Simulating flow through porous media with explicit considerations of complex microstructures is very challenging using conventional sharp-interface methods because of the difficulties in generating meshes conformal to complex geometries. In this work, a diffuse interface embedded boundary method known as the Smoothed Boundary Method (SBM) is utilized to facilitate simulations of fluid dynamics involving complex geometries. In diffuse-interface methods, the geometry is described by a domain parameter. The SBM allows the straightforward reformulation of the time-dependent Navier–Stokes equations in terms of this domain parameter, using only differentiation identities. Thus, enforcing the appropriate boundary conditions at the irregular embedded boundary is greatly simplified. Adaptive mesh refinement is used to increase the accuracy of the diffuse interface method by allowing a thinner interfacial thickness to be used in the domain parameter. The SBM-formulated Navier–Stokes equations are solved with the Finite Difference Method on refined mesh systems. Sharp-interface Finite Element Method simulations using the commercial software COMSOL on body-conforming meshes are also provided for comparison. Favorable agreement between the two methods is observed. Since it is no longer necessary for the mesh to conform to the complex geometry, the grid system for the SBM simulations can be generated rapidly and without additional manual interventions, making the entire simulation process more expedient.

由于难以生成符合复杂几何形状的网格，因此使用传统的锐界面方法模拟通过明确考虑复杂微观结构的多孔介质的流动是非常具有挑战性的。在这项工作中，使用称为平滑边界方法 (SBM) 的扩散界面嵌入边界方法来促进涉及复杂几何形状的流体动力学的模拟。在漫反射界面方法中，几何由域参数描述。SBM 允许仅使用微分恒等式根据该域参数直接重新制定时间相关的 Navier-Stokes 方程。因此，在不规则嵌入边界处强制执行适当的边界条件被大大简化。自适应网格细化用于通过允许在域参数中使用更薄的界面厚度来提高扩散界面方法的精度。SBM 公式化的 Navier-Stokes 方程在细化网格系统上使用有限差分法求解。还提供了使用商业软件 COMSOL 在贴体网格上进行的锐利界面有限元方法模拟，以进行比较。观察到两种方法之间的良好一致性。由于网格不再需要符合复杂的几何形状， SBM 模拟的网格系统可以快速生成，无需额外的人工干预，使整个模拟过程更加方便。