Stability is achieved in most approximate Riemann solvers through ‘flux upwinding’, where the flux at the interface is arrived at by adding a dissipative term to the average of the left and right flux. Motivated by the existence of a collapsed interface state in the gas-kinetic Bhatnagar–Gross–Krook (BGK) method, an alternative approach to upwinding is attempted here; an interface state is arri...

To avoid un-realistic solutions like expansion shocks from appearing as a part of a solution it is necessary to satisfy the entropy condition for the Roe scheme. A variety of entropy fix formulae for the Roe scheme have been addressed in the literature. Three of the most famous are due to Harten-Hyman and Hoffmann-Chiang. These formulations have been assessed in this paper by applying them to t...

In this work, we present a class of fast first order 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 eigenvalue...

The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is explored and bounds derived for such limiters. A class of limiters is presented which includes a very compressive limiter due to Roe, and various limiters are compared both theoretically and numerically.

We present a general framework to design Godunov-type schemes for multidimensional ideal magnetohydrodynamic (MHD) systems, having the divergence-free relation and the related properties of the magnetic field B as built-in conditions. Our approach mostly relies on the Constrained Transport (CT) discretization technique for the magnetic field components, originally developed for the linear induc...