Name
Abstract | ||
|---|---|---|
This paper is devoted to the numerical approximation of the solutions of a system of conservation laws arising in the modeling of two-phase flows in pipelines. The PDEs are closed by two highly nonlinear algebraic relations, namely, a pressure law and a hydrodynamic one. The severe nonlinearities encoded in these laws make the classical approximate Riemann solvers virtually intractable at a reasonable cost of evaluation. We propose a strategy for relaxing solely these two nonlinearities. The relaxation system we introduce is of course hyperbolic but all associated eigenfields are linearly degenerate. Such a property not only makes it trivial to solve the Riemann problem but also enables us to enforce some further stability requirements, in addition to those coming from a Chapman-Enskog analysis. The new method turns out to be fairly simple and robust while achieving desirable positivity properties on the density and the mass fractions. Extensive numerical evidences are provided. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/s00211-004-0558-1 | Numerische Mathematik |
Keywords | Field | DocType |
associated eigenfields,two-phase flow model,conservation law,relaxation system,severe nonlinearities,relaxation method,course hyperbolic,hydrodynamic closure law,riemann problem,numerical approximation,classical approximate riemann,chapman-enskog analysis,extensive numerical evidence,two phase flow | Degenerate energy levels,Nonlinear system,Mathematical analysis,Relaxation (iterative method),Numerical analysis,Partial differential equation,Law,Numerical stability,Riemann problem,Conservation law,Mathematics | Journal |
Volume | Issue | ISSN |
99 | 3 | 0945-3245 |
Citations | PageRank | References |
18 | 3.99 | 1 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Baudin | 1 | 27 | 5.34 |
| Christophe Berthon | 2 | 108 | 17.08 |
| Frédéric Coquel | 3 | 72 | 13.53 |
| Roland Masson | 4 | 54 | 12.19 |
| Quang Huy Tran | 5 | 18 | 3.99 |