FINITE-ELEMENT FORMULATIONS FOR LARGE-SCALE, COUPLED-FLOWS IN ADJACENT POROUS AND OPEN FLUID DOMAINS

Two approaches which employ the finite element method to solve for lar ge-scale, coupled, incompressible flows through adjacent porous and op en domains are developed and evaluated in a model for the spontaneous ignition of coal stockpiles. Both formulations employ the Navier-Stoke s equations do describe flow in the open region; two different descrip tions, Darcy's law and the Brinkman equation, are employed to model fl ows within the porous region. The formulation which uses Darcy's law e mploys the Beavers-Joseph slip condition and a novel implementation of the interfacial conditions. The other approach invokes the Brinkman e quation: this considerably simplifies the implementation of matching c onditions at the interface between the porous and open fluid domains, but also results in velocity boundary layers in' the porous region adj acent to this interface which can be difficult to resolve numerically. A direct comparison of model results shows that the Darcy-slip formul ation produces solutions which are more accurate and more economical t o compute than those obtained using the Brinkman formulation.