An Efficient Implicit Finite-Difference Scheme For Transonic Flow

Abstract

In this paper, transonic flow, where the interaction of a shock wave and a boundary layer often leads to extremely complicated flow phenomena, has been studied numerically. A unique method of implicit formulation is proposed by way of analyzing a model equation, which can separately deal with convection, diffusion and source terms. By combining this idea with Flux Vector Splitting, a Modified Implicit Flux Vector Splitting of the Navier-Stokes equations, which can avoid approximate factorization or block-bidiagonal, has been developed. So it has obvious superiority over the conventional FVS in terms of accuracy, robustness, convergence and computing cost. In the cases of two and three dimensional transonic and separated flows through a double throated nozzle and D’elery Case C, the numerical results agree with the published calculation results and measured data for both shock positions, separation/attachment points and overall flow field.