Elastic wave propagation in curvilinear coordinates with mesh refinement interfaces by a fourth order finite difference method

TL;DR

This paper introduces a high-order finite difference method for 3D elastic wave equations in media with curved interfaces, enabling efficient and accurate simulations with mesh refinement and energy conservation.

Contribution

It presents a fourth order accurate, energy stable finite difference scheme on curvilinear meshes with mesh refinement interfaces for elastic wave modeling.

Findings

Achieves fourth order convergence in numerical experiments.

Maintains energy conservation in the discrete scheme.

Improves computational efficiency through adaptive mesh sizing.

Abstract

We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved interfaces. The governing equations are discretized in second order form on curvilinear meshes by using a fourth order finite difference operator satisfying a summation-by-parts property. The method is energy stable and high order accurate. The highlight is that mesh sizes can be chosen according to the velocity structure of the material so that computational efficiency is improved. At the mesh refinement interfaces with hanging nodes, physical interface conditions are imposed by using ghost points and interpolation. With a fourth order predictor-corrector time integrator, the fully discrete scheme is energy conserving. Numerical experiments are presented to verify the fourth order convergence rate and the energy conserving property.