A Non-stiff Summation-By-Parts Finite Difference Method for the Wave Equation in Second Order Form: Characteristic Boundary Conditions and Nonlinear Interfaces

by   Jeremy E. Kozdon, et al.

Curvilinear, multiblock summation-by-parts finite difference methods with the simultaneous approximation term method provide a stable and accurate method for solving the wave equation in second order form. That said, the standard method can become arbitrarily stiff when characteristic boundary conditions and nonlinear interface conditions are used. Here we propose a new technique that avoids this stiffness by using characteristic variables to "upwind" the boundary and interface treatment. This is done through the introduction of an additional block boundary displacement variable. Using a unified energy, which expresses both the standard as well as characteristic boundary and interface treatment, we show that the resulting scheme has semidiscrete energy stability for the anistropic wave equation. The theoretical stability results are confirmed with numerical experiments that also demonstrate the accuracy and robustness of the proposed scheme. The numerical results also show that the characteristic scheme has a time step restriction based on standard wave propagation considerations and not the boundary closure.



There are no comments yet.


page 20


An energy-based summation-by-parts finite difference method for the wave equation in second order form

We develop an energy-based finite difference method for the wave equatio...

An Efficient and high accuracy finite-difference scheme for the acoustic wave equation in 3D heterogeneous media

Efficient and accurate numerical simulation of 3D acoustic wave propagat...

An explicit predictor/multicorrector time marching with automatic adaptivity for finite-strain elastodynamics

We propose a time-adaptive predictor/multi-corrector method to solve hyp...

Interface learning of multiphysics and multiscale systems

Complex natural or engineered systems comprise multiple characteristic s...

High-order accurate schemes for Maxwell's equations with nonlinear active media and material interfaces

We describe a fourth-order accurate finite-difference time-domain scheme...

A re-formulization of the transfer matrix method for calculating wave-functions in higher dimensional disordered open systems

We present a numerically stable re-formulization of the transfer matrix ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.