A preprint reports different simulated settling behavior for cubes and spheres in modeled suspensions, along with different local arrangements of the particles. Velocity-fluctuation correlations extended across the simulated system at all studied packing fractions and were stronger for cubes than for spheres at the same packing fraction. The document identifies itself as arXiv:2608.26030v1, dated 26 August 2026.
How the framework splits the work
The paper develops an OpenLB-LAMMPS fluid-structure interaction framework for arbitrary rigid bodies and applies it to hindered settling, the collective settling of particles in a fluid. The fluid calculation uses homogenized lattice Boltzmann dynamics based on Brinkman-Navier-Stokes equations, with time-dependent porosity, BGK collision and volume penalization.
LAMMPS handles contacts through discrete-element modeling with a multi-sphere clump representation, while particle geometry is resolved on the fluid grid by voxelization, or mapping the geometry onto that grid. Hydrodynamic loads are passed to the particle solver as external forces and torques, and the contact model uses Hertzian contacts with tangential friction.
The initial validation set comprised single-sphere settling, a sphere-wall collision and drag on a periodic array of spheres.
The benchmarks were mixed
Single-sphere settling showed good agreement with experiments at two conditions, with approximate Reynolds numbers of 1.5 and 32.2. No error metric or uncertainty interval was reported for that comparison.
The cuboid comparison was less close to experiment: the numerical method underestimated the experimental settling velocity, while the empirical relation was lower than both the numerical and experimental values. The size of that discrepancy was not reported.
In the periodic-array test, the calculated drag converged toward the analytical value as relaxation time and spatial resolution were varied. In the sphere-wall test, sphere-wall lubrication was not captured when the gap became smaller than the lattice separation, and the particle radius was enlarged by 5 percent to match experiment.
In bulk runs, cubes and spheres differed
The reported terminal velocities were approximately 0.0457 m/s for a single cube and 0.048 m/s for a single sphere.
When many particles were simulated together, cube and sphere settling differed. At lower packing fractions - the share of space occupied by particles - the bulk numerical results diverged from the empirical formula. At higher packing fractions, the reported velocities were higher than results from prior simulations at comparable Reynolds numbers.
Local structure differed as well. A radial distribution function, a measure of how particles are spaced from one another, showed cubes forming first and second shells without face-parallel contact. Spheres increasingly formed contacts as packing fraction increased.
Velocity fluctuations remained correlated across the system at every studied packing fraction and were stronger for cubes than for spheres at the same packing fraction. At higher packing fraction, cube velocity autocorrelation showed an oscillating decay resembling an under-damped oscillator.
System size and correlation length
To examine system size, the simulations used 3,150, 10,648 and 103,823 cubes. Average settling velocity and local arrangement did not change with system size, while the length of the spatial velocity correlation scaled with system size.
The paper also reports average computational throughput, a measure of simulation update speed, in MLUPs: 24.30, 111.58 and 109.58 for the three runs.
Periodic-boundary effects may explain the system-spanning correlation, so its physical meaning remains unresolved within the tested setup.
What remains unsettled
Taken together, the reported comparisons show good agreement for single-sphere settling and convergence toward the analytical sphere-array drag value, alongside an underestimation of cuboid settling relative to experiment. Average settling and local arrangement were stable across the tested system sizes, but the physical interpretation of the system-wide velocity correlations remains open.
Paper data and sources
Original title: A Scalable OpenLB LAMMPS Framework for Fully Resolved Simulations of Hindered Settling of Arbitrary Non-Spherical Particles
Authors: Varghese Babu, Adrian Kummerländer, Mathias J. Krause et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text