Numerical Simulation And Research Of Multi-Medium Interface

This dissertation discusses multi-medium interface problems.It mainly includes two parts:In the first part,it mainly involves flow field calculation,interface tracing and in-terface boundary condition treatment.The level-set method combined with a revised RGFM is applied for tracking the gas-water and gas-solid interfaces.The fifth order finite difference WENO schemes are employed for solving Eulerian and level-set equa-tions as well as reinitialization equations.In order to solve the problem of nonphysical numerical solution of the flow field near the interface caused by the interface bound-ary conditions of the medium with large density ratio on both sides,we improve the accuracy of constructing Riemann problem along the normal of the interface,and ex-trapolate the Riemann solution to the ghost fluid,and obtain the corresponding physical quantities of the ghost points near the interface.The complex boundary composed of discrete points is regarded as the gas-solid interface,and the method to determine the normal of interface is given.In adition,we review the existing cavitation models in the literature and verify numerically.In this work,the plane moving shock interacted with a single water column and cylindrical water columns,the nozzle flow field bounded by discrete points,and the cavitation on the plane shock interacted with the water column are studied.The main conclusions are as follows:(1)In this paper,the method of determining the normal of gas-water interface is re-vised,and the construction accuracy of Riemann problem is improved.The method is extended to the gas-solid interface to improve the accuracy of the interface bound-ary condition treatments and avoid large numerical disturbance near the interface.The results demonstrate the effectiveness and robustness of the level-set method coupling with a revised RGFM for computing flow field in a complex geometry involving gas-water and gas-solid interfaces.(2)The flow field induced by a moving shock interacted with cylindrical water columns was numerically investigated using the level-set method combined with the revised method in this paper.Schlieren images and pressure time(p-t)histories at specified points are shown to describe shock evolution and mitigation downstream.It indi-cates that complex shock structures are distinguished accurately by the method,and the shock transmission and reflection occur on gas-water interfaces of the neighbor-ing columns in a row and in a column respectively.(3)The nozzle contour is simplified as gas-solid interface,and the nozzle contour pro-file is expressed by splines for the ease of obtaining the normal vector.And the nozzle flow field is simulated numerically using the level-set method combined with the revised method.Pressure contours,density contours and velocity of the nozzle flow field is in agreement with inviscid solution by gas dynamics theory.(4)Combined with high order accuracy method,three cavitation models(cut-off model,modified Schmidt's model and isentropic one fluid model)are numerically cali-brated for typical examples.The results show that the isentropic one fluid model is highly resolving cavitating zones and flexible to a variety cases.Then,by using the isentropic one fluid model,a moving planar shock for different Mach number inter-acted with a cylindrical water column,involving with cavitation,were tested.Pres-sure contours were obtained for demonstrating wave structure and cavitation evo-lution.Due to large density and inertia,a moving shock reflects and diffracts over water-air interface which is almost identical to air-solid interfaces.The transmitted water shock transmits on the air-water interface and induces rarefaction waves.Lo-cal pressure of water decreases simultaneously and appears cavitation.Cavitating zone expands with spreading of rarefaction waves.The larger shock Mach number,the stronger rarefaction waves and wider cavitating water area.Finally,cavitation disappears due to the recovering of local pressure in water.In the second part,we discuss the issue of conservation of the total mass for fi-nite difference WENO schemes solving hyperbolic conservation laws on a Cartesian mesh using the inverse Lax-Wendroff boundary treatments in arbitrary physical do-mains whose boundaries do not coincide with grid lines.The numerical fluxes near the boundary are suitably modified so that strict conservation of the total mass is achieved and the high order accuracy and non-oscillatory performance are not compromised.The key point is a suitable definition of the total mass,which is consistent with the high or-der accuracy finite difference framework over an arbitrary domain with a boundary not necessarily coinciding with grid lines.Extensive numerical examples are provided to demonstrate that our modified method is strictly conservative,and is high order accu-rate and has as good performance as the original high order WENO schemes with the Lax-Wendroff boundary treatments,for both smooth problems and problems with dis-continuities,in both one-and two-dimensional problems involving both scalar equations and systems.