Development of a Meshless Kernel-Based Scheme for Particle-Field Brownian Dynamics Simulations.

Area of Science:

• Computational physics
• Soft matter physics

Background:

• Particle-field Brownian dynamics simulations are crucial for modeling complex fluids.
• Existing methods often face challenges with numerical stability and accuracy.

Purpose of the Study:

• To develop a stable and accurate meshless discretization scheme for particle-field Brownian dynamics.
• To analyze the factors influencing the numerical stability of the proposed scheme.

Main Methods:

• A meshless discretization scheme using a weighting kernel for density assignment.
• Derivation of free energy density from an equation of state with a square gradient term.
• Evaluation of numerical stability by reproducing thermodynamics and dynamics of homogeneous samples.

Main Results:

• Numerical stability is critically dependent on reduced reference compressibility, kernel range, time step, and external pressure.
• Precise thermodynamics are achieved through appropriate parametrization and renormalization.
• Exact restoration of dynamics is possible via time step and friction coefficient manipulation.
• A semiempirical formula for the time step upper bound was derived.

Conclusions:

• The developed meshless scheme offers a stable and accurate approach for particle-field Brownian dynamics simulations.
• The study provides insights into parameter selection for reliable simulation of fluid systems.
• The scheme is validated on mesoscopic fluid models using different equations of state.