Mathematical description of the fluid flow outside and inside a porous medium based on an interpenetrating model
Abstract
In many environmental, industrial and biological processes, flows occur in a saturated porous fluid medium. The transport of substances between surface water and groundwater is a very serious problem. A mathematical model of this problem is studied here. The basis of the mathematical model is based on the interpenetrating model of two-phase media. The proposed equations make it possible to study the flow of a liquid in and outside the porous region in a uniform manner. In this case, the Navier-Stokes equation is obtained in the liquid region. In the porous region, the equations are close to the Brinkman model. In connection with the description of the flow from the standpoint of a single equation for the entire region, there is no need to set boundary conditions in the separation region (such as Beavers Joseph Saffman ). Cross-border conditions arise if the Darcy model is used for the porous region. In this case, the order of the systems of equations in each area is different. On the basis of the proposed model, one-dimensional and two-dimensional problems are considered. For the numerical solution of two-dimensional problems, the SIMPLE algorithm with appropriate modifications.