Nowadays, fuel cells have become the dominant technology in energy transition and environmental protection, because of its zero pollution, high energy density, and stationary power [11]. Fuel cells consist of many components, a membrane, catalytic layer (CL), gas diffusion layer (GDL), flow channel, and bipolar plates. So, the performance and durability of the fuel cell are closely linked to the complexity of multiphase transport phenomena with porous media. The research showed that the difference between simulation with and without considering pore-scale is relatively significant, because of pore-scale effects, for instance, adsorption, diffusion, and slip behavior, etc.There are also multiple methods to evaluate fuel cell’s performance, like in-situation methods that test during the operation, or material characterization methods. Most of them can provide invaluable data on cell performance such as global performance of the cell, however, the pore-scale effects mentioned above and the operating behavior cannot be studied by these methods. This motivates the development of pore-scale numerical simulation by N-phases CFD simulation. According to the inaccuracy of simulation without the effects of pore-scale modeling in multiphase flows that can reduce the accuracy and quality of the performance’s prediction of the fuel cells, this thesis focuses on constructing the solid phase in N-phase flows to represent the porous media of the cells, it might seem to be an easy task by just adding the no-slip condition according to the shape of the solid. However, in the domain of N-phase flows, there is an additional phase field which is coupled with the velocity field. So, we also need to find the appropriate methods that can construct the solid phase without disrupting the phase field and velocity field. By combining a conservative second order phase field model of N-phase flows and utilizing one phase as the indicator of solid phase, several methods have been tested, including removing solid-phase-advection equation, and adding the body force term to induce zero-velocity area.The objectives of this thesis are to:

1. Implement and compare methods to represent the rigid solid structure within N-phase flows framework.

2. Evaluate each methods’ capability to preserve phase field dynamics and no-slip condition.

3. Validate the appropriate methods against benchmark case with known and reliable experimental and numerical results.

4. Demonstrate the applicability to fuel-cells porous geometries