Maxwell-Cattaneo Regularization of Heat Equation

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.

• F. Ekoue
• A. Fouache d'Halloy
• D. Gigon
• G Plantamp
• E. Zajdman

• Maxwell-Cattaneo heat transfers equations
• fourierlaw
• heat conduction
• numerical solution.

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