Computing hydrodynamic interactions in confined doubly periodic geometries in linear time

Area of Science:

• Fluid dynamics
• Computational physics
• Colloidal science

Background:

• Accurate simulation of hydrodynamic interactions is crucial for understanding particle suspensions.
• Existing methods often struggle with computational scaling for large numbers of particles.
• Confined geometries, like walls or channels, introduce complex boundary effects.

Purpose of the Study:

• To develop a computationally efficient, linearly scaling method for simulating hydrodynamic interactions.
• To investigate particle behavior in doubly periodic geometries with wall confinement.
• To analyze the structural and dynamic properties of colloidal suspensions under confinement.

Main Methods:

• A spectrally accurate Stokes solver using Fast Fourier Transforms (FFT) and Chebyshev polynomials.
• Decomposition into a doubly periodic subproblem and a wall boundary condition correction subproblem.
• Utilizing an exponential of a semicircle kernel for modeling particle forces and optimizing parameters for accuracy and invariance.

Main Results:

• A GPU-implemented solver with linear scaling, enabling simulations of ~1 million particles in under a second.
• Demonstrated accuracy in hydrodynamic radius, rotational, and translational invariance.
• Observed that dense microroller suspensions in slit channels maintain a two-layer structure but exhibit reduced collective speed compared to single-wall confinement.

Conclusions:

• The developed method offers a significant speedup for large-scale hydrodynamic simulations.
• Confinement in slit channels impacts the collective dynamics of dense particle suspensions.
• The findings provide insights into the behavior of colloidal systems in restricted environments.