Search results for "Riemann solver"

The Two-Jacobian Scheme for Systems of Conservation Laws

2006

New Types of Jacobian-Free Approximate Riemann Solvers for Hyperbolic Systems

2017

We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Moreover, they can be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems with complex Jacobians, as the relativistic magnetohydrodynamics (RMHD) equations. The proposed solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method. Som…