High-Order Conservative Asymptotic-Preserving Schemes for Modeling Rarefied Gas Dynamical Flows with Boltzmann-BGK Equation |
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Authors: | Manuel A Diaz Min-Hung Chen & Jaw-Yen Yang |
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Abstract: | High-order and conservative phase space direct solvers that preserve the
Euler asymptotic limit of the Boltzmann-BGK equation for modelling rarefied gas
flows are explored and studied. The approach is based on the conservative discrete ordinate
method for velocity space by using Gauss Hermite or Simpsons quadrature rule
and conservation of macroscopic properties are enforced on the BGK collision operator.
High-order asymptotic-preserving time integration is adopted and the spatial evolution
is performed by high-order schemes including a finite difference weighted essentially
non-oscillatory method and correction procedure via reconstruction schemes.
An artificial viscosity dissipative model is introduced into the Boltzmann-BGK equation
when the correction procedure via reconstruction scheme is used. The effects of
the discrete velocity conservative property and accuracy of high-order formulations of
kinetic schemes based on BGK model methods are provided. Extensive comparative
tests with one-dimensional and two-dimensional problems in rarefied gas flows have
been carried out to validate and illustrate the schemes presented. Potentially advantageous
schemes in terms of stable large time step allowed and higher-order of accuracy
are suggested. |
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