. The new discretization thus allows for large time steps in explicit time integrators, even on very skewed grids. It also applies to the variable-coefficient generalization of the Laplacian. We demonstrate the efficacy and versatility of the new method by applying it to acoustic wave propagation problems inspired by marine seismic exploration and infrasound monitoring of volcanoes.

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• Non-stiff narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids
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Cited by in corpus (4)

• Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions
• A Non-stiff Summation-By-Parts Finite Difference Method for the Scalar Wave Equation in Second Order Form: Characteristic Boundary Conditions and Nonlinear Interfaces
• Non-stiff narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids
• Stable and high-order accurate finite difference methods for the diffusive viscous wave equation