## 1 Introduction
In parallel with experimental studies, computational modeling has emerged as a powerful tool for understanding GPF mechanisms, reducing experimental costs, and optimizing design parameters. [PERSON] et al. [20,21] developed GPF models based on pore, wall, and channel scales, incorporating experimental data to simulate particles with non-uniform size distributions. The models also accounted for non-uniform radial porosity distributions in porous medium, revealing that particle accumulation predominantly occurs in localized areas at the top of the filter [22,23]. This non-uniform distribution results in fewer particles penetrating the porous medium, thereby optimizing filtration efficiency and pressure drop [15]. [PERSON] et al. [24] further investigated the impact of inlet gas velocity on GPF performance, demonstrating that axial permeation velocity distribution correlates with the axial distribution of trapped particles. As velocity increases, both distributions become uneven, leading to reduced filtration efficiency [25,26]. To address this, [PERSON] et al. [27] introduced small solid pins into the inlet channels, improving axial flow uniformity and slightly enhancing filtration efficiency. Additionally, the distribution of washcoat on porous medium has been shown to influence permeation velocity and particle filtration, with studies by [PERSON] et al. [28] and [PERSON] et al. [29] highlighting the benefits of high and low coated zones at the front and rear of the filter. Despite these advancements, systematic studies on the combined effects of GPF patterns, coated zones, and pin configurations on axial permeation velocity uniformity and filtration efficiency remain limited. Numerous methods have been developed to simulate gas flow in the inlet and outlet channels of particulate filters and through the porous medium [30]. [PERSON] et al. [31] developed a classical one-dimensional flow model, integrating finite element and finite difference methods for spatial discretization, and simulated the deposition and oxidation of PM by solving the mass, momentum, and energy conservation equations. Based on this model, numerous additional approaches have subsequently been employed in constructing particle filtration models, such as the finite volume method for developing the gas flow model of the filter [24] and statistical theory for establishing the micro-heterogeneous porous media model [15] Flow optimization primarily focuses on gas hydrodynamics, specifically examining the impact of porous media on channel flow [24], and particulate fluid dynamics [32]. Additionally, the model structure was refined by incorporating a filter cake layer [33] and an ash layer [4], as well as redesigning the channel structure [34]. As research has progressed, this flow model has evolved from a one-dimensional to a three-dimensional framework. [PERSON] et al. [35] modified the structure of GPF and constructed a three-dimensional model to further optimize the enhancement of pressure drop and filtration efficiency. Moreover, a comparison between one-dimensional and three-dimensional models conducted by [PERSON] et al. [27] revealed that the three-dimensional model exhibits superior accuracy, particularly under high inlet flow velocities, and can accurately predict the local gas fluid dynamics. Although existing models effectively simulate gas flow dynamics, they remain inadequate for studying factors influencing axial permeation uniformity, particularly due to high computational complexity and limited simulation accuracy. To address these limitations, the particulate filter structure is optimized, and single-phase flow simulation is adopted to reduce computational load and enhance model tractability, enabling a more efficient analysis of key factors affecting axial permeation uniformity. Building on these developments, this study develops a three-dimensional single-channel GPF model by Fluent to simulate gas flow dynamics in porous medium.