Abstract
An AUSM-based discretization method, using an explicit third-order discretization for the convective part and a line-implicit central discretization for the acoustic part and for the diffusive part, has been developed for incompressible and low-speed compressible Navier-Stokes equations. The lines are chosen in the direction of the gridpoints with shortest connection. The semi-implicit line method is used in multistage form because of the explicit third-order discretization of the convective part. Multigrid is used as acceleration technique. Because of the implicit treatment of the acoustic and the diffusive terms, the stiffness otherwise caused by high aspect ratio cells is removed. Low-Mach-number stiffness is treated by a preconditioning technique. To ensure physical correct behavior of the discretization for vanishing Mach number, extreme care has been taken. For vanishing Mach number, stabilization terms are added to the mass flux. Pressure and temperature stabilization terms are necessary. The coefficients of these terms are chosen so that correct scaling with Mach number is obtained. A blend of the low-speed algorithm with the original AUSM algorithm developed for high-speed applications has been constructed so that the resulting algorithm can be used at all speeds
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