A stable finite volume method for extended porous medium equations and its application to identifying physical properties of a thin non-woven fibrous sheet

摘要

A finite volume method (FVM) for numerically solving 1-D extended porous medium equations is proposed. The numerical flux in the FVM is evaluated with the fitting technique, which uses analytical solutions to local two-point boundary value problems, and an isotonicity principle for computing spatially unconditionally stable numerical solutions. The FVM is applied to numerically identifying physical properties of a thin non-woven fibrous sheet based on a try and error approach. The FVM is finally applied to numerical simulation of moisture dynamics in the sheet under different external environments.