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.

中文翻译：

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数值模拟纤维片中水分动力学的方法

在许多工业领域中，必不可少的是要了解纤维片中的水分动力学。本文提出了一个实用的数学模型，称为二维扩展多孔介质方程（PME），以物理描述蒸发环境下纤维片材中的水分动力学。还提出了一种数值方法，称为二维双重有限体积法（DFVM），以一种稳定的方式近似其解，从而合理地模拟了水分动力学。可以选择配备等值通量的二维DFVM，并通过测试案例进行了检验，以显示其令人满意的准确性和多功能性。通过实验室实验确定了非织造纤维片的数学模型中涉及的参数和系数。