On the Forchheimer-extended Darcy-Brinkman flow through a thin fracture

In 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.