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Resolving collisions in Stokes suspensions with an efficient and stable potential-free constrained optimization algorithm

Banff International Research Station for Mathematical Innovation and Discovery

A common challenge in simulating dense suspension of rigid particles in Stokes flow is the numerical inaccuracies and instabilities that arises due to particle collisions. To overcome this problem, a strong repulsive potential between particles is often prescribed. This in turn leads to numerical stiffness and dramatic reduction in stable time-step sizes. In this work, we eliminate such stiffness by introducing contact constraints explicitly and solving the hydrodynamic equations in tandem with a linear complementarity problem with inequality constraints. Satisfaction of Newtons third law for the collision force is explicitly guaranteed, allowing the consistent calculation of collision stresses. Efficient parallelization for shared-memory and distributed-memory architectures is also implemented. This method can be coupled to any Stokes hydrodynamics solver for particles with various shapes and allows us to simulate $10^4-10^7$ spheres on a laptop, depending on the cost of the Stokes hydrodynamics solver. We demonstrate its performance on a range of applications of rigid suspensions.

Mathematics; Fluid mechanics; Mechanics of particles and systems; Fluid dynamics

video/mp4

Author affiliation: Flatiron Institute, Simons Foundation

2018-04-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/65363

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/