Related Experiment Video
Updated: Feb 27, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Parallel O(N) Stokes' solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general
Xujun Zhao1, Jiyuan Li2, Xikai Jiang2
1Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA.
Abstract:
An efficient parallel Stokes' solver has been developed for complete description of hydrodynamic interactions between Brownian particles in bulk and confined geometries. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green's function formalism. A scalable parallel computational approach is presented, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the general geometry Ewald-like method. Our approach employs a highly efficient iterative finite-element Stokes' solver for the accurate treatment of long-range hydrodynamic interactions in arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallel Stokes' solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem leads to an O(N) parallel algorithm. We illustrate the new algorithm in the context of the dynamics of confined polymer solutions under equilibrium and non-equilibrium conditions. The method is then extended to treat suspended finite size particles of arbitrary shape in any geometry using an immersed boundary approach.
More Related Videos
05:00Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs
Published on: August 9, 2024
11:00Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Related Concept Videos
Divergence and Stokes' Theorems
Stokes' Law
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only...
Navier–Stokes Equations
Steady, Laminar Flow Between Parallel Plates
Newtonian Fluid: Problem Solving
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Turbulent Flow: Problem Solving
Temperature is a key factor in CO2 solubility. In this case, the CO2 gas and the liquid are cooled to 20°C. Lower temperatures enhance...