New Computational Method Improves Simulation of Dense Particle Flows in Viscous Fluids
Researchers have developed a preconditioning strategy using the method of fundamental solutions to improve computational efficiency in simulating large collections of nearly-touching rigid particles in 2D Stokes flows. The approach addresses convergence problems that arise when particle gaps shrink and reduces the number of unknowns needed for accurate simulation. This advancement enables faster, more accurate modeling of densely packed particle suspensions, which has applications in understanding complex fluid dynamics.
A new computational method addresses two major challenges in simulating viscous hydrodynamics of dense rigid particle collections: poor iterative convergence as particles approach each other and the large computational burden of discretizing lubrication-driven flows. The researchers introduce a two-body preconditioning strategy implemented with the method of fundamental solutions, where close particle pairs are represented using a basis precomputed from local fine-grid boundary value problems. During iterative solving, the local fine-grid correction refines the coarse representation of all particles, and can be further compressed so that only the particle pair itself is directly affected by fine-grid sources while other particles use equivalent coarse sources. Numerical experiments demonstrate the method's effectiveness: the mobility problem for a random close packing of 10,000 monodisperse disks with area fraction 0.65 and minimum separation 10⁻³ converges in just 47 GMRES iterations with five-digit accuracy using only 72 vector unknowns per body.
What's missing
The study does not discuss computational time comparisons with existing methods, practical applications beyond the theoretical framework, or limitations of the approach for three-dimensional flows or non-Newtonian fluids.
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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