Hybrid upwind splitting scheme by combining the approaches of Roe and AUFS for compressible flow problems

This paper presents a new robust finite volume shock-capturing scheme based on an improved version of the artificially upstream flux vector splitting (AUFS) scheme. This novel numerical scheme, named AUFSR, is obtained by combining AUFS scheme and the Roe solver. The resulting flux functions can be implemented in a very simple manner, in the form of the Roe solver with modified wave speeds, so that converting an existing AUFS flux into the new fluxes is an extremely simple task. The method handles difficulties encountered by the AUFS scheme, when the artificial diffusion is computed with the Steger-Warming approach in the case where the flux vector does not check the homogenous property. The solution accuracy is further improved by extension to high-order spatial and temporal scheme. Accuracy, efficiency and other essential features of the proposed scheme are evaluated by analysing shock propagation behaviours for both the steady and unsteady compressible flows.