Advance in Unified Methods Based on Gas-Kinetic Theory

LIU Sha; WANG Yong; YUAN Rui-feng; ZHANG Rui; CHEN Jian-feng; ZHU Ya-jun; ZHUO Cong-shan; ZHONG Cheng-wen

doi:10.19527/j.cnki.2096-1642.0809

Volume 4 Issue 4

Jul. 2019

Turn off MathJax

Article Contents

Article Navigation > PHYSICS OF GASES > 2019 > 4(4): 1-13

LIU Sha, WANG Yong, YUAN Rui-feng, ZHANG Rui, CHEN Jian-feng, ZHU Ya-jun, ZHUO Cong-shan, ZHONG Cheng-wen. Advance in Unified Methods Based on Gas-Kinetic Theory[J]. PHYSICS OF GASES, 2019, 4(4): 1-13. doi: 10.19527/j.cnki.2096-1642.0809

Citation:

LIU Sha, WANG Yong, YUAN Rui-feng, ZHANG Rui, CHEN Jian-feng, ZHU Ya-jun, ZHUO Cong-shan, ZHONG Cheng-wen. Advance in Unified Methods Based on Gas-Kinetic Theory[J]. PHYSICS OF GASES, 2019, 4(4): 1-13. doi: 10.19527/j.cnki.2096-1642.0809

Citation:

PDF( 3158 KB)

Advance in Unified Methods Based on Gas-Kinetic Theory

doi: 10.19527/j.cnki.2096-1642.0809

1.
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
2.
Shenzhen Research Institute, The Hong Kong University of Science and Technology, Shenzhen 518057, China

Received Date: 20 Jun 2019
Revised Date: 02 Jul 2019
Published: 20 Jul 2019

Abstract

Abstract

In the scientific and engineering practices, such as the aerodynamic loads on near space aircrafts, the orbital transfer and attitude adjustment of spacecrafts, and the mass/heat transfer of micro-scale devices, there are a large amount of multi-regime (multi-scale) flows. The appearance of multi-regimes can be both sequential and spatial, and the latter one is recognized as the complicated local rarefied problem. Since the problem of multi-regime flows is a challenge to the numerical methods, a series of efficient methods which were designed to solve both the continuum flow and rarefied flow in a unified way were proposed in these years, such as the deterministic UGKS, GKUA and DUGKS methods, along with the USP-BGK and UGKWP methods in stochastic particle frameworks. In this paper, the deterministic unified methods and the stochastic unified methods were reviewed and discussed. For each method, the realization of its unified property was discussed along with the theoretical basis. The current advances, potential application value, and extendibility of each method were also discussed in this paper.

FullText(HTML)

References(93)

References

[1]	Bird G A. Molecular gas dynamics and the direct simulation of gas flows[M]. New York:Oxford University Press, 1994.
[2]	Xu K, Huang J C. A unified gas-kinetic scheme for continuum and rarefied flows[J]. Journal of Computational Physics, 2010, 229(20):7747-7764. doi: 10.1016/j.jcp.2010.06.032
[3]	Xu K. Direct modeling for computational fluid dynamics:construction and application of unified gas-kinetic sche-mes[M]. Hackensack:World Scientific, 2015.
[4]	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. doi: 10.3969/j.issn.0258-1825.2000.03.001 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). doi: 10.3969/j.issn.0258-1825.2000.03.001
[5]	Li Z H, Peng A P, Ma Q, et al. Gas-kinetic unified algorithm for computable modeling of Boltzmann equation and application to aerothermodynamics for falling disintegration of uncontrolled Tiangong-No.1 spacecraft[J]. Advances in Aerodynamics, 2019, 1:4. doi: 10.1186/s42774-019-0009-4
[6]	Guo Z L, Xu K, Wang R J. Discrete unified gas kinetic scheme for all Knudsen number flows:low-speed isother-mal case[J]. Physical Review E, 2013, 88(3):033305. doi: 10.1103/PhysRevE.88.033305
[7]	Guo Z L, Wang R J, Xu K. Discrete unified gas kinetic scheme for all Knudsen number flows. Ⅱ. Thermal compressible case[J]. Physical Review E, 2015, 91(3):033313. doi: 10.1103/PhysRevE.91.033313
[8]	Goldstein D, Sturtevant B, Broadwell J E. Investigations of the motion of discrete-velocity gases[R]. 1989: 100-117.
[9]	Yang J Y, Huang J C. Rarefied flow computations using nonlinear model Boltzmann equations[J]. Journal of Computational Physics, 1995, 120(2):323-339. doi: 10.1006/jcph.1995.1168
[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. doi: 10.1006/jcph.2000.6548
[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. doi: 10.1016-j.jcp.2003.08.022/
[12]	Titarev V A. Conservative numerical methods for model kinetic equations[J]. Computers & Fluids, 2007, 36(9):1446-1459. http://cn.bing.com/academic/profile?id=c6f7320c0f4765cd787bc6ce65fb33bf&encoded=0&v=paper_preview&mkt=zh-cn
[13]	Xu K, Huang J C. An improved unified gas-kinetic scheme and the study of shock structures[J]. IMA Journal of Applied Mathematics, 2011, 76(5):698-711. doi: 10.1093/imamat/hxr002
[14]	Bhatnagar P L, Gross E P, Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems[J]. Physical Review, 1954, 94(3):511-525. doi: 10.1103/PhysRev.94.511
[15]	Xu K, Liu C. A paradigm for modeling and computation of gas dynamics[J]. Physics of Fluids, 2017, 29(2):026101. doi: 10.1063/1.4974873
[16]	Huang J C, Xu K, Yu P B. A unified gas-kinetic scheme for continuum and rarefied flows Ⅲ:Microflow simula-tions[J]. Communications in Computational Physics, 2013, 14(5):1147-1173. doi: 10.4208/cicp.190912.080213a
[17]	Yu P B. A unified gas kinetic scheme for all Knudsen number flows[D]. Hong Kong: Hong Kong University of Science and Technology, 2013.
[18]	Liu S, Zhong C W, Bai J. Unified gas-kinetic scheme for microchannel and nanochannel flows[J]. Computers & Mathematics with Applications, 2015, 69(1):41-57. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=9d91c2625c0b4d57aa4a7cab46d76bbc
[19]	Wang R J, Xu X P, Xu K, et al. Onsager's cross coupling effects in gas flows confined to micro-channels[J]. Physical Review Fluids, 2016, 1(4):044102. doi: 10.1103/PhysRevFluids.1.044102
[20]	Huang J C, Xu K, Yu P B. A unified gas-kinetic scheme for continuum and rarefied flows Ⅱ:multi-dimensional cases[J]. Communications in Computational Physics, 2012, 12(3):662-690. doi: 10.4208/cicp.030511.220911a
[21]	Wang R J, Xu K. The study of sound wave propagation in rarefied gases using unified gas-kinetic scheme[J]. Acta Mechanica Sinica, 2012, 28(4):1022-1029. doi: 10.1007/s10409-012-0116-5
[22]	Wang R J, Xu K. Unified gas-kinetic simulation of slider air bearing[J]. Theoretical and Applied Mechanics Letters, 2014, 4(2):022001. doi: 10.1063/2.1402201
[23]	Liu C, Xu K, Sun Q H, et al. A unified gas-kinetic scheme for continuum and rarefied flows Ⅳ:Full Boltzmann and model equations[J]. Journal of Computational Physics, 2016, 314:305-340. doi: 10.1016/j.jcp.2016.03.014
[24]	Rykov V A. A model kinetic equation for a gas with rotational degrees of freedom[J]. Fluid Dynamics, 1975, 10(6):959-966. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=23b71099bce452a2e56f11d08fcb1562
[25]	Liu S, Yu P B, Xu K, et al. Unified gas-kinetic scheme for diatomic molecular simulations in all flow regimes[J]. Journal of Computational Physics, 2014, 259:96-113. doi: 10.1016/j.jcp.2013.11.030
[26]	刘沙.统一气体动理论格式研究[D].西安: 西北工业大学, 2015. http://cdmd.cnki.com.cn/Article/CDMD-10699-1015581075.htm Liu S. Unified gas-kinetic scheme[D]. Xi'an: Northwestern Polytechnical University, 2015(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10699-1015581075.htm
[27]	张贺.统一气体动理论格式分子振动模型研究[D].西安: 西北工业大学, 2015. Zhang H. A kinetic model with vibration for unified gas-kinetic scheme[D]. Xi'an: Northwestern Polytechnical University, 2015(in Chinese).
[28]	Wang Z, Yan H, Li Q B, et al. Unified gas-kinetic scheme for diatomic molecular flow with translational, rotational, and vibrational modes[J]. Journal of Computational Physics, 2017, 350:237-259. doi: 10.1016/j.jcp.2017.08.045
[29]	Li S Y, Li Q B. Thermal non-equilibrium effect of small-scale structures in compressible turbulence[J]. Modern Physics Letters B, 2018, 32(12n13):1840013. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=f7feaed9f999caabfb02c2541ea0b7a5
[30]	Chen S Z, Xu K, Lee C B. The dynamic mechanism of a moving Crookes radiometer[J]. Physics of Fluids, 2012, 24(11):111701. doi: 10.1063/1.4765353
[31]	Chen S Z, Xu K, Lee C B, et al. A unified gas kinetic scheme with moving mesh and velocity space adapta-tion[J]. Journal of Computational Physics, 2012, 231(20):6643-6664. doi: 10.1016/j.jcp.2012.05.019
[32]	Wang R J, Xu K. Unified gas-kinetic scheme for multi-species non-equilibrium flow[C]. AIP Conference Proceedings, 2014, 1628(1): 970-975.
[33]	Xiao T B, Xu K, Cai Q D. A unified gas-kinetic scheme for multiscale and multicomponent flow transport[J]. Applied Mathematics and Mechanics, 2019, 40(3):355-372. doi: 10.1007/s10483-019-2446-9
[34]	Liu C, Wang Z, Xu K. A unified gas-kinetic scheme for continuum and rarefied flows Ⅵ:Dilute disperse gas-particle multiphase system[J]. Journal of Computational Physics, 2019, 386:264-295. doi: 10.1016/j.jcp.2018.12.040
[35]	Xiao T B, Cai Q D, Xu K. A well-balanced unified gas-kinetic scheme for multiscale flow transport under gravitational field[J]. Journal of Computational Physics, 2017, 332:475-491. doi: 10.1016/j.jcp.2016.12.022
[36]	Xiao T B, Xu K, Cai Q D, et al. An investigation of non-equilibrium heat transport in a gas system under external force field[J]. International Journal of Heat and Mass Transfer, 2018, 126:362-379. doi: 10.1016/j.ijheatmasstransfer.2018.05.035
[37]	Sun W J, Jiang S, Xu K. An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations[J]. Journal of Computational Physics, 2015, 285:265-279. doi: 10.1016/j.jcp.2015.01.008
[38]	Sun W J, Jiang S, Xu K, et al. An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations[J]. Journal of Computational Physics, 2015, 302:222-238. doi: 10.1016/j.jcp.2015.09.002
[39]	Sun W J, Jiang S, Xu K. An asymptotic preserving implicit unified gas kinetic scheme for frequency-dependent radiative transfer equations[J]. International Journal of Numerical Analysis and Modeling, 2018, 15(1/2):134-153.
[40]	Sun W J, Jiang S, Xu K. Multiscale radiative transfer in cylindrical coordinates[J]. Communications on Applied Mathematics and Computation, 2019, 1(1):117-139. doi: 10.1007/s42967-019-0007-x
[41]	Zhen Y X, Xiao M, Ni G X. Multi-scale kinetic scheme for the collisional Vlasov-Poisson system[J]. Computers & Fluids, 2016, 140:289-296. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=001971e5187c8669e29e31728513e692
[42]	Liu C, Xu K. A unified gas kinetic scheme for continuum and rarefied flows Ⅴ:Multiscale and multi-component plasma transport[J]. Communications in Computational Physics, 2017, 22(5):1175-1223. doi: 10.4208/cicp.OA-2017-0102
[43]	Pan D X, Zhong C W, Zhuo C S, et al. A unified gas kinetic scheme for transport and collision effects in plasma[J]. Applied Sciences, 2018, 8(5):746. doi: 10.3390/app8050746
[44]	毛枚良, 江定武, 李锦, 等.气体动理学统一算法的隐式方法研究[J].力学学报, 2015, 47(5):822-829. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=lxxb201505013 Mao M L, Jiang D W, Li J, et al. Study on implicit implementation of the unified gas kinetic scheme[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5):822-829(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=lxxb201505013
[45]	Zhu Y J, Zhong C W, Xu K. Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes[J]. Journal of Computational Physics, 2016, 315:16-38. doi: 10.1016/j.jcp.2016.03.038
[46]	Zhu Y J, Zhong C W, Xu K. An implicit unified gas-kinetic scheme for unsteady flow in all Knudsen regimes[J]. Journal of Computational Physics, 2019, 386:190-217. doi: 10.1016/j.jcp.2019.01.033
[47]	Zhu Y J, Zhong C W, Xu K. Unified gas-kinetic scheme with multigrid convergence for rarefied flow study[J]. Physics of Fluids, 2017, 29(9):096102. doi: 10.1063/1.4994020
[48]	Chen S Z, Zhang C, Zhu L H, et al. A unified implicit scheme for kinetic model equations. Part I. Memory reduction technique[J]. Science Bulletin, 2017, 62(2):119-129. doi: 10.1016/j.scib.2016.12.010
[49]	Xiao T B, Xu K, Cai Q D. A velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows[J]. arXiv preprint arXiv: 1802.04972, 2018.
[50]	江定武.基于模型方程解析解的气体动理学算法研究[D].绵阳: 中国空气动力研究与发展中心, 2016. http://cdmd.cnki.com.cn/Article/CDMD-90113-1017018831.htm Jiang D W. Study of the gas kinetic scheme based on the analytical solution of model equation[D]. Mianyang: China Aerodynamics Research and Development Center, 2016(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-90113-1017018831.htm
[51]	Li S Y, Li Q B, Fu S, et al. The high performance parallel algorithm for unified gas-kinetic scheme[C]. AIP Conference Proceedings, 2016, 1786(1): 180007.
[52]	陆林生, 董超群, 李志辉.多相空间数值模拟并行化研究[J].计算机科学, 2003, 30(3):129-137. doi: 10.3969/j.issn.1002-137X.2003.03.037 Lu L S, Dong C Q, Li Z H. Research on parallelization of multiphase space numerical simulation[J]. Computer Science, 2003, 30(3):129-137(in Chinese). doi: 10.3969/j.issn.1002-137X.2003.03.037
[53]	Li S Y, Li Q B, Fu S, et al. A unified gas-kinetic scheme for axisymmetric flow in all Knudsen number regimes[J]. Journal of Computational Physics, 2018, 366:144-169. doi: 10.1016/j.jcp.2018.04.004
[54]	Wang P, Zhu L H, Guo Z L, et al. A comparative study of LBE and DUGKS methods for nearly incompressible flows[J]. Communications in Computational Physics, 2015, 17(3):657-681. doi: 10.4208/cicp.240614.171014a
[55]	Bardow A, Karlin I V, Gusev A A. General characteristic-based algorithm for off-lattice Boltzmann simulations[J]. Europhysics Letters, 2006, 75(3):434-440. doi: 10.1209/epl/i2006-10138-1
[56]	Zhu L H, Wang P, Guo Z L. Performance evaluation of the general characteristics based off-lattice Boltzmann scheme and DUGKS for low speed continuum flows[J]. Journal of Computational Physics, 2017, 333:227-246. doi: 10.1016/j.jcp.2016.11.051
[57]	Zhu L H, Guo Z L, Xu K. Discrete unified gas kinetic scheme on unstructured meshes[J]. Computers & Fluids, 2016, 127:211-225. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=e15d697b3c5333e5499634f723759864
[58]	Wu C, Shi B C, Shu C, et al. Third-order discrete unified gas kinetic scheme for continuum and rarefied flows:Low-speed isothermal case[J]. Physical Review E, 2018, 97(2):023306. doi: 10.1103/PhysRevE.97.023306
[59]	Wu C, Shi B C, Chai Z H, et al. Discrete unified gas kinetic scheme with a force term for incompressible fluid flows[J]. Computers & Mathematics with Applications, 2016, 71(12):2608-2629. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=b1c718765ba1815af44ee789924288ed
[60]	Pan D X, Zhong C W, Zhuo C S. An implicit discrete unified gas-kinetic scheme for simulations of steady flow in all flow regimes[J]. Communications in Computational Physics, 2019, 25(5):1469-1495.
[61]	Yuan R F, Zhong C W. A conservative implicit scheme for steady state solutions of diatomic gas flow in all flow regimes[J]. arXiv preprint arXiv: 1810.13039, 2018.
[62]	Yuan R F, Zhong C W. A multi-prediction implicit scheme for steady state solutions of gas flow in all flow regimes[J]. arXiv preprint arXiv: 1905.06629, 2019.
[63]	Mittal R, Iaccarino G. Immersed boundary methods[J]. Annual Review of Fluid Mechanics, 2005, 37:239-261. doi: 10.1146/annurev.fluid.37.061903.175743
[64]	Li C, Wang L P. An immersed boundary-discrete unified gas kinetic scheme for simulating natural convection involving curved surfaces[J]. International Journal of Heat and Mass Transfer, 2018, 126:1059-1070. doi: 10.1016/j.ijheatmasstransfer.2018.04.166
[65]	Tao S, Chen B M, Yang X P, et al. Second-order accurate immersed boundary-discrete unified gas kinetic scheme for fluid-particle flows[J]. Computers & Fluids, 2018, 165:54-63. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=2deab7ab04a6c0e26d6c2cf1d20ef244
[66]	Tao S, Zhang H L, Guo Z L, et al. A combined immersed boundary and discrete unified gas kinetic scheme for particle-fluid flows[J]. Journal of Computational Physics, 2018, 375:498-518. doi: 10.1016/j.jcp.2018.08.047
[67]	Tao S, He Q, Wang L, et al. A non-iterative direct-forcing immersed boundary method for thermal discrete unified gas kinetic scheme with Dirichlet boundary condi-tions[J]. International Journal of Heat and Mass Transfer, 2019, 137:476-488. doi: 10.1016/j.ijheatmasstransfer.2019.03.147
[68]	Wang P, Wang L P, Guo Z L. Comparison of the lattice Boltzmann equation and discrete unified gas-kinetic sche-me methods for direct numerical simulation of decaying turbulent flows[J]. Physical Review E, 2016, 94(4):043304. doi: 10.1103/PhysRevE.94.043304
[69]	Bo Y T, Wang P, Guo Z L, et al. DUGKS simulations of three-dimensional Taylor-Green vortex flow and turbulent channel flow[J]. Computers & Fluids, 2017, 155:9-21. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=e0b218826c18d6c4e9104761e30fc657
[70]	Liu H T, Kong M C, Chen Q, et al. Coupled discrete unified gas kinetic scheme for the thermal compressible flows in all Knudsen number regimes[J]. Physical Review E, 2018, 98(5):053310. doi: 10.1103/PhysRevE.98.053310
[71]	Zhang Y, Zhu L H, Wang R J, et al. Discrete unified gas kinetic scheme for all Knudsen number flows. Ⅲ. Binary gas mixtures of Maxwell molecules[J]. Physical Review E, 2018, 97(5):053306. doi: 10.1103/PhysRevE.97.053306
[72]	Zhang Y, Zhu L H, Wang P, et al. Discrete unified gas kinetic scheme for flows of binary gas mixture based on the McCormack model[J]. Physics of Fluids, 2019, 31(1):017101. doi: 10.1063/1.5063846
[73]	Huo Y T, Rao Z H. The discrete unified gas kinetic scheme for solid-liquid phase change problem[J]. International Communications in Heat and Mass Transfer, 2018, 91:187-195. doi: 10.1016/j.icheatmasstransfer.2017.12.018
[74]	Zhang C H, Yang K, Guo Z L. A discrete unified gas-kinetic scheme for immiscible two-phase flows[J]. International Journal of Heat and Mass Transfer, 2018, 126:1326-1336. doi: 10.1016/j.ijheatmasstransfer.2018.06.016
[75]	Yang Z R, Zhong C W, Zhuo C S. Phase-field method based on discrete unified gas-kinetic scheme for large-density-ratio two-phase flows[J]. Physical Review E, 2019, 99(4):043302. doi: 10.1103/PhysRevE.99.043302
[76]	McCormack F J. Construction of linearized kinetic models for gaseous mixtures and molecular gases[J]. Physics of Fluids, 1973, 16(12):2095-2105. doi: 10.1063/1.1694272
[77]	Guo Z L, Xu K. Discrete unified gas kinetic scheme for multiscale heat transfer based on the phonon Boltzmann transport equation[J]. International Journal of Heat and Mass Transfer, 2016, 102:944-958. doi: 10.1016/j.ijheatmasstransfer.2016.06.088
[78]	Luo X P, Yi H L. A discrete unified gas kinetic scheme for phonon Boltzmann transport equation accounting for phonon dispersion and polarization[J]. International Journal of Heat and Mass Transfer, 2017, 114:970-980. doi: 10.1016/j.ijheatmasstransfer.2017.06.127
[79]	Zhang C, Guo Z L. Discrete unified gas kinetic scheme for multiscale heat transfer with arbitrary temperature difference[J]. International Journal of Heat and Mass Transfer, 2019, 134:1127-1136. doi: 10.1016/j.ijheatmasstransfer.2019.02.056
[80]	Liu H T, Cao Y, Chen Q, et al. A conserved discrete unified gas kinetic scheme for microchannel gas flows in all flow regimes[J]. Computers & Fluids, 2018, 167:313-323. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=24e3f81c66683ec6bcfa0da08e77cace
[81]	Wang Y, Zhong C W. An ALE-type discrete unified gas kinetic scheme for low-speed continuum and rarefied flow simulations with moving boundaries[J]. arXiv preprint arXiv: 1906.01813, 2019.
[82]	Macrossan M N. A particle simulation method for the BGK equation[C]. AIP Conference Proceedings, 2001, 585(1): 426-433.
[83]	Gallis M A, Torczynski J R. The application of the BGK model in particle simulations[R]. AIAA 2000-2360, 2000.
[84]	Zhang J, John B, Pfeiffer M, et al. Particle-based hybrid and multiscale methods for nonequilibrium gas flows[J]. Advances in Aerodynamics, 2019, 1:12. doi: 10.1186/s42774-019-0014-7
[85]	Holway L H Jr. New statistical models for kinetic theory:methods of construction[J]. Physics of Fluids, 1966, 9(9):1658-1673. doi: 10.1063/1.1761920
[86]	Shakhov E M. Generalization of the Krook kinetic relaxation equation[J]. Fluid Dynamics, 1968, 3(5):95-96.
[87]	Chen S Z, Xu K, Cai Q D. A comparison and unification of ellipsoidal statistical and shakhov BGK models[J]. Advances in Applied Mathematics and Mechanics, 2015, 7(2):245-266. doi: 10.4208/aamm.2014.m559
[88]	Pfeiffer M. Particle-based fluid dynamics:comparison of different Bhatnagar-Gross-Krook models and the direct simulation Monte Carlo method for hypersonic flows[J]. Physics of Fluids, 2018, 30(10):106106. doi: 10.1063/1.5042016
[89]	Tumuklu O, Li Z, Levin D A. Particle ellipsoidal statistical Bhatnagar-Gross-Krook approach for simulation of hypersonic shocks[J]. AIAA Journal, 2016, 54(12):3701-3716. doi: 10.2514/1.J054837
[90]	Pfeiffer M. Extending the particle ellipsoidal statistical Bhatnagar-Gross-Krook method to diatomic molecules including quantized vibrational energies[J]. Physics of Fluids, 2018, 30(11):116103. doi: 10.1063/1.5054961
[91]	Fei F, Zhang J, Li J, et al. A Unified stochastic particle Bhatnagar-gross-Krook method for multiscale gas flows[J]. arXiv preprint arXiv: 1808.03801, 2018.
[92]	Liu C, Zhu Y J, Xu K. Unified gas-kinetic wave-particle methods I: continuum and rarefied gas flow[J]. arXiv preprint arXiv: 1811.07141, 2018.
[93]	Zhu Y J, Liu C, Zhong C W, et al. Unified gas-kinetic wave-particle methods. Ⅱ. Multiscale simulation on unstructured mesh[J]. Physics of Fluids, 2019, 31(6):067105. doi: 10.1063/1.5097645

Relative Articles

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(11) / Tables(2)

Get Citation

PDF

XML

Article Metrics

Article views (286) PDF downloads(21)

Supervised by：	China Aerospace Science and Technology Corporation
Sponsored by：	China Academy of Aerospace Aerodynamics Chinese Society of Astronautics China Aerospace Publishing House Co., LTD

Advance in Unified Methods Based on Gas-Kinetic Theory

doi: 10.19527/j.cnki.2096-1642.0809

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Proportional views

Related

Contact Us

Links

Advance in Unified Methods Based on Gas-Kinetic Theory

doi: 10.19527/j.cnki.2096-1642.0809

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Proportional views

Related

Contact Us

Links

Export File

Citation

Format

Content