New Computational Method Improves Simulation of Dense Particle Flows in Viscous Fluids
Researchers have introduced a two-body preconditioning strategy using the method of fundamental solutions to efficiently simulate large, densely packed collections of rigid particles in 2D viscous (Stokes) flows. The method addresses two longstanding computational challenges: slow iterative solver convergence when particles nearly touch, and the large number of unknowns required to resolve lubrication-driven flows in tight gaps. The work could significantly reduce computational cost for simulating dense suspensions relevant to materials science, biology, and engineering.
A preprint submitted to arXiv by Anna Broms and collaborators presents a numerical method designed to overcome key bottlenecks in simulating the hydrodynamics of large, dense collections of rigid disks in two-dimensional Stokes flow. The core innovation is a two-body preconditioning strategy: for each nearly-touching particle pair, the difficult near-contact interaction is represented using a basis precomputed on a fine local grid, while all other particles are handled on a coarser representation. A compression step further reduces the influence of each close pair to an equivalent set of coarse sources, limiting the computational footprint. The method is implemented within the method of fundamental solutions (MFS) framework and accelerates convergence of the GMRES iterative solver. In benchmark tests, the mobility problem for a random close packing of 10,000 monodisperse disks at area fraction 0.65 and minimum separation of 10⁻³ was solved in just 47 GMRES iterations, achieving five digits of accuracy with only 72 vector unknowns per particle. The approach is general and could in principle be extended to other boundary integral or fundamental-solution methods for dense suspension problems in higher dimensions.
What's missing
As a preprint, this work has not yet undergone formal peer review. The study is limited to two-dimensional geometries; the authors do not demonstrate extension to 3D. The method's performance for non-circular particle shapes is not characterized. The practical impact on real-world suspension modeling applications remains to be validated by independent groups.
What different sources said
- arXiv physicsCenter
Preconditioning for near-contacts in large 2D Stokes flows: a locally compressed method of fundamental solutions
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