Finite element formulations for large-scale, coupled flows in adjacent porous and open fluid domains. (English) Zbl 0807.76039

Salinger, A. G.; Aris, R.; Derby, J. J.

Int. J. Numer. Methods Fluids 18, No. 12, 1185-1209 (1994).

Two approaches which employ the finite element method to solve 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. 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.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76S05	Flows in porous media; filtration; seepage
76D05	Navier-Stokes equations for incompressible viscous fluids
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

Beavers-Joseph slip condition; interfacial conditions; velocity boundary layers; spontaneous ignition of coal stockpiles; Darcy’s law; Brinkman equation

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