Spurious oscillations may occur for nonmonotone discrete methods. Therefore, monotonicity is a desired property for control-volume methods. Control-volume MPFA methods are only conditionally monotone. Sufficient criteria for monotonicity of the MPFA O-method on quadrilateral grids in 2D for the pressure equation has previously been developed. Tests on rough quadrilateral grids show that the monotonicity conditions are often violated. In this work we present modification of rough quadrilateral grids on homogenous and on heterogeneous media obtaining grids where the MPFA O-method is monotone. The reconstruction is based on short moves of the grid nodes. The moves are defined by weighted gradients on functions based on the monotonicity criteria. The main steps of the reconstruction algorithm are described. Examples of rough quadrilateral grids and their modified grids are included in order to show the efficiency of the presented algorithm.


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