Simplified second-order Godunov-type methods
SIAM Journal on Scientific and Statistical Computing
On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High order WENO schemes: investigations on non-uniform converges for MHD Riemann problems
Journal of Computational Physics
Journal of Computational Physics
TVD Fluxes for the High-Order ADER Schemes
Journal of Scientific Computing
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
SIAM Journal on Numerical Analysis
MUSTA Fluxes for systems of conservation laws
Journal of Computational Physics
Journal of Computational Physics
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
Journal of Scientific Computing
Journal of Computational Physics
Short Note: Complement to the "Kolgan project"
Journal of Computational Physics
Hi-index | 31.45 |
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.