Numerically Simulate Multi-medium Flow Based On DPVS Equations

The finite-difference weighted essentially non-oscillatory schemes(FD-WENO) can be described as:instead of using only one candidate stencil, we can use all of the candidate stencils. Thus we can obtain essentially non-oscillatory property in discontinuous region and get higher precision in smooth regions. In1970s, there are many kinds of simplified N-S equations, such as DPNS equations, VSL equations, PNS equations, TLNS equations and so on. From the angle of Fluid Dynamics only DPNS equations can exactly reflect the property of interfere shear flows. DPNS equations are a sort of hydromechanics control equations which are simplified. For flow which have approximate mainstream direction,we neglect vis-cosity in the mainstream direction, reserve part of inviscid items which can reflect the interaction mechanism of viscous flows and inviscous flows,then we can get different kinds of DPNS equations. The basic work of this article is:1. Deduce3-rd FD-WENO scheme, the partial derivative term of time is dis-cretized by the third-order TVD Runge-Kutta method.2. Introduced the background of DPNS equations and deduce the nondimen-sionalized DPNS equations.3. Simulate the Double-Mach reflection and Rayleigh-Taylor instability based on Euler equations、Navier-Stokes equations and DPNS equations. Then analysis the simulated image.