Affiliation:
1. Department of Mathematics, Faculty of Science University of Zagreb Zagreb Croatia
Abstract
AbstractIn this paper, we study the flow through a thin fracture filled with fluid‐saturated sparsely packed porous medium. The problem is described by the Forchheimer extended Darcy‐Brinkman model incorporating the quadratic drag term as a result of the inertial effects. Employing asymptotic analysis with respect to the fracture's thickness, we derive the higher‐order approximation for the velocity and pressure distribution explicitly acknowledging the Forchheimer (inertial) term. We provide numerical example as well and perform a rigorous error analysis to indicate the order of accuracy of the proposed approximate solution.
Funder
Hrvatska Zaklada za Znanost
Subject
Applied Mathematics,Computational Mechanics