The Level Set Method Interface To Track The Use Of Hyperbolic Conservation Laws

For the numerical computation of one-dimensional hyperbolic conservation laws, various difference schemes were established. These schemes are becoming more and more perfect which have higher resolution and accuracy. ENO and WENO are two types of representatives of high resolution schemes now. However, when we use these schemes to compute the initial problem of hyperbolic conservation laws, there is still numerical dissipation near the interface, that is to say, the resolution is decreased near the interface.In 1988, Osher and Sethian puted forward Level Set method and gained success in many complicated interface-tracking problems. They difined and kept the moving interface as zero level of Level Set function. Level Set method can track the interface accurately.In this thesis, we couple high resolution shock capturing method and Level Set method to compute hyperbolic conservation laws. For scalar equation and system of equations, we build different ghost fields, translate one equation (system) into two equations (system). We still use high resolution shock capturing method to compute the two equations (system); Level Set equation is used to track the interface, and the result of original equation (system) is determined by the Level Set function. Thus, we eliminate the numerical dissipation which high resolution shock capturing method cannot avoid near the interface, and the resolution is enhanced. From the experiments in hyperbolic conservation laws, we can see that if we only use high resolution shock capturing method in scalar equation, there would have a transition near the interface; but when coupled with Level Set method, we can get a sharp interface, The interface is tracked exactly. And when we use Level Set method to track the contact discontinuity, the shock respectively in system of equation, we all have good results.