Lattice Boltzmann simulation with arbitrary equilibrium func

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SUMMARY

Simon seeks a Lattice Boltzmann Equation (LBE) method that accommodates arbitrary equilibrium density functions for simulating the Boltzmann equation with known particle scattering. He specifically mentions the D2Q9 method and expresses a preference for a simulation that does not rely on the Bhatnagar-Gross-Krook (BGK) approximation. The discussion highlights the need for flexibility in the collision operator input, emphasizing the importance of higher-order Q methods in achieving accurate simulations.

PREREQUISITES
  • Understanding of Lattice Boltzmann methods, specifically D2Q9
  • Familiarity with Boltzmann equations and collision integrals
  • Knowledge of the Bhatnagar-Gross-Krook (BGK) approximation
  • Experience with numerical simulation techniques in fluid dynamics
NEXT STEPS
  • Research alternative Lattice Boltzmann methods that allow for arbitrary collision operators
  • Explore higher-order Lattice Boltzmann models beyond D2Q9
  • Investigate the implementation of custom scattering functions in LBE simulations
  • Study the implications of removing the BGK approximation in Lattice Boltzmann simulations
USEFUL FOR

This discussion is beneficial for computational fluid dynamicists, researchers in numerical simulations, and anyone developing Lattice Boltzmann methods for complex particle interactions.

simoncks
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Hi everyone,

I plan to do a simulation of a Boltzmann equation with experimentally known scattering between two particles. Initially I intend to incorporate the scattering into the collision integral and use Lattice Boltzmann Equation (LBE) afterwards. But I only see LGBK (DnQb) which requires a specific form of equilibrium density function whereas mine might not suit.
Is there any LBE which does not require a specific form of equilibrium density function? Or is there any LBE which only requires input of scattering function?

I am happy to provide more information if needed.

Thanks
Simon
 
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Specifically, I want a lattice Boltzmann method which can allow me to input arbitrary collision operator. It is ok to make some approximation.
 
A software of D2Q9 method without BGK approximation would be an ideal. Higher order of Q would also be favourable.
 

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