Semiautomatic construction of lattice Boltzmann models

Area of Science:

• Computational fluid dynamics
• Numerical methods

Background:

• Constructing lattice Boltzmann models requires careful selection of lattice velocities and weights.
• High-order models present significant challenges in determining these parameters.

Purpose of the Study:

• To introduce a publicly available Python script that automates the definition of lattice velocities and weights.
• To assist researchers in constructing complex lattice Boltzmann models.

Main Methods:

• The script utilizes Maxwell-Boltzmann constraint equations, treated as a linear system for weight determination.
• Tensor equations are simplified into scalar equations through contractions.
• It checks for unique solutions for weights and calculates the valid range for the speed of sound parameter (c_s).
• Linear programming is employed to find specific solutions when multiple exist.

Main Results:

• The software successfully reproduces existing lattice Boltzmann models, such as D3Q19.
• It demonstrates the capability to discover novel, higher-order lattice Boltzmann models.
• The approach allows for flexible selection of the speed of sound parameter within defined limits.

Conclusions:

• The developed Python script significantly simplifies the process of defining lattice Boltzmann model parameters.
• This tool facilitates the creation of both established and new, advanced lattice Boltzmann models.
• It offers a robust numerical approach to solving the underlying constraint equations.