Brownian dynamics without Green's functions.

Area of Science:

• Computational physics
• Fluid dynamics
• Statistical mechanics

Background:

• Simulating confined particle suspensions requires accurate modeling of hydrodynamic interactions and Brownian motion.
• Traditional methods often rely on analytical Green's functions, which can be limiting for complex geometries.

Purpose of the Study:

• To develop a novel Fluctuating Immersed Boundary (FIB) method for Brownian dynamics simulations.
• To enable efficient and accurate simulation of confined particle suspensions.

Main Methods:

• The FIB method employs a fluctuating finite-volume Stokes solver to generate hydrodynamic interactions and Brownian motion.
• It incorporates stochastic contributions to the stress tensor consistent with fluctuating hydrodynamics.
• Novel temporal integrators and a random finite difference approach are developed for configuration-dependent mobility.

Main Results:

• The FIB method accurately captures both static (equilibrium) and dynamic properties of interacting particles.
• It demonstrates the ability to generate deterministic and stochastic terms from a single numerical solution of steady Stokes equations per time step.
• Numerical results show good agreement with analytical and existing computational data.

Conclusions:

• The FIB method provides an accurate and efficient approach for simulating confined particle suspensions.
• It overcomes limitations of traditional methods by generating hydrodynamic properties on the fly.
• This method advances the simulation capabilities for complex fluid-particle systems.