A finite volume scheme employing the multipoint flux approximation with diamond stencil for the diffusive‐viscous wave equation on general polyhedral meshes

Abstract Based on three‐dimensional seismic wave, simulations have become a pivotal aspect of seismic exploration. The diffusive‐viscous wave equation, initially proposed by Goloshubin et al., is frequently utilized to describe seismic wave propagation in fluid‐saturated media. However, obtaining numerical solutions for this equation has become an urgent issue in recent years. In this study, we present a cell‐centered finite volume scheme utilizing a multipoint flux approximation that employs a “diamond stencil” on general polyhedral meshes to address the diffusive‐viscous wave equation. Numerical tests exhibit that this new scheme attains optimal convergence, and its effectiveness is demonstrated through simulating vibrations induced by an earthquake source.