High-Order Conservative Asymptotic-Preserving Schemes for Modeling Rarefied Gas Dynamical Flows with Boltzmann-BGK Equation (Communications in Computational Physics, 2020)
High-order and conservative phase space direct solvers that preserve theEuler asymptotic limit of the Boltzmann-BGK equation for modelling rarefied gasflows are explored and studied. The approach is based on the conservative discrete ordinatemethod for velocity space by using Gauss Hermite or Simpsons quadrature ruleand conservation of macroscopic properties are enforced on the BGK collision operator.High-order asymptotic-preserving time integration is adopted and the spatial evolutionis performed by high-order schemes including a finite difference weighted essentiallynon-oscillatory method and correction procedure via reconstruction schemes.An artificial viscosity dissipative model is introduced into the Boltzmann-BGK equationwhen the correction procedure via reconstruction scheme is used. The effects ofthe discrete velocity conservative property and accuracy of high-order formulations ofkinetic schemes based on BGK model methods are provided. Extensive comparativetests with one-dimensional and two-dimensional problems in rarefied gas flows havebeen carried out to validate and illustrate the schemes presented. Potentially advantageousschemes in terms of stable large time step allowed and higher-order of accuracyare suggested.