Gks Methods Of Computational Fluid Dynamics Of Multi-media Research

Numerical simulation of multimaterial flows has been one of the important issues in CFD, and significant progress has been made in the construction of schemes of high-order accuracy and high-resolution in the last decades. For the (traditional) Godunov type finite volume method, an approximate Riemann solver is required, this can give difficulties when real materials with general equations of states are under study. In the recent years, the gas kinetic scheme (GKS) has attracted much attention in numerical simulation of fluid dynamics because it is based on the Boltzmann equation which provides more physical information, and is Riemann-solver free. In this thesis, we will analyze and improve the traditional GKS in both Eulerian and ALE framework, and then apply it to simulate multimaterial flows.The main results of this thesis in Eulerian framework read:(1) We carefully analyze the mechanism of inducing spurious oscillations in the vicinity of a contact discontinuity when the traditional GKS is used to solve the Euler equations, and point out that the oscillations come from the inconsistency between the numerical scheme and the differential equations. Then, we derive the necessary condi-tion which a numerical flux should be satisfied in order to be oscillation-free. Finally, according to this consistent condition, we modify the traditional GKS in case of ideal gases to construct a new oscillation-free GKS which also works well for multimaterial problems.(2) Based on the idea of flux splitting, we deduce GKS renewedly to avoid its direct dependence on the form of equations of state. Moreover, by analyzing the stability, positivity and dissipation of the GKS, we construct a robust oscillation-free GKS-Non-Oscillation Kinetic (NOK) scheme which can treat general equations of state.The main result of this thesis in ALE framework is the following:(1) Using a coordinate transformation, we apply the NOK scheme to solve the ALE equation. (2) Consequently, we construct an unstructured arbitrary grid based GKS-ALE method by employing a robust unstructured arbitrary grid based rezoning method-OBM method which can generate convex, smooth and unit grid.Finaly, we obtain a GKS-ALE method which can be used to solve multimaterial problems with general EOS, it can not only track material interfaces sharply, but also keep good quality of computational grid.This thesis consists of two parts:The first part is concerned with the study in Eulerian framework, while the second part in ALE framework.In a word, this thesis is concerned with modification and application of the GKS to multimaterial fluid dynamical problems in both Eulerian and ALE framework. Conse-quently, we propose a new oscillation-free GKS, i.e., the NOK scheme, for multimaterial problems with general EOS. Numerous numerical tests demonstrate the good perfor-mance of our new method for multimaterial problems.