Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation |
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Authors: | Zhihui Li Hanxin Zhang |
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Institution: | (1) National Laboratory for Computational Fluid Dynamics, Beijing, 100083, China;(2) Hypervelocity Aerodynamics Institute, Mianyang, 621000, China |
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Abstract: | A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and
applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified
velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes
can be presented on the basis of the kinetic Boltzmann–Shakhov model equation. The gas-kinetic finite-difference schemes for
the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory
and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical
modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete
velocity numerical integration method can be developed and adopted to attack complex flows with different Mach numbers. HPF
parallel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex
problems. High Mach number flows around three-dimensional bodies are computed preliminarily with massive scale parallel. It
is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can
be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and
used to study micro-channel gas flows including the classical Couette flow, the Poiseuille- channel flow and pressure-driven
gas flows in two-dimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a
powerful tool in the numerical simulation of micro-scale gas flows occuring in the Micro-Electro-Mechanical System (MEMS).
The project supported by the National Natural Science Foundation of China (90205009 and 10321002), and the National Parallel
Computing Center in Beijing.
The English text was polished by Yunming Chen. |
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Keywords: | Gas kinetic theory Velocity distribution function Boltzmann model equation Spacecraft flows Micro-scale gas flows |
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