1. A method for modeling regions in a domain affected by a flow of a quantity, comprising the steps of providing a physical representation of the domain; creating a grid that contains a plurality of grid-points in the domain; identifying sources in the domain; given a vector field that defines a direction of flow of the quantity within the domain, defining a boundary value problem for each of one or more of the sources identified in the domain; solving each of the boundary value problems numerically to obtain a solution for the boundary value problems at each of the grid-points; and post-processing the boundary value problem solutions to model the regions affected by the flow of the quantity on the physical representation of the domain.