Non-conforming interface conditions for the second-order wave equation

TL;DR

This paper introduces two new methods for imposing interface conditions in the second-order wave equation with non-conforming grids, reducing stiffness issues while maintaining accuracy and convergence.

Contribution

It presents a projection method and a hybrid approach that overcome stiffness problems of previous SAT-based methods for non-conforming interface conditions.

Findings

Both methods retain accuracy and convergence of SAT methods.

The new methods significantly reduce stiffness in numerical schemes.

Numerical experiments confirm effectiveness with traditional and order-preserving interpolations.

Abstract

Imposition methods of interface conditions for the second-order wave equation with non-conforming grids is considered. The spatial discretization is based on high order finite differences with summation-by-parts properties. Previously presented solution methods for this problem, based on the simultaneous approximation term (SAT) method, have shown to introduce significant stiffness. This can lead to highly inefficient schemes. Here, two new methods of imposing the interface conditions to avoid the stiffness problems are presented: 1) a projection method and 2) a hybrid between the projection method and the SAT method. Numerical experiments are performed using traditional and order-preserving interpolation operators. Both of the novel methods retain the accuracy and convergence behavior of the previously developed SAT method but are significantly less stiff.