A Runge–Kutta,Taylor–Galerkin scheme for hyperbolic systems with source terms. Application to shock wave propagation in viscoplastic geomaterials

This paper presents an alternative formulation of Solid Dynamics problems based on (i) a mathematical model consisting of a system of hyperbolic PDEs where the source term is originated by the viscoplastic strain rate and (ii) a splitting scheme where the two‐step Taylor–Galerkin is used for the advective part of the PDE operator while the sources are integrated using a fourth‐order Runge–Kutta. Use of the splitting scheme results in a higher accuracy than that of the original two‐step Taylor–Galerkin. The scheme performs well when used with linear triangle or tetrahedra for (i) bending‐dominated situations (ii) localized failure under dynamic conditions and keeps the advantages of the two‐step Taylor–Galerkin concerning numerical dispersion and damping of short wavelengths. Copyright © 2006 John Wiley & Sons, Ltd.