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Stabilizing the thermal lattice Boltzmann method by spatial filtering.

J J J Gillissen1

  • 1Center for Environmental Sensing and Modeling (CENSAM) IRG Singapore-MIT Alliance for Research and Technology (SMART) Centre, 3 Science Drive 2, Singapore 117543.

Physical Review. E
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Summary
This summary is machine-generated.

We stabilized the thermal lattice Boltzmann method (TLBM) using moment filtering. This approach enhances stability for smaller transport coefficients without sacrificing hydrodynamic accuracy in simulations.

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Area of Science:

  • Computational fluid dynamics
  • Numerical methods
  • Statistical physics

Background:

  • The thermal lattice Boltzmann method (TLBM) is a powerful computational fluid dynamics tool.
  • Standard TLBM can suffer from stability issues, especially with small transport coefficients.
  • Existing stabilization techniques may introduce excessive numerical diffusion.

Purpose of the Study:

  • To enhance the linear stability of the thermal lattice Boltzmann method.
  • To reduce numerical diffusivity introduced by stabilization techniques.
  • To maintain the accuracy of hydrodynamic predictions.

Main Methods:

  • Applying a filtering technique to the second- and third-order moments of the collision operator in TLBM.
  • Utilizing Chapman-Enskog expansion to analyze the impact of filtering on numerical diffusivity.
  • Conducting simulations using a 3D thermal lattice Boltzmann system with 33 discrete velocities.
  • Validating results against standardized test cases, including 2D natural convection.

Main Results:

  • The proposed filtering method significantly extends the linear stability range of TLBM.
  • Stability is improved by up to a tenfold decrease in transport coefficients.
  • The Chapman-Enskog expansion confirms diminished numerical diffusivity in the low-wavenumber limit.
  • Numerical simulations show no compromise in hydrodynamic accuracy compared to reference solutions.

Conclusions:

  • Moment filtering is an effective strategy for stabilizing the thermal lattice Boltzmann method.
  • This technique offers a robust way to simulate complex fluid dynamics problems with improved stability.
  • The method provides a balance between enhanced stability and preserved accuracy for TLBM.