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Study on the unified algorithm for three-dimensional complex problems covering various flow regimes using Boltzmann model equation

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Science china(Physics,Mechanics & Astronomy) 2009年第1期52卷 124-138页

作者： li zhihui1,2 & zhang hanxin1 1 national laboratory for Computational Fluid Dynamics, Beijing 100083, china 2 china aerodynamics research and development center, hypervelocity aerodynamics institute, mianyang 621000, china national laboratory for Computational Fluid Dynamics Beijing China china aerodynamics research and development center Hypervelocity Aerodynamics Institute Mianyang China

The Boltzmann simplified velocity distribution function equation describing the gas transfer phenomena from various flow regimes will be explored and solved numerically in this study. The discrete velocity ordinate method of the gas kinetic theory is studied and applied to simulate the complex multi-scale flows. Based on the uncoupling technique on molecular movement and colliding in the DSMC method, the gas-kinetic finite difference scheme is constructed to directly solve the discrete velocity distribution functions by extending and applying the unsteady time-splitting method from computational fluid dynamics. The Gauss-type discrete velocity numerical quadrature technique for different Mach number flows is developed to evaluate the macroscopic flow parameters in the physical space. As a result, the gas-kinetic numerical algorithm is established to study the three-dimensional complex flows from rarefied transition to continuum regimes. The parallel strategy adapted to the gas-kinetic numerical algorithm is investigated by analyzing the inner parallel degree of the algorithm, and then the HPF parallel processing program is developed. To test the reliability of the present gas-kinetic numerical method, the three-dimensional complex flows around sphere and spacecraft shape with various Knudsen numbers are simulated by HPF parallel computing. The computational results are found in high resolution of the flow fields and good agreement with the theoretical and experimental data. The computing practice has confirmed that the present gas-kinetic algorithm probably provides a promising approach to resolve the hypersonic aerothermodynamic problems with the complete spectrum of flow regimes from the gas-kinetic point of view of solving the Boltzmann model equation.

关键词： Boltzmann model equation kinetic theory velocity distribution function discrete velocity ordinate technique hypersonic flow parallel computing numerical methods

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Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

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Science china(Physics,Mechanics & Astronomy) 2005年第4期48卷 496-512页

作者： li zhihui1,2, zhang hanxin1 & fu song2 ⒈ national laboratory for cfd, hypervelocity aerodynamics institute,china aerodynamics research and development center,mianyang 621000,china 2.Department of Engineering Mechanics,Tsinghua University,Beijing 100084,china national laboratory for cfd Hypervelocity Aerodynamics Institute China Aerodynamics Research and Development Center Mianyang China Department of Engineering Mechanics Tsinghua University Beijing China

The gas-kinetic unified algorithm using Boltzmann model equation have been extended and developed to solve the micro-scale gas flows in Poiseuille-like micro-channels from Micro-Electro-Mechanical Systems (MEMS). The numerical modeling of the gas kinetic boundary conditions suitable for micro-scale gas flows is presented. To test the present method, the classical Couette flows with various Knudsen numbers, the gas flows from short microchannels like plane Poiseuille and the pressure-driven gas flows in two-dimensional short microchannels have been simulated and compared with the approximate solutions of the Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary theory, the gas-kinetic BGK-Burnett solutions and the experimental data. The comparisons show that the present gas-kinetic numerical algorithm using the mesoscopic Boltzmann simplified velocity distribution function equation can effectively simulate and reveal the gas flows in microchannels. The numerical experience indicates that this method may be a powerful tool in the numerical simulation of micro-scale gas flows from MEMS.

关键词： Boltzmann model equation, discrete velocity ordinate method, finite-difference scheme, Couette flow, Poiseuille flow, gas flow in short-microchannel.

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