- The paper introduces a finite volume method paired with Delaunay triangulation to upscale viscous flow in granular media.
- The approach accurately predicts pressure fields, forces on particles, and permeability with discrepancies within 20% compared to FEM simulations.
- The method offers significant computational savings, enabling efficient large-scale simulations for applications in soil mechanics and petroleum engineering.
Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings
The paper presents a methodological approach to upscaling incompressible viscous flow in large random polydispersed sphere packings, with a particular focus on the forces exerted by the fluid on the solid particles. The authors propose an innovative method that leverages regular Delaunay triangulation for local definitions of pore bodies and their connections, thereby advancing the modeling of viscous fluid dynamics at the pore level with a finite volume numerical scheme.
Methodology and Numerical Comparisons
The research utilizes pore networks derived from regular Delaunay triangulations, which effectively define pore throats and pore bodies in granular materials. The finite volume scheme allows for the upscaling of fluid equations within these defined geometries. By comparing their numerical models to finite element method (FEM) simulations of the Stokes equations within sphere assemblies ranging from 8 to 200 spheres, the authors demonstrate an exemplary alignment of results in terms of forces exerted on solid particles and effective permeability coefficients.
Key Numerical Findings
The study finds that the finite volume (FV) approach accurately predicts the pressure fields and flow distributions when compared to detailed FEM simulations. The permeability predictions from the FV model, when calculated using hydraulic radius definitions, show discrepancies generally within 20% of FEM results, which the authors consider satisfactory given the computational savings. Notably, the FV scheme demonstrates considerable computational efficiency, as indicated by the significant reduction in degrees of freedom and CPU time when compared to FEM.
Theoretical and Practical Implications
The implications of this research extend to both theoretical and practical realms. Theoretically, the study establishes a robust groundwork for modeling fluid-particle systems in granular media using pore network techniques derived from geometrically regularized Delaunay triangulations. Practically, the methods proposed can aid in efficient large-scale simulations of hydromechanical phenomena in fields such as soil mechanics, petroleum engineering, and materials science, where understanding the fluid-solid interactions at the granular scale is crucial.
Considerations and Future Directions
The study suggests that future research could involve the adjustment of conductance factors for different geometrical conditions and investigate more complex couplings involving particle movement. Furthermore, this approach could be extended to non-spherical particles approximated by assemblies of spheres with varying diameters, enhancing the applicability of the model to a broader range of granular materials.
In summary, the research represents a significant advancement in the modeling of viscous flows in granular systems and presents a potential pathway toward more comprehensive and computationally feasible upscaled models for large, complex particulate systems.