Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media
Control volume methods are frequently used in porous media flow. This article gives an example on how one method, the Multipoint Flux Approximation method (MPFA), fails to satisfy the maximum principle for strong anisotropies or grid skewnesses, and develops conditions for when the monotonicity property holds for uniform parallelogram grids in homogeneous media. The conditions developed are applicable to any nine-point scheme in 2D or 27-point scheme in 3D, and is useful when the method produces a system matrix which is not an M-matrix.
monotonicity maximum principle control volume discretization