A Godunov-type finite-volume scheme for unified solid-liquid elastodynamics on arbitrary two-dimensional grids

Abstract

A Godunov-type finite-volume scheme is presented for the elastodynamic equations written in terms of displacement velocities and stresses. The mathematical model universally includes elastic solids and liquids resulting in a method highly suitable for studies of acoustic wave scattering at solid-liquid interfaces. The scheme is written for a generic grid of control volumes in two spatial dimensions. The governing equations in an integral conservation form are applied to the control volumes. The exact one-dimensional Riemann problem solution at the volumes’ borders is used to evaluate fluxes. The spatial accuracy of the scheme is enhanced to second order using linear extrapolation of variables to the volumes’ faces where the Riemann solver is applied. A predictor-corrector technique is used to improve the accuracy in time. The scheme is then considered in a triangular unstructured grid environment with a dual grid of node-centered control volumes. A dynamic reversible refinement/derefinement procedure is described to enhance resolution locally at sharp variations in the solution or in subdomains of special interest. Implementation of the external and internal boundary conditions is discussed. A demonstrative application to acoustic pulse interaction with a solid shell in liquid is presented.