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; setting a cutoff value for each of the boundary problems; solving each of the boundary value problems numerically to obtain a solution for the boundary value problems at each of the grid-points, wherein a given one of the grid-points is within one of the regions affected by the flow of the quantity when the solution for the boundary value problems at the given grid-point is greater than or equal to the cutoff value; 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 and thus whereby the boundary value problems are used to identify boundaries of the regions, and thereby the regions themselves in the domain, affected by the flow of the quantity.