Numerical methods to simulate moisture dynamics in fibrous sheet

*Correspondence: [email protected] Faculty of Life and Environmental Science, Shimane University, Nishikawatsu-cho 1060, Matsue, Shimane, 690-8504, Japan Abstract Comprehension of moisture dynamics in fibrous sheets is indispensable in a wide variety of industrial areas. This paper proposes a practical mathematical model, which is referred to as the 2-D extended porous medium equation (PME), to physically describe moisture dynamics in fibrous sheets under evaporative environment. A numerical method, which is referred to as the 2-D dual-finite volume method (DFVM), to approximate its solutions in a stable manner is also presented so that the moisture dynamics is reasonably simulated. The 2-D DFVM, which can optionally be equipped with isotone numerical fluxes, is examined with test cases to show its satisfactory accuracy and versatility. The parameters and coefficients involved in the mathematical model for a non-woven fibrous sheet are identified with laboratory experiments. Numerical simulation of moisture dynamics in the horizontally or vertically placed sheet is performed as a demonstrative application example of the present model and the numerical method.