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CONVERGENCE OF VANISHING CAPILLARITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH DISCONTINUOUS FLUXES.
- Source :
- Networks & Heterogeneous Media; Dec2013, Vol. 8 Issue 4, p969-984, 16p
- Publication Year :
- 2013
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15561801
- Volume :
- 8
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Networks & Heterogeneous Media
- Publication Type :
- Academic Journal
- Accession number :
- 92959025
- Full Text :
- https://doi.org/10.3934/nhm.2013.8.969