Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials

In this paper, we study heat and moisture transport through porous textile materials with phase change, described by a degenerate, nonlinear and strongly coupled parabolic system. An uncoupled finite difference method with semi-implicit Euler scheme in time direction is proposed for the system. We prove the existence and uniqueness of the solution of the finite difference system. The optimal error estimates in both discrete L ² and H ¹ norms are obtained under the condition that the mesh sizes τ and h are smaller than a positive constant, which depends solely upon physical parameters involved. Numerical results are presented to confirm our theoretical analysis and compared with experimental data.