Numerical analysis of coupled flows in porous and fluid domains by the Darcy-Brinkman equations

A numerical method to achieve the simultaneous computation of the seepage flows in porous media and the Navier-Stokes flows in the domain occupied purely by a fluid is presented in this paper. The method uses the Darcy-Brinkman equations with the continuous modelling of the interfacial flow velocity, and applies the finite volume method to the spatial discretization and the fractional step method to the numerical simulation of the incompressible fluid. The coupling of the two different flows is realized by the relevant interpolation of the pressure and the flow velocity onto the interface at which permeability and porosity are discontinuous. The interpolation schemes provide simple solutions to overcome the computational instability caused by the discontinuous change in permeability and to avoid having to resolve the considerably thin transition zone near the interface. Numerical analyses of the one-dimensional uniform flow, the lid-driven cavity flow, and the pipe-flow in a porous medium have been carried out. The results have shown that the proposed schemes enable a stable computation and fulfill the accurate and physically realistic numerical solutions.