Stable Coupling of Nonconforming, High-Order Finite Difference Methods

Abstract

A methodology for handling block-to-block coupling of nonconforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction of projection operators that move a finite difference grid solution along an interface to a space of piecewise defined functions; we specifically consider discontinuous, piecewise polynomial functions. The constructed projection operators are compatible with the underlying summation-by-parts energy norm. Using the linear wave equation in two dimensions as a model problem, energy stability of the coupled numerical method is proven for the case of curved, nonconforming block-to-block interfaces. To further demonstrate the power of the coupling procedure, we show how it allows for the development of a provably energy stable coupling between curvilinear finite difference methods and a curved-triangle discontinuous Galerkin method. The theoretical results are verified through numerical simulations on curved meshes as well as eigenvalue analysis.

30 pages, 7 figures, 4 tables

References in corpus (1)

• Stable difference methods for block-oriented adaptive grids

Cited by in corpus (10)

• High order finite difference methods for the wave equation with non-conforming grid interfaces
• Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner
• 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
• Order Preserving Interpolation for Summation-by-Parts Operators at Non-Conforming Grid Interfaces
• Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids
• High-order numerical methods for 2D parabolic problems in single and composite domains
• Hybridized Summation-By-Parts Finite Difference Methods
• Simultaneous approximation terms for elastic wave equations on nonuniform grids
• Energy stable and accurate coupling of finite element methods and finite difference methods