Numerical analysis of a supersonic rarefied gas flow past a flat plate

Abstract

A uniform supersonic flow of a rarefied gas past a flat plate at zero angle of attack is considered, and the steady behavior of the gas around the plate is investigated numerically on the basis of the Boltzmann–Krook–Welander equation (or the so-called BGK model) and the diffuse reflection boundary condition. An accurate finite-difference analysis, which gives the correct description of the discontinuity of the velocity distribution function of the gas molecules occurring in the gas, is carried out, and the features of the flow field (the velocity distribution function and the macroscopic variables such as the density, temperature, and flow velocity of the gas), in particular, those around the leading and trailing edges, are clarified for a wide range of the Knudsen number. The drag acting on the plate and the energy transferred to it are also obtained accurately. In addition, on the basis of the results for small Knudsen numbers, the behavior of the gas around the leading edge of a semi-infinite plate is investigated in detail.

Discrete-Velocity Models and Numerical Schemes for the Boltzmann-BGK Equation in Plane and Axisymmetric Geometries

“…Some drawbacks of this model, such as the incorrect value of the Prandtl number, can be corrected by modified models. A lot of works have been devoted to numerical approximations of the BGK equation, essentially by the discrete-ordinate method (see Yang and Huang [36] and Aoki et al [3] and their references), but also by particle methods (see Issautier [20]). However, to our knowledge, none of these methods satisfy at the discrete level the macroscopic properties known as conservation laws and dissipation of entropy.…”

“…Many works use precise quadratures of Gauss-Hermite type (see [3,36]), but despite the accuracy of their quadratures, these methods lack the properties of conservation and dissipation of entropy. This makes necessary a fine velocity mesh to ensure robust algorithms, which then are expensive.…”

Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation

“…The schemes have successfully simulated some problems, such as one-dimensional shock wave structures and two-dimensional shock wave re ections, inviscid and viscous turbulent ows, etc. In the computation of the rareÿed gas ows, the high resolution explicit and implicit ÿnite-di erence methods to solve two-dimensional BGK-Boltzmann model equations have been set forth [9,[13][14][15][16] based on the introduction of the reduced velocity distribution functions and the application of the discrete ordinate method. The reliability and e ciency of the methods have been demonstrated in applications to both steady and unsteady one-and two-dimensional rareÿed gas dynamical problems.…”

Gas-Kinetic Unified Algorithm for Re-Entering Complex Problems Covering Various Flow Regimes by Solving Boltzmann Model Equation

“…(15) can be integrated with respect to z V with weighting factors 1 and 2 z V so that the number of independent variables is reduced by integrating out the dependence of f on z V . The following reduced distribution functions are introduced, see Morinishi & Oguchi (1984); Yang & Huang (1995) and Aoki, Kanba & Takata (1997).…”