TU Guo-hua, CHEN Jian-qiang, MAO Mei-liang, ZHAO Xiao-hui, LIU Hua-yong. On the Splitting Methods of Inviscid Fluxes for Implementing High-Order Weighted Compact Nonlinear Schemes[J]. Applied Mathematics and Mechanics, 2016, 37(12): 1324-1344. doi: 10.21656/1000-0887.370518
Citation: TU Guo-hua, CHEN Jian-qiang, MAO Mei-liang, ZHAO Xiao-hui, LIU Hua-yong. On the Splitting Methods of Inviscid Fluxes for Implementing High-Order Weighted Compact Nonlinear Schemes[J]. Applied Mathematics and Mechanics, 2016, 37(12): 1324-1344. doi: 10.21656/1000-0887.370518

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

doi: 10.21656/1000-0887.370518
Funds:  National Key Research and Development Project of China (2016YFA0401200);National Natural Science Foundation of China (11301525)
  • Received Date: 2016-11-16
  • Rev Recd Date: 2016-12-01
  • Publish Date: 2016-12-15
  • 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 discretization 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 interfaces. 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 simulated 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 splitting and the HLL-type flux splitting.
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