Numerical modelling of nonlinear and degenerate diffusion equations on connected graphs: application to moisture dynamics in non-woven fibrous strip networks

Abstract

A numerical model of a nonlinear and degenerate diffusion equation on connected graphs, arising in a diversity of industrial applications, is presented. This paper shows that concurrently using a staggered finite volume spatial discretization with an analytical solution-based flux evaluation method and an operator-splitting technique computes stable and physically-consistent numerical solutions to the equation. A demonstrative application example of the numerical model to moisture dynamics in a hypothetical non-woven fibrous strip network under an evaporative environment is presented in order to show its versatility. Mathematical issues to be addressed in a future for better comprehending the model are finally discussed.