Numerical Study of High-Resolution Scheme Based on Preconditioning Method

In this paper, an efficient and accurate method based on the preconditioned advection upstream splitting method (AUSM) scheme is studied. Turkel's preconditioning method in conjunction with the second-order finite-volume monotone upwind schemes for conservation laws (MUSCL)-type AUSMDV (a mixture of AUSMD and AUSMV where D and V denote a flux-difference splitting-biased scheme and flux-vector-splitting-biased one, respectively) and AUSM(+)-up schemes based on the primitive variables is used to solve Navier-Stokes equations. These two schemes used in computational fluid dynamics with or without preconditioning methods are compared. The surface pressure distributions are compared with those calculated from a central difference scheme. The preconditioning method used in this paper obtains an improved convergence, stability, and the capability for the calculation of the low Mach number flows and transonic flows. The preconditioning high-resolution scheme strengthens the capability of identifying discontinuities and reducing the numerical dissipation. The present method that combines the multigrid algorithm further accelerates the convergence. Flow-independent convergence rates of the method are also observed from the numerical results for the low Mach number flows.