混合初边值问题解的渐近性质及其差分解

 本文讨论了当t→∞时拟线性方程组初边值解的一些渐近性质。在假设非定常问题的解唯一、定常问题的解存在时,对同一边界条件,证明了当t→∞时非定常方程组的解趋于定常问题的解,讨论了用差分方法求解这种问题时,边界点上一些量的精确算法;为了消除在物体尖角附近出现的局部非物理解,得到正确解,我们还给出了一个简单的耗散型物面边界格式;最后给出了一些尖角凹形体的算例。

ASYMPTOTICAL BEHAVIOURS IN SOLUTION OF MIXED INITIAL-BOUNDARY VALUE PROBLEMS OF QUASI- LINEAR EQUATIONS AND DIFFERENCE SOLUTIONS

Some asymptotical behaviours in solution of mixed initial-boundary value problems of quasi-linear equations as t→∞ are discussed in this paper. It is shown that the solution of the system of non-steady equations with steady boundary conditions tends to the solution of the steady system with the same boundary conditions as t→∞, provided that the solution of the steady problem exists and the solution of the non-steady problem is unique. The exact computational method for some quantities at the boundary points is also considered when a finite-difference method is applied to solving this kind of problems.In order to get rid of the local non-physical solution in the vicinity of a sharp edge on the body, and get correct solution of boundary value problems about concave bodies, a simple boundary scheme of dissipative type is given. some numerical examples of concave bodies with sharp corners are presented.