论文标题
基于气体和HLLC通量的高阶方案的性能比较
Comparison of the performance of high-order schemes based on the gas-kinetic and HLLC fluxes
论文作者
论文摘要
在本文中，在结构化的矩形网格中对两种基于气体运动方案（GKS）和HLLC通量进行的两种高阶有限体积方法的性能进行了比较。对于这两个方案，都采用了五阶Weno-AO重建来实现高阶空间精度。在时间离散化方面，WENO5-AO-GKS方案采用了两阶段的四阶（S2O4）时间行进策略，而Weno5-AO-HLLC方案采用了四阶Runge-Kutta（RK4）方法。对于粘性流量计算，GKS在单个细胞界面气体分布函数的演变中包括无粘性和粘性通量。对于WENO5-AO-HLLC方案，Indiscid通量由HLLC Riemann求解器提供，并且粘性通量通过第六阶中心差方法离散化。根据远期马赫步骤和粘性冲击管的测试，这两个方案均显示出出色的震撼捕获物业。从titarev-toro和双剪切层测试中，Weno5-AO-GKS方案似乎比WENO5-AO-HLLC方案具有更好的分辨率。在极端情况下，这两种方案都表现出极好的鲁棒性，例如Le Blanc问题。从NOH问题的情况和可压缩的各向同性湍流中，WENO5-AO-GKS方案显示出最喜欢的鲁棒性。在可压缩的各向同性湍流和三维泰勒绿色涡流问题中，weno-ao-gks可以使用高达0.5的CFL数，而不是0.3，而对于weno5-ao-hllc。就计算效率而言，在二维粘性流问题中，WENO5-AO-HLLC方案比WENO5-AO-GKS方案高约27％，但在三维情况下，速度快15％。由于多维性，WENO5-AO-GKS方案在层层边界层和双剪切层测试中的性能优于WENO5-AO-HLLC方案。
In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out in structured rectangular mesh. For both schemes, the fifth-order WENO-AO reconstruction is adopted to achieve a high-order spatial accuracy. In terms of temporal discretization, a two-stage fourth-order (S2O4) time marching strategy is adopted for WENO5-AO-GKS scheme, and the fourth-order Runge-Kutta (RK4) method is employed for WENO5-AO-HLLC scheme. For the viscous flow computation, the GKS includes both inviscid and viscous fluxes in the evolution of a single cell interface gas distribution function. While for the WENO5-AO-HLLC scheme, the inviscid flux is provided by HLLC Riemann solver, and the viscous flux is discretized by a sixth-order central difference method. Based on the tests of forward Mach step and viscous shock tube, both schemes show outstanding shock capturing property. From the Titarev-Toro and double shear layer tests, WENO5-AO-GKS scheme seems to have a better resolution than WENO5-AO-HLLC scheme. Both schemes show excellent robustness in extreme cases, such as the Le Blanc problem. From the cases of the Noh problem and the compressible isotropic turbulence, WENO5-AO-GKS scheme shows favorite robustness. In the compressible isotropic turbulence and three-dimensional Taylor-Green vortex problems, WENO-AO-GKS can use a CFL number up to 0.5, instead of 0.3 for WENO5-AO-HLLC. In terms of computational efficiency, WENO5-AO-HLLC scheme is about 27% more expensive than WENO5-AO-GKS scheme in the two-dimensional viscous flow problems, but is about 15% faster in the three-dimensional case. Due to the multi-dimensionality, WENO5-AO-GKS scheme performs better than WENO5-AO-HLLC scheme in the laminar boundary layer and the double shear layer test.
