Numerical Solution of Temperature-Dependent Thermal Conductivity Problems Using a Meshless Method
Numerical Solution of Temperature-Dependent Thermal Conductivity Problems Using a Meshless Method
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DOI：
10.1080/10407780500507111
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发表时间：
2006-03
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影响因子：
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通讯作者：
Akhilendra Singh;I. Singh;R. Prakash
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文献类型：
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作者：
Akhilendra Singh;I. Singh;R. Prakash
本文将无网格无单元伽辽金法推广到求解导热系数随温度变化的非线性热传导问题。假设材料的导热系数随温度线性变化。采用拟线性化方法避免非线性解的迭代，时间积分采用向后差分法。本质边界条件采用拉格朗日乘子法。无网格配方提出了一维和二维非线性热传导问题。MATLAB代码已被开发，以获得EFG的结果。通过EFG方法得到的结果进行了比较与有限元和解析方法得到的结果。
In this article, the meshless element-free Galerkin (EFG) method is extended to obtain numerical solution of nonlinear heat conduction problems with temperature-dependent thermal conductivity. The thermal conductivity of the material is assumed to vary linearly with temperature. A quasi-linearization scheme is adopted to avoid the iteration for nonlinear solution, and time integration is performed by the backward difference method. The essential boundary conditions are enforced by Lagrange multiplier technique. Meshless formulations are presented for one- and two-dimensional nonlinear heat conduction problems. MATLAB codes have been developed to obtain the EFG results. The results obtained by the EFG method are compared with those obtained by finite-element and analytical methods.