Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Volume 42, Issue 4, Pages 361-382Publisher
JOHN WILEY & SONS LTD
DOI: 10.1002/fld.517
Keywords
Boltzmann model equation; gas kinetic theory; discrete velocity ordinate method; NND finite-difference scheme; rarefied gas flow; continuum flow
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Based on the Bhatnagar-Gross-Krook (BGK) Boltzmann model equation, the unified simplified velocity distribution function equation adapted to various flow regimes can be presented. The reduced velocity distribution functions and the discrete velocity ordinate method are developed and applied to remove the velocity space dependency of the distribution function, and then the distribution function equations will be cast into hyperbolic conservation laws form with non-linear source terms. Based on the unsteady tithe-splitting technique and the non-oscillatory, containing no free parameters, and dissipative (NND) finite-difference method, the gas kinetic finite-difference second-order scheme is constructed for the computation of the discrete velocity distribution functions. The discrete velocity numerical quadrature methods are developed to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a unified simplified gas kinetic algorithm for the gas dynamical problems froth various flow regimes is developed. To test the reliability of the present numerical method, the one-dimensional shock-tube problems and the flows past two-dimensional circular cylinder with various Knudsen numbers are simulated. The computations of the related flows indicate that both high resolution of the flow fields and good qualitative agreement with the theoretical, DSMC and experimental results can be obtained. Copyright (C) 2003 John Wiley Sons, Ltd.
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