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将杂交边界点法与迭代法相结合,求解有自由面的渗流问题。杂交边界点法基于杂交位移变分原理和移动最小二乘近似,利用基本解插值域内的场函数,而边界上的变量则用移动最小二乘近似,是一种纯边界类型的无网格方法。利用该方法只需在边界上布点而不需要划分任何网格的特性,先假定自由面的初始位置,再进行迭代求解。数值算例表明,该方法精度较高、计算量较小,适合于求解各种具有自由面的渗流问题。
The hybrid boundary point method and iterative method are combined to solve the seepage problem with free surface. The hybrid boundary point method is based on the hybrid displacement variational principle and the moving least square approximation, using the field functions in the basic solution interpolation domain, while the variables on the boundary are approximated by moving least squares, which is a meshless method of pure boundary type . By using this method, we only need to lay out the boundary without the need of dividing the grid. The initial position of the free surface is assumed first and then iteratively solved. Numerical examples show that this method is more accurate and less computationally expensive and is suitable for solving a variety of seepage problems with free surfaces.