ACTA AERONAUTICAET ASTRONAUTICA SINICA >
A massively parallel algorithm for hypersonic covering various flow regimes to solve Boltzmann model equation
Received date: 2014-07-02
Revised date: 2014-10-20
Online published: 2015-01-24
Supported by
National Basic Research Program of China(2014CB744100); National Natural Science Foundation of China (91016027,91130018,11325212); National Defense Basic Research Program (51313030104)
The unified equation on the molecular velocity distribution function is presented for describing complex hypersonic flow transport phenomena covering various flow regimes by the computable model of Boltzmann collision integral. The discrete velocity ordinate method is used to discretize and reduce velocity space dimensionality of the velocity distribution function, and the gas-kinetic numerical schemes of coupling iteration are constructed directly to solve the molecular velocity distribution function. The computing models of hypersonic aerothermodynamics for the complex vehicles are developed by the evolution and updating based on the molecular velocity distribution function. The new parallel strategy of the gas-kinetic numerical algorithm is established by using the parallelizing technique of domain decomposition with the analysis from variable dependency relations, data communication and parallel expansibility. The data parallel distribution and parallel implementation are researched, the large-scale parallel program design is carried out and then the high-performance parallel algorithm has been established to simulate the hypersonic flow problems around complex vehicles covering various flow regimes, which can run stably in the tens of thousands of CPU or more scale. The hypersonic aerothermodynamics problems from high rarefied transition to continuum flow regimes around three-dimensional sphere-cone satellite body and complex wing-body combination shape with various Knudsen numbers, different Mach numbers, and diverse flying of angles have been computed and verified in high-performance computer with massive scale parallel. The computed results are found in high resolution of the flow fields and good agreement with the related reference experimental data, direct simulation Monte Carlo (DSMC) and theoretical predictions, and the hypersonic complex flow mechanism and changing laws are revealed. It is probably practical that the applying research approaches of the gas-kinetic unified algorithm can be provided to simulate complex hypersonic flow problems covering the whole of flow regimes.
LI Zhihui , WU Junlin , JIANG Xinyu , MA Qiang . A massively parallel algorithm for hypersonic covering various flow regimes to solve Boltzmann model equation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015 , 36(1) : 201 -212 . DOI: 10.7527/S1000-6893.2014.0219
[1] Tsien H S. Superaerodynamics,mechanics of rarefied gases[J]. Journal of Aeronautics Science, 1946, 13(12): 653-664.
[2] Whitehead A H, Jr. NASP aerodynamics, AIAA-1989-5013[R]. Reston: AIAA, 1989.
[3] Zhuang F G, Cui E J, Zhang H X. Some development of future spacecrafts and aerodynamics tasks[C]//Proceedings of First Aerodynamics and Aerothermodynamics. Beijing: National Defense Industry Press, 2006: 1-12 (in Chinese). 庄逢甘, 崔尔杰, 张涵信. 未来空间飞行器的某些发展和空气动力学的任务[C]//中国第一届近代空气动力学与气动热力学会议论文集. 北京: 国防工业出版社, 2006: 1-12.
[4] Chapmann S, Cowling T G. The mathematical theory of non-uniform gases[M]. 3rd ed. Cambridge: Cambridge University Press, 1990.
[5] Bhatnagar P L, Gross E P, Krook M. A model for collision processes in gases: I.small amplitude processes is charged and neutral one-component system[J].Physics of Review, 1954, 94: 511-525.
[6] Abe T, Oguchi H. A hierarchy kinetic model and its applications[C]//Potter J I. Rarefied Gas Dynamics. Reston: AIAA, 1977: 781-793.
[7] Shakhov E M. Kinetic model equations and numerical results[C]//Oguchi H. Proceedings of 14th International Symposium on Rarefied Gas Dynamics. Tokyo: University of Tokyo Press, 1984: 137-148.
[8] Yang J Y, Huang J C. Rarefied flow computations using nonlinear model Boltzmann equtions[J]. Journal of Computational Physics, 1995, 120(2): 323-339.
[9] Li Z H, Zhang H X. Study on gas kinetic algorithm for flows from rarefied transition to continuum[J]. Acta Aerodynamica Sinica, 2000, 18(3): 255-263 (in Chinese). 李志辉, 张涵信. 稀薄流到连续流的气体运动论统一数值算法初步研究[J]. 空气动力学学报, 2000, 18(3): 255-263.
[10] Mieussens L. Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries[J]. Journal of Computational Physics, 2000, 162(2): 429-466.
[11] Li Z H, Zhang H X. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J]. Journal of Computational Physics, 2004, 193(2): 708-738.
[12] Li Z H, Zhang H X. Study on gas kinetic numerical algorithm using Boltzmann model equation[J].Advances in Mechanics, 2005, 35(4): 559-576 (in Chinese). 李志辉, 张涵信. 基于Boltzmann模型方程的气体运动论统一算法研究[J]. 力学进展, 2005, 35(4): 559-576.
[13] Cercignani C. Kinetic theories and the Boltzmann equation[M]. Berlin: Springer-Verlag, 1984.
[14] Zhang H X, Shen M Y. Computational fluid dynamics—principle and application of difference method[M]. Beijing: National Defense Industry Press, 2003 (in Chinese). 张涵信, 沈孟育.计算流体力学——差分方法的原理和应用[M]. 北京: 国防工业出版社, 2003.
[15] Golub G H,Welsch J. Calculation of Gauss quadrature rules [J]. Mathematics of Computation, 1969, 23(106): 221-230.
[16] Li Z H, Zhang H X. HPF parallel computation based on Boltzmann model equation for flows past complex body from various flow regimes[J]. Acta Aeronautica et Astronautica Sinica, 2006, 27(2): 175-181 (in Chinese). 李志辉, 张涵信. 基于Boltzmann模型方程不同流区复杂三维绕流HPF并行计算[J]. 航空学报, 2006, 27(2): 175-181.
[17] Long L N, Kamon M, Myczkowski J. A massively parallel algorithm to solve the Boltzmann (BGK) equation,AIAA-1992-0563[R]. Reston: AIAA, 1992.
[18] Sharipov F. Hypersonic flow of rarefied gas near the Brazilian satellite during its reentry into atmosphere[J]. Brazilian Journal of Physics, 2003, 33(2): 398-405.
/
| 〈 |
|
〉 |
CJA