Control Volume Method to Model Fluid Flow on 2D Irregular Meshing

Modelling fluid flow in porous media requires the approximation of an elliptic partial differential operator such as div which appears when substituting Darcy’s law m mass conservation equation. When the medium is heterogeneous, the permeability tensor K is discontinuous and depends on the lithologic nature of the medium. In order to take this dependence well into account, the grid used to discretize the set of equations is such that cell boundaries are aligned with geological discontinuities.