非线性问题的MPS无网格算法

Modified MPS Method for Nonlinear Dynamic Problems

给出了修正的MPS(MovingParticleSemi implicit)无网格方法 ,指出恰当选取权函数可避免使用虚节点来处理边界 ,从而解决复杂边界处虚节点难设定的问题 .以非线性Burgers方程为算例分析了其数值特性 ,结果表明 :以样条函数为权函数时不采用虚节点的结果与使用虚节点的结果一致 ;对一维问题 ,光滑权函数性能明显优于非光滑权函数 ;而对二维问题 ,近边界处加权域不对称性的影响则不很显著 .与精确解或由传统方法所得结果的对比分析表明该方案可行 .该方法物理概念清晰 。

A modified moving particle semi implicit (MPS) method was presented. Neighbor interaction models for differential operators are presented, without the use of ghost nodes to deal with boundary conditions. The performance of the proposed method was demonstrated by solving Burgers's equations. It was shown that the results using spline function as kernel without ghost nodes agree well with those with ghosts,and both results coincide with exact results or other existing solutions. It was also found that for 1D problems smooth weight functions perform better than non smooth ones, while for 2D problems the effect of weight function's asymmetry near boundaries is negligible. This method was demonstrated to be quite straightforward, simple and easy to code.