杂交边界点法求解带自由面的渗流问题

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。

Solution of seepage problem with free surface by hybrid boundary node method

The seepage problem with a free surface is solved by combining the hybrid boundary node method (HBNM) and iterative method. The HBNM is based on a hybrid displacement variational principle and moving least square(MLS) approximation. The domain variables are interpolated by fundamental solution, while the boundary variables are approximated by MLS. Therefore, the HBNM is a truly boundary-type meshless method. Only nodes on the boundary are required and any mesh is not required. At first, the initial position of free surface is assumed; then the solution is obtained by the iterative method. The numerical example indicates that this method has high precision, little computation work; and it is suitable for solving various seepage problems with free surfaces.