Velocity dependent up-winding scheme for node control volume finite element method for fluid flow in porous media

We present a novel velocity based up-winding scheme for the node control volume finite element (NCVFE) method. The NCVFE method solves for the pressure at the vertices of elements and a control volume mesh is constructed around them; where the advection of fluids is modelled. Therefore, each element shares several control volumes, and traditionally the fluid saturations used in calculating the mobilities over each element − hence updating pressure − are arithmetically weighted. In this paper, we use the velocity vector to allocate the upstream direction of the fluid flow in each element and use the upstream fluid saturation in calculating the mobility needed for the pressure equation. We test his novel approach using triangle and tetrahedron elements, and we show that it produces more accurate fluid saturation profiles than the traditional approach. The method can easily be implemented in current NCVFE simulators.