Numerical simulation of flow and transport at the pore scale

The study of flow and transport mechanisms at the pore level is fundamental in order to obtain a better understanding of flow and transport processes in porous media. The Navier-Stokes equations are considered as a very good model in simulating the Newtonian flow at the microscale. Due to its nonlinear nature, usually the Navier-Stokes equations are approximated by the Stokes equations for very small Reynolds numbers or solved by complex nonlinear approaches for large Reynolds numbers. An additional difficulty is the irregular geometry of the pores. In this paper, we present a linear direct scheme for the non-stationary Navier-Stokes problems. By applying this scheme, we are able to solve a linear system of equations at each time step, while keeping the nonlinearity in the whole. An almost optimal error estimate is obtained. Transport is dealt in a similar way. Numerical test cases are then applied to typical porous computational domains at pore level.