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Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models.

Yiming Qi1, Lian-Ping Wang2, Zhaoli Guo3

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This study introduces two lifting relations for kinetic models to initialize hydrodynamic flows. The Hermite-expansion-based relation is robust, while the Chapman-Enskog-based one may cause oscillations in advanced discrete velocity models.

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Area of Science:

  • Computational fluid dynamics
  • Kinetic theory
  • Mesoscopic modeling

Background:

  • Accurate initialization of non-uniform hydrodynamic flows is crucial for Boltzmann equation-based mesoscopic approaches.
  • Existing lifting relations are essential for connecting distribution functions with hydrodynamic variables.

Purpose of the Study:

  • To derive and compare two novel lifting relations for Guo et al.'s total-energy double-distribution-function (DDF) kinetic model.
  • To investigate the performance and potential numerical issues of these lifting relations with optimized discrete velocity models.
  • To establish a theoretical framework for predicting numerical oscillations and determining Hermite equilibria order.

Main Methods:

  • Derivation of two lifting relations: one via Hermite expansion of moments, the other via Chapman-Enskog (CE) approximation.
  • Theoretical analysis of consistency with Navier-Stokes-Fourier system and potential oscillations with optimized discrete velocity models (D3V27A7, D3V13A5).
  • Three-dimensional compressible Taylor-Green vortex flow simulations to validate lifting relations and predict oscillations.

Main Results:

  • Both derived lifting relations are theoretically consistent with the compressible Navier-Stokes-Fourier system.
  • The Hermite-expansion-based lifting relation demonstrates robust performance across various conditions.
  • The CE-based lifting relation exhibits numerical oscillations with optimized discrete velocity models, necessitating a predictive theoretical model.

Conclusions:

  • The Hermite-expansion-based lifting relation is recommended for initializing hydrodynamic flows due to its stability.
  • A theoretical framework is established to predict and mitigate oscillations associated with the CE-based lifting relation.
  • The derived lifting relations and theoretical insights are generalizable to other DDF kinetic models, including Qi et al.'s.