奇异边界法求解多连通域的瞬态热传导问题  被引量:2

Singular boundary method for transient heat conduction problems in multiply connected domain

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作  者:弓健[1,2] 傅卓佳[1,2] 陈文[1,2] 

机构地区:[1]河海大学力学与材料学院,南京211100 [2]河海大学水文水资源与水利工程科学国家重点实验室,南京210098

出  处:《应用力学学报》2016年第2期181-187,365,共7页Chinese Journal of Applied Mechanics

基  金:国家自然科学基金(11372097;11302069);高等学校学科创新引智计划("111"计划)(B12032)

摘  要:提出一种基于奇异边界法结合双重互易法的数值模型来求解瞬态热传导问题。奇异边界法属于配点型边界无网格方法,相对于网格方法,其具有无需划分网格,只需边界配点的优势。运用差分格式来处理热传导方程中的时间变量,将原热传导方程化为非齐次修正Helmholtz方程。修正Helmholtz方程的解由齐次解和特解两部分组成,齐次解通过奇异边界法求出,特解由双重互易法求出,源项由径向基函数近似。通过数值算例检验了本文数值模型的精度及有效性;算例结果表明,该数值模型计算精度较高,误差基本都在1%以内,具有很好的稳定性,能有效地应用于求解多连通域的瞬态热传导问题。A numerical model based on singular boundary method and dual reciprocity method for solving transient heat conduction problems is presented. Singular boundary method is a point allocation boundary-type meshless method. The advantage of the method is that it just requires boundary collocation instead of dividing the mesh. The transient heat conduction equation can be converted into a series of nonhomogeneous modified Helmholtz equation by implementing finite difference scheme to deal with the time derivative term. The solution of the nonhomogeneous modified Helmholtz equation is divided into two parts, the homogeneous solution and the particular solution. The singular boundary method is used to approximate the homogeneous solution, and the dual reciprocity method with radial basis functions is used to obtain the particular solution. The accuracy and efficiency of the present numerical model is assessed through several numerical examples. The numerical results are presented for illustrating high accuracy and excellent stability, and the relative errors in calculation are all within 1%. The numerical model can solve transient heat conduction problems in multiply connected domain.

关 键 词:瞬态热传导 修正Helmholtz方程 奇异边界法 双重互易法 多连通域 

分 类 号:O241.82[理学—计算数学]

 

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