A new approach for numerical-diffusion control of flux-vector-splitting schemes for viscous-compressible flows

Abstract

Purpose The flux vector splitting (FVS) schemes are known for their higher resistance to shock instabilities and carbuncle phenomena in high-speed flow computations, which are generally accompanied by relatively large numerical diffusion. However, it is desirable to control the numerical diffusion of FVS schemes inside the boundary layer for improved accuracy in viscous flow computations. This study aims to develop a new methodology for controlling the numerical diffusion of FVS schemes for viscous flow computations with the help of a recently developed boundary layer sensor. Design/methodology/approach The governing equations are solved using a cell-centered finite volume approach and Euler time integration. The gradients in the viscous fluxes are evaluated by applying the Green’s theorem. For the inviscid fluxes, a new approach is introduced, where the original upwind formulation of an FVS scheme is first cast into an equivalent central discretization along with a numerical diffusion term. Subsequently, the numerical diffusion is scaled down by using a novel scaling function that operates based on a boundary layer sensor. The effectiveness of the approach is demonstrated by applying the same on van Leer’s FVS and AUSM schemes. The resulting schemes are named as Diffusion-Regulated van Leer’s FVS-Viscous (DRvLFV) and Diffusion-Regulated AUSM-Viscous (DRAUSMV) schemes. Findings The numerical tests show that the DRvLFV scheme shows significant improvement over its parent scheme in resolving the skin friction and wall heat flux profiles. The DRAUSMV scheme is also found marginally more accurate than its parent scheme. However, stability requirements limit the scaling down of only the numerical diffusion term corresponding to the acoustic part of the AUSM scheme. Originality/value To the best of the authors’ knowledge, this is the first successful attempt to regulate the numerical diffusion of FVS schemes inside boundary layers by applying a novel scaling function to their artificial viscosity forms. The new methodology can reduce the erroneous smearing of boundary layers by FVS schemes in high-speed flow applications.

Numerical dissipation of flux splitting schemes for contact discontinuities

“…In Computational Fluid Dynamics(CFD), numerical dissipation is considered to derive from the truncation error introduced by the discrete convection term of the spatial discrete schemes, which is closely related to the computational accuracy and stability of the scheme. CFD researchers often use the method of reducing numerical dissipation to construct higher precision computational schemes [1][2][3]. The spatial discrete scheme consists of two parts, the difference scheme and the flux splitting scheme, and this paper mainly discusses the numerical dissipation characteristics of the flux splitting scheme, while the upwind scheme, as the mainstream scheme for solving convective fluxes in CFD at present [4], becomes the object of study in this paper.…”