Abstract
The purpose of this work is to present some recent developments about incomplete Riemann solvers for general hyperbolic systems. Polynomial Viscosity Matrix (PVM) methods based on internal approximations to the absolute value function are introduced, and they are compared with Chebyshev-based PVM solvers. 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 for which the Jacobians involve complex expressions. Some numerical experiments involving the relativistic magnetohydrodynamic equations are presented, both in one and two dimensions. The obtained results are in good agreement with those found in the literature and show that our schemes are robust and accurate, running stable under a satisfactory time step restriction.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
