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Recursive regularization step for high-order lattice Boltzmann methods.

Christophe Coreixas1, Gauthier Wissocq1, Guillaume Puigt1

  • 1CERFACS, 42 Avenue G. Coriolis, 31057 Toulouse Cedex, France.

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|January 20, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces an improved lattice Boltzmann method (LBM) using recursive Hermite polynomial calculations. This novel approach significantly enhances numerical stability and accuracy for fluid dynamics simulations, reducing computational costs.

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Mesoscopic physics

Background:

  • The lattice Boltzmann method (LBM) is a powerful numerical technique for simulating fluid flows.
  • Standard LBM implementations can face limitations in stability and accuracy, particularly in under-resolved conditions.
  • Hermite tensor-based lattice structures offer advanced capabilities for LBM.

Purpose of the Study:

  • To present a lattice Boltzmann method (LBM) with enhanced stability and accuracy for Hermite tensor-based lattice structures.
  • To improve the collision operator's regularization step through recursive computation of nonequilibrium Hermite polynomial coefficients.
  • To demonstrate the benefits of this recursive approach in terms of computational cost, stability, and accuracy.

Main Methods:

  • Implementation of a recursive computation for nonequilibrium Hermite polynomial coefficients in the LBM collision operator.
  • Application of the enhanced LBM to simulate isothermal doubly periodic shear layers across a range of Reynolds numbers (10^4 to 10^6).
  • Comparison of the proposed method against the Bhatnagar-Gross-Krook LBM using standard (D2Q9) and high-order (D2V17, D2V37) lattices.
  • Extension and application of the method to simulate thermal and fully compressible flows, including Sod shock tubes with the D2V37 lattice.

Main Results:

  • The recursive computation significantly reduces computational cost compared to standard methods.
  • The enhanced LBM demonstrates a considerable increase in stability and accuracy, especially in under-resolved conditions.
  • Simulations of shear layers show a tremendous increase in the stability range of the proposed approach.
  • Numerical simulations of Sod shock tubes confirm the enhanced stability for thermal and compressible flows.

Conclusions:

  • The recursive computation of Hermite polynomial coefficients offers a substantial improvement in LBM stability and accuracy.
  • This method effectively filters non-hydrodynamic contributions, enhancing performance in challenging flow regimes.
  • The proposed LBM approach provides a more robust and efficient tool for a wide range of fluid dynamics simulations.