High Order Scheme And Its Application In RM Instability

Aiming at high order and high resolution computation for numerical simulation of compressible fluid flows,in this study,based on the smoothness measurement of the flux function of the stencil,the new kind of weighted factor is constructed.On the basis,the hybrid scheme(H-WENO7-CD8)combines the characteristics of WENO scheme and central flux scheme,it improves the resolution of the scheme and the ability to capture the shock wave.The Fourier method is adopted to analysis the mathematical characteristics of the discrete scheme.The adaptive hybrid scheme has the lower dissipation.By the numerical simulation tests of the Shu-Osher shock-density interference problem,the two-dimensional Rayleigh-Taylor instability problem and the double Mach reflection,compared with the numerical tests of the WENO scheme,the results show that the present hybrid scheme can capture the shock wave better,and it has higher resolution to shock waves and small-scale waves with a low computation cost.Therefore,the present scheme lays an algorithm foundation for high resolution numerical simulation of compressible fluid flows.Finally,the constructed hybrid scheme is used to simulate the instability of the interaction between shock wave and density interface.Set up two kinds of density interface,lighter gas with air and heavy gas with air,then the numerical simulation results were compared with experimental results,the calculation results compared with the experimental results,It can show the evolution of the flow field of fluid clearly at all times.the results of numerical simulation and experimental results are consistent.At the same time,describe the development of the density interface and the change of the density and velocity of the whole flow field in details,and a theoretical analysis is given to the cause of the change.