Flow of two phases in a heterogeneous porous medium is modeled by a scalar conservation law with a discontinuous coefficient. As solutions of conservation laws with discontinuous coefficients depend explicitly on the underlying small scale effects, we consider a model where the relevant small scale effect is dynamic capillary pressure. We prove that the limit of vanishing dynamic capillary pressure exists and is a weak solution of the corresponding scalar conservation law with discontinuous coefficient. A robust numerical scheme for approximating the resulting limit solutions is introduced. Numerical experiments show that the scheme is able to approximate interesting solution features such as propagating non-classical shock waves as well as discontinuous standing waves efficiently.

Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes / Coclite, Giuseppe Maria; di Ruvo, L.; Ernest, J.; Mishra, S.. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - 8:4(2013), pp. 969-984. [10.3934/nhm.2013.8.969]

Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes

COCLITE, Giuseppe Maria;
2013-01-01

Abstract

Flow of two phases in a heterogeneous porous medium is modeled by a scalar conservation law with a discontinuous coefficient. As solutions of conservation laws with discontinuous coefficients depend explicitly on the underlying small scale effects, we consider a model where the relevant small scale effect is dynamic capillary pressure. We prove that the limit of vanishing dynamic capillary pressure exists and is a weak solution of the corresponding scalar conservation law with discontinuous coefficient. A robust numerical scheme for approximating the resulting limit solutions is introduced. Numerical experiments show that the scheme is able to approximate interesting solution features such as propagating non-classical shock waves as well as discontinuous standing waves efficiently.
2013
Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes / Coclite, Giuseppe Maria; di Ruvo, L.; Ernest, J.; Mishra, S.. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - 8:4(2013), pp. 969-984. [10.3934/nhm.2013.8.969]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/93816
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