不定边界问题的边界元和有限元数学模型

MATHEMATICAL MODELS FOR PROBLEMS WITH MOVING BOUNDARIES

对于不可压缩有势流动,有两类典型的不定边界或可动边界问题,即定常型不定边界如常水位闸门出流、过水坝或过水闸、水堰绕流及射流等,非定常型的不定边界如装液容器内的流体晃动问题.它们的共同特点是自由面位置与形状事先是的,需在计算过程中调整网格作自由面拟合.且由于自由面条件呈强烈非线性,给不确定数值计算带来困难.本文综述了两类不定边界问题的有限元和边界元模式,简述了笔者的一些计算经验.

For incompressible flows, there are two kinds of moving boundary problems, i.e. the steady case, such as the over-gate flow with constant elevation, spillway, wiers and jet flows; the unsteady case, sueh as the liquid sloshing in a container. The principal difficulty of these problems lies in the undetermined free surfaces, where an iterative scheme has to be used together with the correction of the network in computation. In particular, the computational effort will be considerable because of the strong nonlirtearities of the free surface conditions. In this paper, the finite element and boundary element methods for two kinds of moving doundary problems are presented together with some computational experience of the authors.