MPFA methods applied to irregular grids and faults

Recent contributions to discretising the mass balance equations for the fluid phases in porous media flow, have been presented by Aavatsmark et. al. The methods are termed multipoint flux approximation methods, and are derived from a control volume formulation of the governing equations. The methods are locally mass conservative, and allow for flexible geometry, heterogeneity and/or anisotropy. We will here emphasize the discretisation principles on irregular grids and on grids for which adjacent control volumes do not share corners. Such cases may occur for locally refined grids and faulted media.