An upwinded state approximate Riemann solver.

SUMMARY 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 arrived at by taking an upwinded average of left and right states, and then the flux is calculated as a function of this 'collapsed' interface state. This so called 'state-upwinding' approach gives rise to a new scheme called the linearized Riemann solver for the Euler and Navier-Stokes equations. The scheme is shown to be closely associated with the Roe scheme. It is, however, computationally less expensive and gives qualitatively comparable results over a wide range of problems. Most importantly, this scheme is found to preserve stationary contacts while not exhibiting the carbuncle phenomenon which plagues the Roe and other contact-preserving schemes. The scheme is therefore motivated as a new starting point to analyze the origin of the carbuncle phenomenon. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]