A continuous one-domain framework for fluid flow in superposed clear and porous media

Abstract

Based on generalized porous flow model, we present a one-domain framework for the simulation of incompressible flow in superposed clear and porous media. The continuous change in the characteristics of the porous medium is naturally taken into account by the model. In presence of any strong discontinuities in the domain, the sudden changes are approximated as a continuous but rapid variations over a thin layer across the regions of contrast. The governing equations are solved by a consistent second-order projection scheme on finite volume octree cells. The numerical scheme evaluates advection as well as porous drag terms at fractional time step and employs Godunov type procedure to obtain fractional step velocity at face center. The consistent property of the scheme ensures a discrete balance between pressure gradient and porous drags and, thereby, recovers Darcy-Forchheimer law exactly. The implication of inconsistent discretization of porous drags and pressure gradient is also highlighted. Benchmark problems with flow parallel and perpendicular to the homogeneous porous layer are considered to test the accuracy of the proposed numerical model especially with regard to the artificial transition region. Although the incorporation of the transition layer introduces error into the system, it reduces non-linearity in the field variables and, therefore, decreases the demand of higher grid density near the interface in one-domain approach. Furthermore, we simulate a series of physical problems with varying complexity in flow and characteristics of porous medium. The simulation results illustrate the ability of our solver to handle flows with viscous as well as inertial effects around a planar or circular interface geometry without loss of stability.