THE NONOSCILLATORY CHARACTERISTIC DIFFERENCE METHOD FOR THE NONLINEAR CONVECTION-DIFFUSION EQUATION OF TWO DIMENSIONS
二维非线性对流扩散方程的非振荡特征差分方法

The nonosillatory characteristic diffeence method for the nonlinear convectiondiffusion equation in 2D is discussed in the paper. We constructed quadratic UNO and ENO interpolations based on six mesh points in 2D. Combing them with characteristic difference method, we establish the high-resolution difference schemes for the nonlinear convection-dominated diffusion problem. Because theses schemes are nonlinear inherently, we use a new method to give the strict error analyses of these schemes, solving the difficulties resulted from the nonlinearity. The numerical computation is given in the paper for the model problem.