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N G Kallikounis1, B Dorschner1, I V Karlin1

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Summary
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This study introduces a multi-scale lattice Boltzmann scheme that adaptively refines particle velocity sets. This computational fluid dynamics method efficiently couples different velocity models, reducing computational cost for complex flow simulations.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Methods
  • Kinetic Theory

Background:

  • Traditional lattice Boltzmann methods often require high-order velocity sets for accurate non-equilibrium flow simulation.
  • This can lead to significant computational overhead.
  • Adaptive methods are needed to balance accuracy and efficiency.

Purpose of the Study:

  • To develop a multi-scale lattice Boltzmann scheme with adaptive velocity space refinement.
  • To enable efficient coupling of different velocity set orders.
  • To reduce computational requirements for complex flow problems.

Main Methods:

  • A multi-scale lattice Boltzmann scheme is presented, adaptively refining particle velocity space.
  • Consistent and efficient coupling of lower and higher-order velocity sets is achieved through projection or lifting.
  • The scheme is formulated for static and co-moving reference frames, inspired by the Particles on Demand method.

Main Results:

  • The multi-scale scheme was validated using an athermal vortex advection and a jet flow setup.
  • Performance was investigated in shock structure and high-Knudsen-number Couette flow problems.
  • Accurate results were obtained with flexibility and reduced computational cost.

Conclusions:

  • The proposed multi-scale lattice Boltzmann scheme offers an accurate and flexible approach for simulating complex flows.
  • Adaptive refinement of velocity sets significantly reduces computational demands.
  • This method is suitable for highly non-equilibrium flow regimes where velocity set order is critical.