Geometric Perturbation Theory and Travelling Waves profiles analysis in a Darcy–Forchheimer fluid model.

Abstract

The intention along the presented analysis is to develop existence, uniqueness and asymptotic analysis of solutions to a magnetohydrodynamic (MHD) flow saturating porous medium. The influence of a porous medium is provided by the Darcy–Forchheimer conditions. Firstly, the existence and uniqueness topics are developed making used of a weak formulation. Once solutions are shown to exist regularly, the problem is converted into the Travelling Waves (TW) domain to study the asymptotic behaviour supported by the Geometric Perturbation Theory (GPT). Based on this, analytical expressions are constructed to the velocity profile for the mentioned Darcy–Forchheimer flow. Afterwards, the approximated solutions based on the GPT approach are shown to be sufficiently accurate for a range of travelling waves speeds in the interval [2.5, 2.8].