Name
Title | ||
|---|---|---|
First- and second-order finite volume methods for the one-dimensional nonconservative Euler system |
Abstract | ||
|---|---|---|
Gas flow in porous media with a nonconstant porosity function provides a nonconservative Euler system. We propose a new class of schemes for such a system for the one-dimensional situations based on nonconservative fluxes preserving the steady-state solutions. We derive a second-order scheme using a splitting of the porosity function into a discontinuous and a regular part where the regular part is treated as a source term while the discontinuous part is treated with the nonconservative fluxes. We then present a classification of all the configurations for the Riemann problem solutions. In particularly, we carefully study the resonant situations when two eigenvalues are superposed. Based on the classification, we deal with the inverse Riemann problem and present algorithms to compute the exact solutions. We finally propose new Sod problems to test the schemes for the resonant situations where numerical simulations are performed to compare with the theoretical solutions. The schemes accuracy (first- and second-order) is evaluated comparing with a nontrivial steady-state solution with the numerical approximation and convergence curves are established. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.jcp.2009.07.038 | J. Comput. Physics |
Keywords | Field | DocType |
new sod problem,nonconservative euler system,euler system,second-order finite volume method,resonant situation,new class,finite volumes,rusanov,muscl,nonconservative flux,riemann problem solution,inverse riemann problem,riemann problem,hyperbolic,nonconservative,discontinuous part,schemes accuracy,regular part,one-dimensional nonconservative euler system,resonant,exact solution,finite volume method,eigenvalues,numerical simulation,source term,finite volume,porous media,steady state,second order | Convergence (routing),Exact solutions in general relativity,Inverse,Mathematical analysis,Euler system,Inverse problem,Finite volume method,Mathematics,Riemann problem,Eigenvalues and eigenvectors | Journal |
Volume | Issue | ISSN |
228 | 22 | Journal of Computational Physics |
Citations | PageRank | References |
2 | 0.43 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stéphane Clain | 1 | 25 | 3.57 |
| D. Rochette | 2 | 7 | 1.42 |