This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity dis...This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.展开更多
为分析SF_6/CF_4混合气体的饱和蒸气压与绝缘特性,进而探讨SF_6/CF_4混合气体替代SF_6气体应用于高寒地区的可行性。首先,采用全局最优化算法拟合得到了SF_6和CF_4的Antoine特性常数,然后通过Antoine蒸汽压方程和汽液平衡基本定律相结合...为分析SF_6/CF_4混合气体的饱和蒸气压与绝缘特性,进而探讨SF_6/CF_4混合气体替代SF_6气体应用于高寒地区的可行性。首先,采用全局最优化算法拟合得到了SF_6和CF_4的Antoine特性常数,然后通过Antoine蒸汽压方程和汽液平衡基本定律相结合,计算了SF_6/CF_4混合气体的饱和蒸气压特性。然后,基于Boltzmann解析法获得了SF_6/CF_4混合气体的临界击穿场强数据。最后,综合SF_6/CF_4混合气体的饱和蒸气压特性与临界击穿场强数据,讨论了SF_6/CF_4混合气体的绝缘特性及在高寒地区应用的可行性。结果表明:在低温条件下,SF_6/CF_4混合气体所允许的压力明显高于纯SF_6,从而可以获得较纯SF_6更高的绝缘强度,如–40℃时摩尔分数50%SF_6/50%CF_4混合气体和SF_6气体的饱和蒸气压分别约为0.64 MPa和0.35 MPa,相应压力下的临界击穿场强分别约为43.5 k V/mm和31.34 k V/mm,即50%SF_6/50%CF_4混合气体的绝缘强度可以达到纯SF_6气体的1.4倍,说明SF_6/CF_4混合气体采用恰当的混合比例和充气压力能够有效解决SF_6在高寒地区的液化问题。展开更多
This paper presents a class of high resolution KFVS (kinetic flux vector split-ting) finite volum methods for solving three-dimensional compressible Euler equa-tions with γ-gas law. The schemes are obtained based on ...This paper presents a class of high resolution KFVS (kinetic flux vector split-ting) finite volum methods for solving three-dimensional compressible Euler equa-tions with γ-gas law. The schemes are obtained based on the important connection between the Boltzmann equation and the Euler equations. According to the sign of the normal molecular velocity component at the surface of ally control volumes,one gives a splitting of the macroscopic flux vector, i.e. writes the macroscopic flux vector into the sum form of a positive flux and a negative flux. The initial reconstruction is applied to improve resolution of the schemes. Several numerical results are also presented to show the performance of our schemes.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 91016027 and 91130018)
文摘This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.
文摘为分析SF_6/CF_4混合气体的饱和蒸气压与绝缘特性,进而探讨SF_6/CF_4混合气体替代SF_6气体应用于高寒地区的可行性。首先,采用全局最优化算法拟合得到了SF_6和CF_4的Antoine特性常数,然后通过Antoine蒸汽压方程和汽液平衡基本定律相结合,计算了SF_6/CF_4混合气体的饱和蒸气压特性。然后,基于Boltzmann解析法获得了SF_6/CF_4混合气体的临界击穿场强数据。最后,综合SF_6/CF_4混合气体的饱和蒸气压特性与临界击穿场强数据,讨论了SF_6/CF_4混合气体的绝缘特性及在高寒地区应用的可行性。结果表明:在低温条件下,SF_6/CF_4混合气体所允许的压力明显高于纯SF_6,从而可以获得较纯SF_6更高的绝缘强度,如–40℃时摩尔分数50%SF_6/50%CF_4混合气体和SF_6气体的饱和蒸气压分别约为0.64 MPa和0.35 MPa,相应压力下的临界击穿场强分别约为43.5 k V/mm和31.34 k V/mm,即50%SF_6/50%CF_4混合气体的绝缘强度可以达到纯SF_6气体的1.4倍,说明SF_6/CF_4混合气体采用恰当的混合比例和充气压力能够有效解决SF_6在高寒地区的液化问题。
文摘This paper presents a class of high resolution KFVS (kinetic flux vector split-ting) finite volum methods for solving three-dimensional compressible Euler equa-tions with γ-gas law. The schemes are obtained based on the important connection between the Boltzmann equation and the Euler equations. According to the sign of the normal molecular velocity component at the surface of ally control volumes,one gives a splitting of the macroscopic flux vector, i.e. writes the macroscopic flux vector into the sum form of a positive flux and a negative flux. The initial reconstruction is applied to improve resolution of the schemes. Several numerical results are also presented to show the performance of our schemes.
