Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 100
Routes to the chaos of the 5D model of a thermo-hydrodynamic system in a porous medium
Youssef Joundy, Abdelaziz Beljadid, Ahmed Taik, Hamza Rouah
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 09, 2022
March 03, 2095
April 15, 2095

Abstract: In this paper, we study the dynamics of a fluid in a porous medium subjected to a temperature gradient. The system is described by a heat equation coupled to the Navier-Stokes equations under the Boussinesq-Darcy approximation introduced by B. Saltzman. We use spectral analysis to reduce our problem to a system of five ordinary differential equations which we have solved using the fourth order Runge-Kutta method [1]. The numerical results show that from a critical value of the Rayleigh number, the system passes from stationary convection to chaos via a doubling of period or by a homoclinic ...