Analysis and computation of fluid dynamics in a coupled free air porous domain

Abstract

We present analysis and computations of a 2D steady-state fluid dynamics in a coupled free air and porous domain. The 2D model is a simplification of the Hydrogen Fuel Cell (HFC) fluid dynamics for the case of one gas component and constant temperature. The problem involves the Stokes equation and the mass conservation equation in the cathode channel and the Darcy equation with the mass conservation equation in the porous gas diffusive layer (GDL). On the interface are imposed the Saffman's condition, continuity of the pressure and the normal velocity. Our main concern here is to find and implement an efficient computational method for solving the problem with a real data and a coupled domain with large aspect ratio. For this purpose we implement the finite element method with the classical MINI finite element space for the velocity in the channel and the P1 finite element space for the pressure in the channel and GDL. The resulting linear system is solved by using the iterative Gauss-Seidel overlapping block method and alternatively with the direct Gaussian Elimination method. Existence and uniqueness of the weak solution is proved only for the problem with the reduced Saffman's condition on the interface.