Nonlinear heat diffusion simulation using Volterra series expansion

作者：Battaglia Jean Luc^*; Maachou Asma; Malti Rachid; Melchior Pierre

来源：International Journal of Thermal Sciences, 2013, 71: 80-87.

DOI：10.1016/j.ijthermalsci.2013.03.016

• Nonlinear heat diffusion
• Volterra series

A method for solving a nonlinear heat diffusion problem based on the use of the Volterra series is presented. Application in a practical configuration shows that the method comes to solve a linear problem at time t with a source term that depends on solutions calculated at previous instants. Unknowns of this linear problem are the generalized transfer functions H-k(P-1, ... p(k)), k = 1,2, ... , that are the kth order Laplace transforms L-(k) of the Volterra kernels h(k)(t). The method allows splitting naturally the solution as a linear contribution and a nonlinear one. Interest of such a method stands on the fact that a very small number of kernels is required to simulate accurately the nonlinear contribution (in practice 1 or 2). Furthermore, it is demonstrated that the Volterra method can be used efficiently to find the expression of a single simplified kernel that simulates well the entire nonlinear contribution.

• 出版日期2013-9