基于函数梯度无网格自适应方法研究

The Research of the Adaptive Method about Adjusting the Node Density Based on the Meshless Method

以计算一维泊松方程为例,通过研究节点分布对无网格法数值模拟的影响,提出了一种基于函数梯度大小调整节点密度的自适应方法.首先利用无网格法求出函数的近似梯度函数,然后分析该函数的梯度值,在梯度较大的位置加密计算节点,以提高计算精度,减少数值模拟的误差.利用该方法计算二维圆柱绕流N-S方程,模拟计算的结果基本符合圆柱绕流现象,表明了基于函数梯度进行节点加密的方法达到了很好的效果.

This paper is based on calculating the Poisson equation as an example,through the study of node distribution effect on numerical simulation in the flow field by using the meshless method,presents an adaptive method about adjusting the node density based on the function gradient size.It is using meshless method to calculate the approximate gradient functions,and analyze the gradient value of the function.Using the multi-distribution of some nodes in the location of function gradient higher,to improve the calculation accuracy and reduce the error of the numerical simulation.By using this method to calculate the N-S equation of the flow around a circular cylinder,the simulation results are basically in accord with the flow around the cylinder.It is indicated that the method of node encryption based on functional gradient has achieved good results.