论文部分内容阅读
用传统的有限元方法求解复杂边界的自由面渗流是很困难的,为此提出了基于适体坐标变换的有限差分法。该方法通过求解Poisson方程自动生成计算区域的曲线网格,并将其变换至规则统一的直角网格系统下进行有限差分离散和数值求解。这种数值网格生成技术可以精确而有效率地模拟复杂几何边界,算法成熟,通用性强,可以避免有限元法的网格在迭代过程中变化的问题,对不同的几何边界可以实现统一的数值求解算法,自动化程度高。计算实例表明,基于适体坐标变换的有限差分法计算结果的精度和有限元法相当,但计算效率上较有限元方法有很大的提高,并具有简单、灵活的优点。
It is very difficult to solve the free surface seepage flow of complex boundary by the traditional finite element method. Therefore, a finite difference method based on the transformation of the coordinate of the body is proposed. The method automatically generates the curve grid of the calculation area by solving the Poisson equation and transforms it into a regular uniform grid system for finite difference discretization and numerical solution. This numerical mesh generation technique can accurately and efficiently simulate complex geometric boundaries, the algorithm is mature and versatile, which can avoid the problem that the finite element method’s grid changes during the iteration process. The geometric boundaries can be unified Numerical solution algorithm, high degree of automation. The calculation example shows that the accuracy of the finite difference method based on the transformation of apodized coordinates is equivalent to that of the finite element method, but the computational efficiency is greatly improved compared with the finite element method, and has the advantages of simplicity and flexibility.