  The formulation of combinatorial differential forms, proposed by Forman for
analysis of topological properties of discrete complexes, is extended by
defining the operators required for analysis of physical processes dependent on
scalar variables. The resulting description is intrinsic, different from the
approach known as Discrete Exterior Calculus, because it does not assume the
existence of smooth vector fields and forms extrinsic to the discrete complex.
In addition, the proposed formulation provides a significant new modelling
capability: physical processes may be set to operate differently on cells with
different dimensions within a complex. An application of the new method to the
heat/diffusion equation is presented to demonstrate how it captures the effect
of changing properties of microstructural elements on the macroscopic behavior.
The proposed method is applicable to a range of physical problems, including
heat, mass and charge diffusion, and flow through porous media.
