Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6932351 | Journal of Computational Physics | 2014 | 28 Pages |
Abstract
Following Cattaneo's original idea, in this article we first present two relaxation formulations for time-dependent, non-linear systems of advection-diffusion-reaction equations. Such formulations yield time-dependent non-linear hyperbolic balance laws with stiff source terms. Then we present a locally implicit version of the ADER method to solve these stiff systems to high accuracy. The new ingredient of the numerical methodology is a locally implicit solution of the generalised Riemann problem. We illustrate the formulations and the resulting numerical approach by solving the compressible Navier-Stokes equations.
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Authors
Gino I. Montecinos, Eleuterio F. Toro,