Finite element formulations for large‐scale, coupled flows in adjacent porous and open fluid domains

Abstract

AbstractTwo approaches which employ the finite element method to solve for large‐scale, coupled, incompressible flows through adjacent porous and open domains are developed and evaluated in a model for the spontaneous ignition of coal stockpiles. Both formulations employ the Navier‐Stokes equations do describe flow in the open region; two different descriptions, Darcy's law and the Brinkman equation, are employed to model flows within the porous region. The formulation which uses Darcy's law employs the Beavers‐Joseph slip condition and a novel implementation of the interfacial conditions. The other approach invokes the Brinkman equation: this considerably simplifies the implementation of matching conditions at the interface between the porous and open fluid domains, but also results in velocity boundary layers in the porous region adjacent to this interface which can be difficult to resolve numerically. A direct comparison of model results shows that the Darcy‐slip formulation produces solutions which are more accurate and more economical to compute than those obtained using the Brinkman formulation.