基于四边形积分子域的一致性高阶无网格法

Consistent high order meshfree method based on quadrilateral integration sub-domains

近来提出的一致性高阶无网格法通过发展导数修正技术大幅度减少了所需积分点数目,并能够精确地通过分片试验,从而显著改善无网格计算的效率、精度和收敛性。然而,由于导数修正方程数目须与积分点数目相匹配,该方法仅限于使用三角形积分子域。在保留原有导数修正方程的基础上,提出了修正导数的共面条件,并据此建立补充方程,使得方程总数可匹配于所需的积分点数目,从而将一致性高阶无网格法方便地拓展到使用四边形积分子域。数值结果表明,本文方法精确地通过了分片试验,并展现出极好的计算精度、效率和收敛性。

The consistent high order meshfree method developed in recent years dramatically reduces the number of quadrature points and accurately passes the patch tests by developing derivative correction techniques.Consequently,it remarkably improves the computational efficiency,accuracy and convergence of meshfree computations. However,only triangular integration sub-domains can be employed in this method due to the restriction that the number of equations for derivative correction must be equal to the number of quadrature points. In this work,all the original equations for derivative correction are retained. In addition,a coplanar condition for the corrected nodal derivatives is proposed and is used to establish complementary equations. In such a way,quadrilateral integration sub-domains can be conveniently used in the consistent high order meshfree method since the total number of equations for derivative correction can be equal to the required number of quadrature points. Numerical results show that,the proposed method exactly passes patch tests and exhibits excellent accuracy,efficiency and convergence.