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.
Titolo: | Reformulations for general advection–diffusion–reaction equations and locally implicit ADER schemes |
Autori: | Montecinos Guzman, Gino Ignacio; Toro, Eleuterio Francisco |
Autori Unitn: | |
Titolo del periodico: | JOURNAL OF COMPUTATIONAL PHYSICS |
Anno di pubblicazione: | 2014 |
Codice identificativo Scopus: | 2-s2.0-84904905421 |
Codice identificativo ISI: | WOS:000341308900023 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jcp.2014.06.018 |
Handle: | http://hdl.handle.net/11572/125878 |
Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |
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