## 1 Introduction  
As one of the most potential energy conversion devices, the solid oxide fuel cell (SOFC) has attracted attention due to its advantages of low pollution and noise and high energy conversion efficiency [1; 2]. It can be practically applied in many fields, such as mobile power, aerospace, submarines, and so on; and has a broad application prospect [3; 4]. In the past decades, many novel materials [5; 6; 7; 8; 9] and fuel cell unit types [10; 11] have been proposed and developed due to the contributions of a large number of scientists and funding support. Generally, the current art of the fuel cell unit manufacture technology and performance can well satisfy the commercialization requirements [12; 13; 14]. However, when the SOFC units are constructed into a stack, the average performance of the units is greatly decreased. Thus, achieving the high performance and durability of the stack design is still one of the key factors for commercializing SOFC technology on a stack level. In the past decades, many different structure designs of SOFC have been proposed and the 3D numerical approach was proven to be the proper approach to study the working details within the stack and achieve optimized geometric parameters [15; 16; 17]. [PERSON] et al. [16] described the development and application of a new computational fluid dynamics model that allows large SOFC stacks to be studied within a practical calculation time. This model was used to demonstrate that the flow distribution of each cell in the 100-cell stack significantly affected the temperature distribution and overall electrochemical performance. The 3D large-scale multiphysics models were developed to find out the effect of the key structure parameters on the air flow distribution features within the planar SOFC stacks [18]. [PERSON] et al. [19] developed a large-scale 3D multiphysics model to figure out the multiphysics field distribution features within those fuel cell stacks with manifolds penetrating through the plane zone and open outlet features. [PERSON] et al. [20] have discussed the temperature distribution quality between two proton exchange membrane fuel cell (PEMFC) stacks with conventional rib and interdigitated rib cases, respectively. It was found that replacing the traditional straight ribs with interdigitated ribs would increase the local maximum temperature value inside the PEMFC. [PERSON] et al. [21] studied the properties of the cathode and interdigitated ribs in a typical PEMFC stack and found that using the interdigitated ribs could enhance the migration of oxygen within the porous cathode. The interdigitated design promotes forced diffusion of the reactant gas in the porous medium. Studies have shown that the water management effect of this design was much better than other designs of PEMFC stacks because it can improve the vapor transmission within the porous cathode [20; 22]. Generally, the SOFC stack is considered to have characteristics that are distinct from the PEMFC stack. Firstly, within the SOFC stack, the vapor is produced on the anode side instead of on the cathode side of the PEMFC stack. Secondly, high flow resistance within the fuel flow path of the SOFC stack is recommended because of the consideration of high fuel utilization and low molecular mass. Conversely, low flow resistance within the air flow path of the SOFC stack is recommended to reduce the additional pump requirement because air flow is the main heat carrier within the SOFC stack and its large molecular mass and velocity will lead to a high pressure drop. Thus, a SOFC stack with an interdigitated design for the fuel flow path and conventional paralleled line-type rib channels for the air flow path may be expected to have good performance. In this paper, a steady 3D numerical model for a one-cell SOFC stack with the above design structure is developed, which couples the momentum, species, energy, and quasi-electrochemical control equations.