Dynamics of Convective Thermal Explosion in Porous Media

Author:

Allali Karam1,Joundy Youssef1ORCID,Taik Ahmed12,Volpert Vitaly345

Affiliation:

1. Laboratory of Mathematics and Applications, University Hassan II of Casablanca, FST Mohammedia, P.O. Box 146, 20650, Morocco

2. Complex Systems Engineering and Human Systems, Mohammed VI Polytechnic University, Benguerir, Morocco

3. Institut Camille Jordan, Université Claude Bernard Lyon1, UMR 5208, CNRS, 69622, Villeurbanne, Cedex, France

4. INRIA, Université de Lyon, Université Lyon1, Institut Camille Jordan, 43, Bd. du 11 Novembre 1918, 69622 Villeurbanne, Cedex, France

5. People’s Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Abstract

In this paper, we study complex dynamics of the interaction between natural convection and thermal explosion in porous media. This process is modeled with the nonlinear heat equation coupled with the nonstationary Darcy equation under the Boussinesq approximation for a fluid-saturated porous medium in a rectangular domain. Numerical simulations with the Radial Basis Functions Method (RBFM) reveal complex dynamics of solutions and transitions to chaos after a sequence of period doubling bifurcations. Several periodic windows alternate with chaotic regimes due to intermittence or crisis. After the last chaotic regime, a final periodic solution precedes transition to thermal explosion.

Funder

RUDN University Program 5-100

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

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