王晓飞,李兴国,任红萍

• 1:太原科技大学应用科学学院

摘要(Abstract)：

由插值型复变量MLS法的理论,根据瞬态热传导问题的伽辽金积分弱形式,推导了二维瞬态热传导的第一类边值问题的插值型CVEFG方法。为了证明此方法的有效性,分别对两个瞬态热传导的第一类边值问题通过使用插值型CVEFG方法进行了数值求解,并与解析解进行了比较,二者吻合较好,证明了插值型CVEFG方法的有效性。

关键词(KeyWords)： 瞬态热传导问题;插值型复变量移动最小二乘法;插值型复变量无单元伽辽金方法

Abstract:

Keywords:

基金项目(Foundation): 国家青年科学基金(11802194);; 山西省青年科技研究基金(201801D221018)

作者(Author): 王晓飞,李兴国,任红萍

参考文献(References)：

• [1] BELYTSCHKO T,LU Y Y,GU L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,2010,37(2):229-256.
• [2] CHEN L,CHENG Y M.The complex variable reproducing kernel particle method for elasto-plasticity problems[J].Science China(Physics,Mechanics & Astronomy),2010,53(5):954-965.
• [3] 程荣军，程玉民.弹性力学的无单元Galerkin方法的误差估计[J].物理学报：2011,60(7):264-271.
• [4] WANG J F,CHENG Y M.A new complex variable meshless method for transient heat conduction problems[J].Chinese Physics B,2012,21(12):120-206.
• [5] PENG M,Li D,CHENG Y.The complex variable element-free Galerkin(CVEFG) method for elasto-plasticity problems[J].Engineering Structures,2011,33(1):127-135.
• [6] CHEN L,CHENG Y.The complex variable reproducing kernel particle method for two-dimensional elastodynamics[J].Chinese Physics B,2010,19(9):59-70.
• [7] CHENG R J,CHENG Y M.The meshless method for solving the inverse heat conduction problem with a source parameter[J].Acta Physica Sinica,2007,56(10):5569-5574.
• [8] SINGH A,SINGH I V,PRAKASH R.Meshless analysis of unsteady-state heat transfer in semi-infinite solid with temperature-dependent thermal conductivity[J].International Communications in Heat & Mass Transfer,2006,33(2):231-239.
• [9] REN H,CHENG J,HUANG A.The complex variable interpolating moving least-squares method[J].Applied Mathematics & Computation,2012,219(4):1724-1736.
• [10] REN H P,CHENG Y M,ZHANG W.An improved boundary element-free method(IBEFM) for two-dimensional potential problems[J].Chinese Physics B,2009,18(10):4065-4073.
• [11] ZHANG Z,WANG J F,CHENG Y M.The improved element-free Galerkin method for three-dimensional transient heat conduction problems[J].Science China,2013,56(8):1568-1580.
• [12] 张国达.瞬态热传导问题的插值型无单元伽辽金方法及误差分析[D].太原：太原科技大学，2017.