A robust shock-capturing scheme based on rotated Riemann solvers

This paper presents a robust finite volume shock-capturing scheme based on the rotated approximate Riemann solver. A general framework for constructing the rotated Riemann solver is described and a rotated Roe scheme is discussed in detail. It is found that the robustness of the rotated shock-capturing scheme is closely related to the way in which the direction of upwind differencing is determined. When the upwind direction is determined by the velocity-difference vector, the rotated Roe scheme demonstrates a robust shock-capturing capability and the shock instabilities or carbuncle phenomena can be eliminated completely. The dissipation property associated with the linear field of the rotated flux-difference splitting scheme is analyzed, and several test cases are presented to validate the proposed scheme. (C) 2003 Elsevier Science Ltd. All rights reserved.