A computer-implemented method for modeling behavior of at least one fluid in a reservoir, the method comprising: obtaining a plurality of measurements of a plurality of physical parameters at a plurality of locations within the reservoir, the plurality of physical parameters comprising at least pressure; discretizing a system of partial differential equations that model, based on the plurality of measurements, the plurality of physical parameters; iterating, for each of a plurality of time steps, and until convergence upon a solution to the system of partial differential equations, characterized in that: approximating a rough solution to the system of partial differential equations; applying a constrained pressure residual technique to extract a system of pressure linear equations from the rough solution to the system of partial differential equations; applying a pre-smoothing technique at a fine scale to determine an approximate solution to the system of pressure linear equations; applying multi-scale multi-level processing to improve the approximate solution to the system of pressure linear equations; applying a post-smoothing technique at a fine scale to further improve the approximate solution to the system of pressure linear equations; and solving the system of partial differential equations for remaining physical parameters based on the further improved approximate solution to the system of pressure linear equations; and outputting the solution to the system of partial differential equations. obtaining a plurality of measurements of a plurality of physical parameters at a plurality of locations within the reservoir, the plurality of physical parameters comprising at least pressure; discretizing a system of partial differential equations that model, based on the plurality of measurements, the plurality of physical parameters; iterating, for each of a plurality of time steps, and until convergence upon a solution to the system of partial differential equations, characterized in that: approximating a rough solution to the system of partial differential equations; applying a constrained pressure residual technique to extract a system of pressure linear equations from the rough solution to the system of partial differential equations; applying a pre-smoothing technique at a fine scale to determine an approximate solution to the system of pressure linear equations; applying multi-scale multi-level processing to improve the approximate solution to the system of pressure linear equations; applying a post-smoothing technique at a fine scale to further improve the approximate solution to the system of pressure linear equations; and solving the system of partial differential equations for remaining physical parameters based on the further improved approximate solution to the system of pressure linear equations; and approximating a rough solution to the system of partial differential equations; applying a constrained pressure residual technique to extract a system of pressure linear equations from the rough solution to the system of partial differential equations; applying a pre-smoothing technique at a fine scale to determine an approximate solution to the system of pressure linear equations; applying multi-scale multi-level processing to improve the approximate solution to the system of pressure linear equations; applying a post-smoothing technique at a fine scale to further improve the approximate solution to the system of pressure linear equations; and solving the system of partial differential equations for remaining physical parameters based on the further improved approximate solution to the system of pressure linear equations; and outputting the solution to the system of partial differential equations.