This article presents an innovative approach to modeling particle bed growth through suspension dead-end filtration, a process of paramount importance in various industrial and environmental contexts. More precisely, it focuses on the numerical formulation of a continuous approach based on a Stokes–Darcy coupling. In a Level-Set/FEM frame, this model effectively captures the dynamic evolution of particle beds (cake), taking into account the interaction between suspended particles and porous media. Model validation is also a key focus of this paper. Numerical tests are carried out under various conditions, and their results are compared with analytical solutions and experimental data drawn from the literature. This permits corroboration of the predictive capabilities of the model, confirming the robustness and accuracy of the proposed approach. Firstly, Stokes–Darcy coupled flows are investigated in simplified cases such as rectangular geometries and coaxial cylinders. These scenarios serve as benchmarks to assess the model performance under simple and varied conditions. Additionally, the more challenging case of a three-dimensional anisotropic flow between two ellipsoids is addressed, where the evolution of the cake takes place in three dimensions. Through rigorous analysis and comparison with analytical solutions, the model is proved efficient in capturing the inherent complexities of such scenarios. Finally, richer two-dimensional Stokes–Darcy flows are considered, in the presence of both impermeable and permeable obstacles, representing a crucial step towards modeling real industrial processes. This last study highlights not only the formation of particle-free zones but also the practical relevance of this work.

中文翻译：

---

斯托克斯-达西悬浮过滤中颗粒床生长的 Level-Set/FEM 方法


本文提出了一种通过悬浮死端过滤来模拟颗粒床生长的创新方法，该过程在各种工业和环境环境中都至关重要。更准确地说，它侧重于基于斯托克斯-达西耦合的连续方法的数值公式。在 Level-Set/FEM 框架中，该模型有效地捕获了颗粒床（饼）的动态演化，同时考虑了悬浮颗粒与多孔介质之间的相互作用。模型验证也是本文的重点。在各种条件下进行数值试验，并将其结果与解析解和文献中得出的实验数据进行比较。这可以证实模型的预测能力，确认所提出方法的稳健性和准确性。首先，在矩形几何形状和同轴圆柱体等简化情况下研究斯托克斯-达西耦合流。这些场景作为评估模型在简单和变化的条件下性能的基准。此外，还解决了两个椭球体之间的三维各向异性流动的更具挑战性的情况，其中蛋糕的演化发生在三个维度上。通过严格的分析以及与解析解的比较，该模型被证明能够有效地捕捉此类场景的固有复杂性。最后，在存在不可渗透和可渗透障碍物的情况下，考虑了更丰富的二维斯托克斯-达西流，这代表了对真实工业过程进行建模的关键一步。最后一项研究不仅强调了无颗粒区域的形成，而且强调了这项工作的实际意义。