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Matrix lattice Boltzmann reloaded.

Ilya Karlin1, Pietro Asinari, Sauro Succi

  • 1Aerothermochemistry and Combustion Systems Laboratory, ETH Zurich, 8092 Zurich, Switzerland. karlin@lav.mavt.ethz.ch

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
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Summary
This summary is machine-generated.

Researchers developed a new lattice Boltzmann equation model. This two-parameter operator enhances stability and accuracy while maintaining simplicity for computational fluid dynamics simulations.

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Fluid mechanics

Background:

  • The lattice Boltzmann equation (LBE) is a powerful computational fluid dynamics (CFD) method.
  • Existing LBE collision operators, like single-relaxation time (SRT) schemes, offer simplicity but can lack stability and accuracy.
  • Matrix-based collision models provide enhanced stability and accuracy but are often complex.

Purpose of the Study:

  • To introduce a novel two-parametric family of lattice Boltzmann collision operators.
  • To combine the stability and accuracy of matrix models with the simplicity of SRT schemes.
  • To demonstrate the efficacy of the revised lattice Boltzmann equation through simulations.

Main Methods:

  • Revisiting the formulation of the lattice Boltzmann collision integral (matrix model).
  • Developing a new two-parametric family of collision operators.
  • Performing numerical simulations of a three-dimensional lid-driven cavity flow.

Main Results:

  • The new two-parametric operators successfully integrate enhanced stability and accuracy.
  • The proposed method retains the simplicity characteristic of single-relaxation time schemes.
  • Numerical simulations validated the improved performance of the revised lattice Boltzmann equation.

Conclusions:

  • The novel two-parametric collision operators offer a superior balance of accuracy, stability, and simplicity in LBE.
  • This advancement provides a more versatile and efficient tool for computational fluid dynamics.
  • The revised lattice Boltzmann equation is well-suited for complex flow problems, as demonstrated by the cavity flow simulation.