Name
Title | ||
|---|---|---|
Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. |
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.3934/nhm.2013.8.969 | NETWORKS AND HETEROGENEOUS MEDIA |
Keywords | Field | DocType |
Conservation laws,discontinuous fluxes,capillarity approximation | Convergence (routing),Mathematical optimization,Mathematical analysis,Flow (psychology),Scalar (physics),Standing wave,Capillary pressure,Weak solution,Shock wave,Conservation law,Mathematics | Journal |
Volume | Issue | ISSN |
8 | 4 | 1556-1801 |
Citations | PageRank | References |
2 | 0.50 | 3 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Giuseppe Maria Coclite | 1 | 27 | 10.75 |
| Lorenzo di Ruvo | 2 | 3 | 2.23 |
| Jan Ernest | 3 | 15 | 1.22 |
| Siddhartha Mishra | 4 | 170 | 21.36 |