A robust flux splitting method with low dissipation for all‐speed flows

Abstract

Summary In this paper, we propose a simple robust flux splitting method for all‐speed flows with low dissipation. Following the Toro‐Vazquez splitting, the inviscid flux is split into the convective and the pressure parts first. Then, we apply the Harten‐Lax‐van Leer (HLL) algorithm to each parts with low dissipation modification. Here, the modification improves the method with accurately resolving contact discontinuity and high resolution for low speed flows. Several carefully chosen numerical tests are investigated, and the results show that the proposed scheme is capable of resolving contact discontinuity, robust against the shock anomaly and accurate at all‐speeds. Because of these properties, it is expected to be widely applied to all‐speed flow studies. Copyright © 2016 John Wiley & Sons, Ltd.

Diffusion and dissipation in acoustic propagation simulation by convection-pressure split algorithms in all Mach number form

“…Because S L is an approximation of v L − c L and S R is an approximation of v R + c R , the equations ( 31) are similar to the characteristic equations ( 21) and (22). The solution of the set of the two equations ( 31) is similar to ( 23) and ( 24): 23) and ( 24) are recovered.…”

“…Li and Gu [15] demonstrate good functioning of the HLL, with their adaptation for low Mach number, for a Riemann problem and for steady state 2-D low Mach number flows. Sun et al [22] demonstrate good functioning of the HLLP-CPS-TV with the low Mach number adaptation of Li and Gu for Riemann problems, steady state 2-D low Mach number flows and steady state 2-D high Mach number flows.…”

A Review of Riemann Solvers for Hypersonic Flows

“…Inspired by the Liou-Steffen splitting procedure, scholars proposed two more procedures to split the Euler flux vector into a convective part and a pressure part. These two procedures are the Toro splitting procedure [ 80 – 82 ] and the Zha-Bilgen splitting procedure [ 83 – 85 ].…”

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

“…The upwind schemes are mostly preferred in the computation of high-speed flows because of their higher numerical stability (Laney, 1998, pp. 214–593; Sun et al , 2017). These schemes derive their robustness from the methods of stencil selection, which respect the advection direction (van Leer, 2006).…”

“…The reason for poor resolution of shear layers by the FVS schemes was associated with high numerical diffusion of the momentum flux in FVS schemes (van Leer, 1991). To alleviate unduly high numerical diffusion, several improvements took place including Hänel et al ’s (1987) FVS, Liou and Steffen’s (1993) AUSM, Zha and Bilgen’s (1993) FVS, Toro and Vázquez-Cendón (2012) FVS, Xie et al ’s (2015) low diffusion flux splitting (LDFS), Sun et al ’s (2017) flux-splitting scheme etc.…”