Maxwell-Cattaneo Regularization of Heat Equation
Maxwell-Cattaneo Regularization of Heat Equation
复制标题
热方程的 Maxwell-Cattaneo 正则化
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
E. Zajdman
中科院分区：
文献类型：
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作者：
F. Ekoue;A. F. d’Halloy;D. Gigon;G. Plantamp;E. Zajdman
本文重点分析了用麦克斯韦-卡塔内奥传递定律正则化的经典传热方程。在MATLAB环境下进行了计算机仿真。首先对经典傅里叶方程进行了数值实验，然后考虑了麦克斯韦-卡塔尼奥定律。利用平衡扩散项对相应方程进行正则化，使离散方案具有稳定的时间和空间数值步长。讨论了模型方程中包含对流项的几种情况，并给出了结果。证明了在对流情况下，Maxwell-Cattaneo正则化必须满足正则化参数的极限条件才能给出物理上可接受的解。在所有有效的情况下，用傅里叶定律求解初始热方程都是一致收敛的，即使在非线性情况下也是如此。
— This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.