Name
Title | ||
|---|---|---|
A second order PVM flux limiter method. Application to magnetohydrodynamics and shallow stratified flows |
Abstract | ||
|---|---|---|
In this work we propose a second order flux limiter finite volume method, named PVM-2U-FL, that only uses information of the two external waves of the hyperbolic system. This method could be seen as a natural extension of the well known WAF method introduced by E.F. Toro in [23]. We prove that independently of the number of unknowns of the 1D system, it recovers the second order accuracy at regular zones, while in presence of discontinuities, the scheme degenerates to PVM-2U method, which can be seen as an improvement of the HLL method (see [6,10]). Another interesting property of the method is that it does not need any spectral decomposition of the Jacobian or Roe matrix associated to the flux function. Therefore, it can be easily applied to systems with a large number of unknowns or in situations where no analytical expression of the eigenvalues or eigenvectors are known. In this work, we apply the proposed method to magnetohydrodynamics and to stratified multilayer flows. Comparison with the two-waves WAF and HLL-MUSCL methods are also presented. The numerical results show that PVM-2U-FL is the most efficient and accurate among them. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.jcp.2013.12.059 | J. Comput. Physics |
Keywords | Field | DocType |
finite volume method,hyperbolic system,shallow stratified flow,large number,pvm-2u method,hll-muscl method,flux function,waf method,order accuracy,order pvm flux limiter,hll method,second order,flux limiters,magnetohydrodynamic,riemann solver | Mathematical optimization,Jacobian matrix and determinant,Stratified flows,Matrix (mathematics),Mathematical analysis,Matrix decomposition,Finite volume method,Flux limiter,Eigenvalues and eigenvectors,Mathematics,Riemann solver | Journal |
Volume | ISSN | Citations |
262, | 0021-9991 | 1 |
PageRank | References | Authors |
0.37 | 10 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. J. Castro Díaz | 1 | 22 | 2.77 |
| E. D. FernáNdez-Nieto | 2 | 61 | 7.52 |
| G. Narbona-Reina | 3 | 8 | 2.43 |
| Marc de la Asunción | 4 | 15 | 1.29 |