A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method
SIAM Journal on Numerical Analysis
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
SIAM Journal on Numerical Analysis
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
Asymptotic Preserving Scheme for Euler System with Large Friction
Journal of Scientific Computing
Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis
SIAM Journal on Numerical Analysis
Maxwellian Decay for Well-balanced Approximations of a Super-characteristic Chemotaxis Model
SIAM Journal on Scientific Computing
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We consider Euler equations with a friction term that describe an isentropic gas flow in a porous domain. More precisely, we consider the transition between low and high friction regions. In the high friction region the system is reduced to a parabolic equation, the porous media equation. In this paper we present a hyperbolic approach based on a finite volume technique to compute numerical solutions for the system in both regimes. The Upwind Source at Interfaces (USI) scheme that we propose satisfies the following properties. Firstly it preserves the nonnegativity of gas density. Secondly, and this is the motivation, the scheme is asymptotically consistent with the limit model (porous media equation) when the friction coefficient goes to infinity. We show analytically and through numerical results that the above properties are satisfied. We shall also compare results given with the use of USI, hyperbolic-parabolic coupling and classical centered sources schemes.