二维非线性对流扩散方程的非振荡特征差分方法

１．引言 近十几年来，双曲守恒律问题的高分辨率格式已取得很大发展，具有局部自适应选取节点的非振荡插值算法（如 ＵＮＯ［１］， ＥＮＯ［２］等）在这些格式的构造中起着重要的作用．特征差分法是求解对流扩散问题的一种较为有效方法，但在求解具有陡峭前线问题时，也会产生非物理振荡阻（见４）．本文将把特征差分法与非振荡插值算法相结合构造对流扩散问题的高分辨率差分格式． ［１］中的 ＵＮＯ及［２］中的 ＥＮＯ插值都是一维的，有关讨论二维 ＵＮＯ及ＥＮＯ插值的文章还不多见，本文将构造二维基于六节点的二次非振荡插值以及…

THE NONOSCILLATORY CHARACTERISTIC DIFFERENCE METHOD FOR THE NONLINEAR CONVECTION-DIFFUSION EQUATION OF TWO DIMENSIONS

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.