Finite Volume Method For Heat And Moisture Transfer Of Textile Materials At Low Temperature And Its Application To Inverse Problem Of Parameter Design

In this paper,the finite volume method with first order convergence in time and space is proposed for a class of existing heat and moisture transfer models of textile materials.On this basis,the finite volume method with first order convergence in time and second order convergence in space is proposed,and to prove the existence,uniqueness and stability of the solution.The proposed algorithm is applied to the inverse problem of determining the thickness or porosity of multilayer textile materials.This article is mainly composed of the following parts:In the first chapter,the research background and significance of heat and moisture transfer process of textile materials,the research status at home and abroad,as well as the research content and research results of this article,are mainly introduced.In the second chapter,an existing heat and moisture transfer model for a class of singlelayer textile materials under low temperature is given.Firstly,a finite volume scheme for solving the model is constructed,and the existence and uniqueness of numerical solutions of the scheme are proved,and the stability and first-order convergence of the scheme are proved by using the Gronwall inequality.On this basis,a new finite volume scheme is developed to improve the numerical accuracy.Similarly,the existence,uniqueness,convergence and stability of the numerical solution of the scheme under initial perturbation are proved,and the numerical solution converges to the first order in time and second order in space.Finally,numerical experiments are carried out to verify the effectiveness and convergence of the single-layer textile material finite volume scheme.In the third chapter,combining with the boundary conditions between layers,the heat and moisture transfer model of multilayer textile materials under low temperature is given.Two schemes of heat and moisture transfer model for single-layer textile materials are extended to multi-layer textile materials.For two finite volume schemes of multilayer textile materials,the existence and uniqueness of numerical solutions are proved respectively,and the convergence and stability of the two schemes are proved again by using the Gronwall inequality.In the fourth chapter,based on the optimal thermal and moisture permeability performance of textile materials under low temperature conditions,the proposed finite-volume scheme is applied to the inverse problem of thickness determination and the inverse problem of porosity determination of multilayer textile materials.The finite volume scheme is combined with particle swarm optimization algorithm to obtain the optimal solution of the inverse problem.In the fifth chapter,the research content and innovation of this article is given,and the next research direction are pointed out.