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劈开因子法是一种对扩散问题进行数学模拟的有效手段。该法中,对流和扩散独立进行计算。霍利—普列斯曼的两点四阶法,对于一维情况的对流计算,精度很高,但对于二维情况,这种算法过于复杂。小松-霍利-仲敷提出的六点法,格式简单,而且只要已知浓度即可求解。他们阐明,对于那些对边界条件要求不甚严格的计算域,六点法的效果很好。但是实际上,在绝大多数场合,边界条件却是确定扩散的主要因素。本文论述了当采用六点法时,怎样处理一维和二维的边界条件问题。并阐明,其计算精度并不因不均匀网格的布设以及不均匀流场而受到影响。将六点法用于计算河流交会处的水流和转弯处的扩散,没有额外的数值衰减和跳动。
Split-factor method is an effective means to simulate the diffusion problem. In the law, convection and proliferation are calculated independently. Holly-Priesman’s two-fourth-order method is highly accurate for one-dimensional convective calculations, but for two-dimensional cases this algorithm is too complicated. Komatsu - Holly - Zhong Fushu proposed six-point method, the format is simple, and as long as the known concentration can be solved. They clarified that the six-point method worked well for those computational domains that did not require strict boundary conditions. However, in most cases, the boundary conditions are the main factors that determine the spread. This article discusses how to deal with one-dimensional and two-dimensional boundary conditions when using the six-point method. And it is clarified that the calculation precision is not affected by the layout of uneven grid and the uneven flow field. The six-point method is used to calculate the water flow at the river intersection and the spread at the turn without additional numerical attenuation and jerkiness.