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In this paper, a pore-scale network modeling method, based on the flowcontinuity residual in conjunction with a Newton-Raphson non-linear iterativesolving technique, is proposed and used to obtain the pressure and flow fieldsin a network of interconnected distensible ducts representing, for instance,blood vasculature or deformable porous media. A previously derived analyticalexpression correlating boundary pressures to volumetric flow rate in complianttubes for a pressure-area constitutive elastic relation has been used torepresent the underlying flow model. Comparison to a preceding equivalentmethod, the one-dimensional Navier-Stokes finite element, was made and theresults were analyzed. The advantages of the new method have been highlightedand practical computational issues, related mainly to the rate and speed ofconvergence, have been discussed.

Pore-Scale Modeling of Navier-Stokes Flow in Distensible Networks and Porous Media