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| Finite difference solution of nonlinear model equations for rarified gas using discrete velocity ordinate method |
| Revised:April 05, 2004 |
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| DOI：10.7511/jslx20062043 |
| KeyWord:rarified flow,Boltzmann equation,discrete ordinate method,numerical quadrature,finite difference |
| WANG Qiang CHENG Xiao-li ZHUANG Feng-gan |
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| Abstract: |
| Considering the general nonlinear Boltzmann equation,a uniform algorithm has been developed to simulate rarified flows at a wide Knudsen number range numerically.The collision term is approximated by BGK model and Shakov model,and two bi-velocity non-dimensionalized reduced distribution functions are introduced.The single tri-velocity model equation is transformed into a bi-velocity differential equation system through integrating weightedly the non-dimensionalized model equation about the third component of molecule velocity.The discrete velocity ordinate method associated with Gauss-Hermite quadrature and orthogonal polynomial quadrature is used to eliminate dependency of the reduced model equations on continuous molecule velocity space,then a set of hyperbolic conservative discrete equations with source terms are obtained from phase space to physical space,and a finite difference method related to a second-order upwind TVD scheme is selected to solve them both explicitly and implicitly.A two-dimensional supersonic Ar-gas flow around a cylinder is computed to show the effectivity of algorithm.Moreover,numerical results of two wall reflection models of gas molecules,namely diffuse reflection model and specular reflection model,are compared and analyzed. |
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