  Diluted pore networks or networks that are obtained directly from image
analysis are commonly used to evaluate flow through complex porous media. These
networks are often subjected to singular points and regions, that is, isolated
sub-networks that are not connecting the inlet and outlet. These regions impair
the invertibility of the modified Laplacian matrix and affect the accuracy and
robustness of pore network models. Searching and eliminating these
singularities is commonly done by preconditioning or searching algorithms like
breadth-first search or depth-first search. Here, we propose using singular
value decomposition (SVD) to simultaneously solve for single-phase flow and
locate isolated regions. We demonstrate the performance of the method for
networks obtained from images of a partially saturated medium, and for diluted
networks close to the percolation threshold.
