In some embodiments, a system, as well as a method and an article, may operate to generate a first matrix, based on equations that model a reservoir, that includes mass conservation and volume balance information for grid blocks in the reservoir; to generate a second matrix, based on the first matrix, that includes saturation information and pressure information of each grid block; to remove the saturation information from the second matrix to generate a third matrix that includes only pressure information; to solve the third matrix to generate a first pressure solution; to solve the second matrix based on the first pressure solution to generate a first saturation solution and a second pressure solution; and to use the first saturation solution and the second pressure solution to generate a solution of the first matrix. Additional apparatus, systems, and methods are disclosed.