A Hamiltonian-Preserving Scheme for High Frequency Elastic Waves in Heterogeneous Media
Shi Jin and Xiaomei Liao
Abstract: We develop a class of Hamiltonian-preserving numerical schemes for high frequency elastic waves in heterogeneous media. The approach is based on the high frequency approximation governed by the Liouville equations with singular coefficients due to material interfaces. As previously done by Jin and Wen, we build into the numerical flux the wave scattering information at the interface, and use the Hamiltonian preserving principle to couple the wave numbers at both sides of the interface. This gives a class of numerical schemes that allows a hyperbolic CFL condition, is positive and $l^\infty$ stable, and captures correctly wave scattering at the interface with a sharp numerical resolution. We also extend the method to curved interfaces. Numerical experiments are carried out to study the numerical convergence and accuracy.