用于降低网格穿越误差的对流粒子高斯积分插值法  

A convected particle Gauss-quadrature interpolation for the cell crossing error reduction

作　　者：彭雪峰 傅中志 吉恩跃 陈生水 钟启明 Xuefeng Peng;Zhongzhi Fu;Enyue Ji;Shengshui Chen;Qiming Zhong(Department of Geotechnical Engineering,Nanjing Hydraulic Research Institute,Nanjing 210024,China;Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-rock Dam of the Ministry of Water Resources,Nanjing 210029,China)

机构地区：[1]Department of Geotechnical Engineering,Nanjing Hydraulic Research Institute,Nanjing 210024,China [2]Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-rock Dam of the Ministry of Water Resources,Nanjing 210029,China

出　　处：《Acta Mechanica Sinica》2023年第6期108-124,共17页力学学报（英文版）

基　　金：supported by the National Key Research and Development Program of China(Grant No.2021YFC3090101);the Fundamental Research Funds for Central Commonweal Research Institutes(China)(Grant No.Y320008).

摘　　要：对流粒子域插值法(CPDI)是物质点法(MPM)的一种改进算法,能够抑制粒子跨越网格引起的数值噪声.然而,在大变形情况下,CPDI仍无法保证预期的收敛率.因此,本文提出了一种新方法,称为对流粒子高斯积分插值法(CPGI).通过高斯积分极大地提高了计算精度,并为扩展到三维计算提供了便捷路径.CPGI将粒子域视为多个独立的角点组成,利用高斯积分推导出粒子到网格节点的插值方程.通过三个数值基准算例:轴向振动、广义涡流和三维碰撞,证明了CPGI算法在粒子穿越网格的过程中有效地减少了数值噪声.此外,通过比较不同初始构型和派生物质点法,对CPGI的综合运算能力进行了评估.从结果来看,本算法在精度方面具有明显的优势,并能有效地降低计算成本.Convected particle domain interpolation(CPDI)is a developed extension technique of the material point method(MPM),which can effectively reduce cell crossing error.However,it is still possible that CPDI does not ensure the convergence rate expected in the case of large deformation.Thus,this paper presents a new method,named convected particle Gauss-quadrature interpolation(CPGI),enhancing CPDI formulation by gauss quadrature.The CPGI considers the particle domain as four independent corner points and derives the particle-to-node mapping equations using gauss quadrature.Through numerical examples of axial vibration,generalized vortex,and collision,this work demonstrates the CPGI algorithm’s effectiveness in reducing the cell crossing error over the time of traversing the grid.Furthermore,the CPGI is evaluated using other different algorithms and initial configurations.As a result of the results,the algorithm has significant advantages in terms of accuracy and can provide reasonable efficiency.

关 键 词：计算成本 物质点法 高斯积分 网格节点 CPG 三维计算 轴向振动 收敛率 

分 类 号：O212.1[理学—概率论与数理统计]