Aiming at the heat conduction problems of materials in high temperatures,the boundary knot method was applied to simulate the 2D and 3 D transient heat conduction problems,corresponding software program was also written.The boundary knot method which is a sort of mesh-less methods,and homogeneous solution of radial basis function was used to fulfil the controlling program.By employing implicit Euler finite difference to discrete time derivatives,the non-homogeneous modified Helmholtz equation without time derivatives can be expressed by the sum of the particular solution and the homogeneous solution.The dual reciprocity method is employed to present the particular solution,and the boundary knot method is employed for the homogeneous solution,thereby simulating the original equation.Preliminary numerical experiments illustrate that,the boundary knot method has advantages such as high accuracy,simple mathematic theory and fast convergence,and can simulate 2D and 3D transient heat conduction problems well.This paper also introduced a Matlab toolbox which is easy to operate.The Matlab toolbox with a friendly graphical user interface is freely available as an open source software.%针对高温条件下材料热传导问题,采用边界节点法数值模拟二维和三维瞬态热传导问题并编写了相应的计算软件.边界节点法是无网格方法的一种,采用径向基函数的非奇异通解来满足控制方程.对于热传导方程,采用Implicit-Euler差分离散其时间项,将不含时间项的非齐次亥姆赫兹方程以特解与通解的和的形式给出.使用双重互易法在计算区域配点求出方程的特解,使用边界节点法在边界配点来求出方程的齐次解.使用结果表明:该方法计算精度高,数学简单,收敛快,能很好地数值模拟二维及三维瞬态热传导问题.基于上述的算法,使用Matlab语言开发了一个热传导问题的数值模拟工具箱,该工具箱具有简单易操作、代码开源、界面友好等特点.
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