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. © 2014.

Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes / Montecinos, G. I.; Toro, E. F.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 275:(2014), pp. 415-442. [10.1016/j.jcp.2014.06.018]

Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes

Montecinos G. I.;Toro E. F.
2014-01-01

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. © 2014.
2014
Montecinos, G. I.; Toro, E. F.
Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes / Montecinos, G. I.; Toro, E. F.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 275:(2014), pp. 415-442. [10.1016/j.jcp.2014.06.018]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/332098
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