Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes
Di Ruvo, L.
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 Show more
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Journal / seriesResearch Report
PublisherETH, Seminar für Angewandte Mathematik
Organisational unit03851 - Mishra, Siddhartha
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