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Consistent lattice Boltzmann methods for incompressible axisymmetric flows.

Liangqi Zhang1,2, Shiliang Yang1, Zhong Zeng2,3

  • 1School of Chemical and Biomedical Engineering, Nanyang Technological University, Singapore 637459, Singapore.

Physical Review. E
|September 15, 2016
PubMed
Summary

New incompressible lattice Boltzmann (LB) methods for axisymmetric flows enhance accuracy by reducing compressibility errors. These improved LB models offer greater numerical stability for complex fluid dynamics simulations.

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Area of Science:

  • Computational Fluid Dynamics
  • Fluid Mechanics
  • Numerical Analysis

Background:

  • Existing lattice Boltzmann (LB) models for axisymmetric flows often suffer from compressibility errors and numerical instability.
  • Standard LB methods can involve complex gradient calculations in source terms, impacting efficiency.
  • Hermite expansion for incompressibility conditions is a known technique with potential for error reduction.

Purpose of the Study:

  • To develop consistent and accurate lattice Boltzmann (LB) methods for incompressible axisymmetric flows.
  • To improve the numerical stability and reduce compressibility errors in existing LB models.
  • To theoretically and numerically validate the proposed incompressible axisymmetric LB methods.

Main Methods:

  • Development of two novel axisymmetric LB models based on existing efficient models.
  • Incorporation of Hermite expansion to satisfy incompressibility conditions.
  • Addition of an extra relaxation parameter to the Bhatnagar-Gross-Krook (BGK) collision operator for stability.
  • Theoretical analysis using Chapman-Enskog expansion and equivalent moment system.
  • Numerical validation using four benchmark tests for accuracy and applicability.

Main Results:

  • The proposed LB models successfully evolve within the standard LB framework without gradient calculations in source terms.
  • The use of Hermite expansion is shown to reduce compressibility errors compared to existing models.
  • The modified BGK collision operator significantly enhances numerical stability by suppressing ghost variable effects.
  • Theoretical analysis confirms the derivation of macroscopic equations and quantifies truncation errors.
  • Numerical validations demonstrate the accuracy and wide applicability of the developed incompressible axisymmetric LB models.

Conclusions:

  • The developed lattice Boltzmann (LB) methods provide a consistent and accurate approach for simulating incompressible axisymmetric flows.
  • These novel LB models offer improved numerical stability and reduced compressibility errors, advancing the field of computational fluid dynamics.
  • The methods are validated and suitable for various benchmark fluid dynamics problems.