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 we propose
satisfies the following properties. Firstly it preserves the nonnegativity
of gas density. Secondly and this is the motivation, the scheme
is asympotically 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.
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