Fast Computation of Many-Particle Hydrodynamic and Electrostatic Interactions in a Confined Geometry

Abstract

An O(N) method is presented for calculation of hydrodynamic or electrostatic interactions between N point particles in a confined geometry. This approach splits point forces or sources into a local contribution for which rapidly decaying free-space analytical solutions to the Stokes or Poisson equations are used, and a global contribution whose effect is determined numerically using a fast iterative method. The scheme is applied to Brownian dynamics simulations of flowing confined polymer solutions, and the effects of concentration on hydrodynamically induced migration phenomena are illustrated.

A method for the computation of turbulent polymeric liquids including hydrodynamic interactions and chain entanglements

“…This is plausible, since, by construction, this is the short range velocity field that is due to the delta function type of forcing. In addition, as mentioned already, there is an exact analytical solution for this field (stokeslet) [35] …”

“…Similarly, the Stokes relaxation time τ = m b /(6πµa) (where a is the polymer-bead radius) is very small, so, since the aim is to accurately resolve the dynamics of inertial turbulence fluctuations that evolve at much larger time scales, one can solve the polymer dynamics in the diffusive limit [34,35], when the inertial force has settled to zero.…”

“…Hence, the availability of parallel finite volume turbulent flow solvers, as well as the O(N ) character of the Stokesian dynamics method of [35] are important features. Additional algorithmic complexity improvements could be made in the future.…”

“…There are a number of methods available [34,35,38], however, I am going to base the discussion on the approach of [35], since this method was employed in the entangled polymer dynamics computation of [21], hence the latter reference could be consulted for various numerical and computational details, as required. I am presenting here only the method aspects that are relevant in the context of the present approach.…”

“…is composed of the free space stokeslet (corresponding to the delta function part) minus a smoothed free space stokeslet obtained from the analytical solution of the Stokes equations with the forcing term given by the function θ g (x) [35]. The force density θ g (x) corresponds to a global velocity field u S g (x) that varies on the scale α −1 , hence it can be solved in bounded domains, with finite volume solvers and suitable boundary conditions [21].…”