High Resolution Level-Set Methods For Moving Interfaces Of Multiple Material Fluids

Compressible multiphase flows have a growing interest in developing numerical algorithms and efficient implementation to complex flow phenomenon in CFD. In this paper, we focus on numerical methods for material interfaces and strong discontinuities in multimaterial flows. A series of numerical experiments are presented which demonstrate the ability of capturing interface and tracking discontinuities. The main contributions of this dissertation are summarized as follows:Firstly, An improved reinitialization algorithm is developed for implementation of level set methods. The new algorithm can keep level set function approximately equal to the signed distance function in the two sides of fluid interface and avoid the incorrect movement of the fluid interface during the time evolution of the level set equation.Secondly, by coupled conservative Euler equations of gas dynamics with level set function, nonconservative evolved equations for the material-dependent variablesγandπor mass fraction equations, unexpected physical oscillations near the material interfaces can be prevented. Moreover, the method guarantees the positivity of mass fraction. The high order accurate (M)WENO scheme is applied to solve coupled equations of gas dynamics based on decomposed waves. Using standard Roe averaging approach for nonlinear systems and the technology for decomposing waves, left and right going flux differences by high order (M)WENO interpolating polynomials. Then we add up flux differences of each wave and obtain uniform numerical scheme in computing domain. Moreover, A high order accurate NND and central numerical schemes are applied to simulate the interface of inviscid compressible multi-component flow with stiffened state equation.Thirdly, the robust boundary conditions of the interface are presented based on Riemann solutions which are able to provide more precise interface flow states. A simple and robust algorithm is provided for solving Riemann problem in multidimensional multimaterial flows along normal direction of the material interface. At each node of a narrow strip of the interface, Riemann problems are solved using iterative numerical method. Predicted isobaric values and ghost fluid...