Finite point method of nonlinear convection diffusion equation

Abstract

Aiming at the nonlinear convection diffusion equation with the numerical oscillations, a numerical stability algorithm is constructed. The basic principle of the finite point algorithm is given and the computational scheme of the nonlinear convection diffusion equation is deduced. Then, the numerical simulation of the one-dimensional and two-dimensional nonlinear convection-dominated diffusion equation is carried out. The relationship between the calculation result and the support domain size, step size and time is discussed. The result shows that the algorithm has the characteristics of simplicity, stability and efficiency. Compared with the traditional finite element method and finite difference method, the new algorithm can attain a higher calculation accuracy. And, it proves that the method given in this paper is effective to solve the nonlinear flow diffusion equation and can eliminate the numerical oscillations.