Abstract:
In this talk, we introduce a class of fast finite volume solvers, named as PVM (Polynomial Viscosity Matrix), for balance laws or, more generally, for nonconservative hyperbolic systems.
They are defined in terms of viscosity matrices computed by a suitable polynomial evaluation of a Roe matrix. These methods have the advantage that they only need some information about the eigenvalues of the system to be defined, and no spectral decomposition of Roe Matrix is needed. As consequence, they are faster than Roe method. These methods can be seen as a generalization of the scheme introduced by Degond, Peyrard and Russo in 1999 for conservation laws to balance laws and nonconservative systems. In this work, some well known solvers as Rusanov, Lax-Friedrichs, FORCE, GFORCE or HLL are redefined under this form, and then some new solvers are proposed.
The performance of the numerical schemes are compared among them and with Roe scheme. Finally, some application to geophysical flows are presented. |