Dynamical behaviour of miscibles fluids in porous media (Q2289547)

Summary: In this paper, we are interested in studying the dynamics of miscible fluids in porous media. The model describing this issue is a system of equations, coupling the standard Navier-Stokes equations with gravity \(g\) as external force and a convective diffusion equation for a dilute concentration in the carrier fluid. By assuming that the fluids are incompressible, we first derive a new system of equations, by taking into account additional terms, due to the concentration inhomogeneities and an interfacial tension between the fluids. Then, we propose a numerical approach to solve our system in order to illustrate the effectiveness of the dynamics during the fluid miscibility process. At this stage, we start by showing a stability result for our numerical scheme and then present numerical results.