Numerical Solutions And Research Of The Local Phase Equilibrium Model Equations

Local Phase Equilibrium Model (LPEM) is not only used in the problem of soil pollution due to the oil pollutants, but also widely used in the handling of issues such as river pollution, air pollution, and nuclear waste pollution and so on. The pollution problem has attracted the general concern of hydro geological environment scholars both at home and abroad. It also has become the focus issue in the study of underground pollution controlling. In the study of science and technology, the numerical simulation of such issues always boils down to the Partial differential equations issues. The analytical method is generally limited to the relative simple and ideal circumstances, so the study of Local Phase Equilibrium Model (LPEM) seems to be of great theoretical and practical significance.There are so many numerical solution algorithms for the Partial differential equations, for example the Finite Difference Method, the Finite Element Method, the Finite Volume Method and so on. The Finite Difference Method is one of the most important numerical solution algorithms. It has been developed for more than ten years, and has acquired enormous success. Especially, in the recently twenty years, the harvest is without number. Von Neumann,Courant,Friedrichs,Lax,Wendroff and many other mathematics had done a lot of efforts on the study unremittingly.This paper presents the constitute process of the Local Phase Equilibrium Model, investigates the differential formats of the value solution algorithm to the Local Phase Equilibrium Model equations. For the Local Phase Equilibrium Model equations, at first, the differential equation is semi-discrete approximation. Then, the diffusion term is eliminated.,and difference schemes for the equation are structured. At last, we analyze theoretically the satiability and convergence of the difference schemes.