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.
|Titolo:||Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.3934/nhm.2013.8.969|
|Appare nelle tipologie:||1.1 Articolo in rivista|