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Multiscale gas-kinetic simulation for continuum and near-continuum flows.

Kun Xu1, Hongwei Liu

  • 1Department of Mathematics, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China. makxu@ust.hk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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This study introduces a multiscale model for rarefied gas dynamics, improving predictions where traditional methods fail. The gas-kinetic approach offers enhanced efficiency and accuracy across flow regimes, bridging continuum and near-continuum physics.

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Area of Science:

  • Fluid dynamics
  • Computational physics
  • Rarefied gas dynamics

Background:

  • Continuum fluid formulations like Navier-Stokes equations lose accuracy in rarefied flow fields.
  • Higher-order continuum models (Burnett, moment equations) show limited success in improving predictions.
  • Accurate modeling of gas flows requires methods valid across various rarefaction levels.

Purpose of the Study:

  • To present a novel multiscale model for gas flows applicable to both continuum and near-continuum regimes.
  • To enhance the predictive accuracy of fluid flow simulations in rarefied conditions.
  • To develop a unified framework that transitions smoothly to established solvers in limiting cases.

Main Methods:

  • A multiscale approach combining macroscopic conservation laws with microscopic gas-kinetic equations.
  • Fluxes are determined on the microscopic level using the gas-kinetic equation.
  • Macroscopic flow variables are updated based on conserved quantities (mass, momentum, energy).

Main Results:

  • The multiscale model accurately simulates nonequilibrium shock structure, Poiseuille flow, nonlinear heat conduction, and unsteady Rayleigh problems.
  • Gas-kinetic simulations demonstrate superior efficiency compared to direct Boltzmann solvers and direct-simulation Monte Carlo methods in near-continuum flows.
  • The formulation automatically reverts to a gas-kinetic Navier-Stokes solver in the continuum flow limit.

Conclusions:

  • The proposed multiscale gas-kinetic model provides a robust and efficient method for simulating gas flows across a wide range of rarefaction.
  • This approach overcomes the limitations of traditional continuum methods in rarefied environments.
  • The model offers a unified framework, enhancing computational efficiency and predictive accuracy for complex flow phenomena.