Techniques for analyzing flow of a quantity in a given domain are provided. In one aspect, a method for modeling regions in a domain affected by a flow of a quantity is provided which includes the following steps. A physical representation of the domain is provided. A grid that contains a plurality of grid-points in the domain is created. Sources are identified in the domain. Given a vector field that defines a direction of flow of the quantity within the domain, a boundary value problem is defined for each of one or more of the sources identified in the domain. Each of the boundary value problems is solved numerically to obtain a solution for the boundary value problems at each of the grid-points. The boundary value problem solutions are post-processed to model the regions affected by the flow of the quantity on the physical representation of the domain.