中文摘要：

无网格法是一种不需要生成网格就可模拟复杂形状流场计算的流体力学问题求解算法.为了提高基于Galerkin弱积分形式的无网格方法求解三维稳态对流扩散问题的计算效率,提出了在空间离散上采用基于凸多面体节点影响域的无网格形函数,并通过选取适当节点影响半径因子避免节点搜索问题,同时减少系统刚度矩阵带宽.计算中当节点影响因子为1.01时,无网格方法的形函数近似具有插值特性且本质边界条件的施加与有限元一样简单.三维立方体区域的稳态对流扩散数值算例表明：在保证计算精度的同时,采用凸多面体节点影响域的无网格方法比传统无网格方法最高可节省计算时间42%.因此从计算效率和精度考虑,在运用无网格方法求解三维问题时建议采用凸多面体节点影响域的无网格方法.

英文摘要：

The meshless method is a numerical algorithm for the simulation of flowfields in complicated shapes and solves fluid mechanics problems without grids.In order to improve the computation efficiency of meshless methods based on the Galekrin weak integration form for solving 3D steady convection-diffusion problems,a meshless shape function was proposed based on convex-polyhedral nodal influence domain in the discrete space.Then with a properly selected factor of nodal influence radius,the nodesearching process was avoided and the bandwidth of the stiffness matrix for the system was reduced.With a factor of nodal influence radius at 1.01 during the calculation,the shape function of the meshless method almost possesses interpolation properties and the imposition of essential boundary conditions is simplified as that for the FEM.The numerical results of 2 exemplary steady convection-diffusion problems for 3D cubic regions showthat： compared with the traditional meshless methods,the present meshless method based on convex-polyhedral nodal influence domain enables the computing time to be reduced by up to42% without impairing the calculation accuracy.Finally,in the cases that both the computation efficiency and the accuracy are highly demanded,this meshless method based on convex-polyhedral nodal influence domain is suggested for the solution of 3D steady convection-diffusion problems.