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Probing double-distribution-function models in discrete-velocity Boltzmann methods for highly compressible flows:

S A Hosseini1, A Bhadauria1, I V Karlin1

  • 1Department of Mechanical and Process Engineering, <a href="https://ror.org/05a28rw58">ETH Zurich</a>, 8092 Zurich, Switzerland.

Physical Review. E
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Summary
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The double distribution function approach offers efficient kinetic solvers for compressible flows. The total energy split method provides optimal performance for high-speed flows, balancing accuracy and computational cost.

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Area of Science:

  • Computational fluid dynamics
  • Kinetic theory
  • High-speed compressible flows

Background:

  • Kinetic solvers are extended to compressible flows using the double distribution function approach.
  • Various realizations and energy partition strategies exist for this method.

Purpose of the Study:

  • To present an overview and comparative study of double distribution function realizations for high-speed compressible flows.
  • To analyze different energy partition strategies, hydrodynamic limits, and numerical performance.

Main Methods:

  • Comparative analysis of three energy partition strategies: nontranslational, internal, and total energy splits.
  • Numerical study of accuracy and performance using the particles on demand realization.
  • Analysis of hydrodynamic limits and quadrature requirements.

Main Results:

  • The nontranslational energy split requires higher-order quadrature for Navier-Stokes-Fourier equation recovery.
  • The internal energy split recovers the hydrodynamic limit but introduces nonlocal source terms, increasing computational cost.
  • The total energy split demonstrates optimal overall performance in terms of accuracy and efficiency.

Conclusions:

  • The total energy split is the most effective strategy for high-speed compressible flows within the double distribution function approach.
  • Careful consideration of energy partition is crucial for balancing accuracy and computational demands in kinetic solvers.
  • This study provides valuable insights for selecting and implementing kinetic solvers for complex fluid dynamics problems.