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A Runge–Kutta, Taylor–Galerkin scheme for hyperbolic systems with source terms. Application to shock wave propagation in viscoplastic geomaterials
Author(s) -
Mabssout M.,
Pastor M.,
I. Herreros M.,
Quecedo M.
Publication year - 2006
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.528
Subject(s) - taylor series , viscoplasticity , galerkin method , mathematics , runge–kutta methods , shock wave , advection , discontinuous galerkin method , mathematical analysis , finite element method , mechanics , numerical analysis , physics , constitutive equation , thermodynamics
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.