关于高阶精度WCNS格式的无粘通量分裂方法（英文）  

On the Splitting Methods of Inviscid Fluxes for Implementing High-Order Weighted Compact Nonlinear Schemes

作　　者：涂国华[1] 陈坚强[1,2] 毛枚良[1,2] 赵晓慧[1] 刘化勇[1] 

机构地区：[1]空气动力学国家重点实验室(中国空气动力研究与发展中心),四川绵阳621000 [2]中国空气动力研究与发展中心计算空气动力研究所,四川绵阳621000

出　　处：《应用数学和力学》2016年第12期1324-1344,共21页Applied Mathematics and Mechanics

基　　金：Project supported by the National Key Research and Development Project of China(2016YFA0401200);the National Natural Science Foundation of China(11301525)~~

摘　　要：高阶精度加权紧致非线性格式(WCNS)越来越广泛地应用于复杂流动数值模拟.WCNS可以与多种无粘通量分裂方法结合起来使用.但是,常见的通量分裂方法都是基于低阶格式发展起来的,目前还不清楚哪些通量分裂方法最适合WCNS,也不知道这些方法与高阶格式结合时将会产生什么效果.表面热流计算是高超声速流动数值模拟的难点之一,为了在热流计算时选择合适的通量,研究了多种通量分裂方法的耗散大小.每种通量都可以表示成中心部分与耗散部分之和.这些通量的中心部分相同且非常简单,但是耗散部分较为复杂,且不同的通量分裂方法可导致不同的耗散表达式.通过对通量耗散进行分析可以发现耗散大小与网格界面两侧的物理量跳跃近似线性正相关.数值计算表明高阶格式得到的网格界面左右两侧的物理量跳跃通常远比低阶格式小,因而带来的通量耗散小.通过3个典型算例考察了通量耗散对热流计算的影响,其中包括高超激波/边界层干扰算例.基于对van Leer通量、Steger-Warming通量、KFVS通量、Roe通量、AUSM类通量和HLL类通量的考察,给出了通量选择建议.There is increasing popularity in using high-order weighted compact nonlinear schemes（WCNS） for complex flow simulations. The WCNS can be used in combination with many inviscid flux splitting methods. However, it is still uncertain which flux splitting is most suitable for the WCNS because most of the methods are devised on the basis of low-order dis- cretization methods. It is also not very clear what will happen when these splitting methods are mounted directly in high-order accurate schemes. In order to provide some guide for selecting inviscid fluxes in the computation of surface heat transfer, the dissipations of the fluxes are studied. Every inviscid flux can be expressed as a summation of a central part and a dissipation part. All the fluxes have an identical central part which is very simple. However, different fluxes have different dissipation parts which are more or less complicated. The analysis on the source of flux dissipation shows that the dissipation is nearly proportional to flux jumps on grid inter- faces. Numerical experiments show that high-order schemes usually produce far less flux jumps than low-order schemes in smooth regions, and logically the flux dissipations are quite lower. 3 canonical flows including hypersonic shock wave/boundary layer interactions（SWBLI） are sim- ulated to show the influence of inviscid fluxes on heat transfer computing. Finally, a suggestion is given for selecting inviscid fluxes based on the dissipations and shock instabilities of van Leer＇s flux splitting, the Steger-Warming（SW） flux splitting, the kinetic flux vector splitting （KFVS）, Roe＇s flux splitting, the AUSM（ advection upwind splitting method）-type flux split- ting and the HLL-type flux splitting.

关 键 词：加权紧致非线性格式 激波/边界层干扰 Euler通量 高阶精度 热流 

分 类 号：O35[理学—流体力学]