희박기체 유동 해석에 대한 CFD와 Kinetic 모델의 비교 연구 = A Comparative Study of CFD and Kinetic Models for Rarefied Gas Flows

국문 초록 (Abstract)

일반적으로 Navier-Stokes-Fourier 방정식에 근거한 Computational Fluid Dynamics (CFD) 방법은 연속체 영역에 적용되고, Boltzmann 방정식에 근거한 Direct Simulation Monte Carlo (DSMC) 방법은 희박기체 영역에 적용된다. 하지만 재진입 비행체와 같이 공기역학의 많은 문제는 국소적으로 밀도가 크게 변하는 멀티-스케일 희박 유동으로 알려져 있다. 멀티-스케일 희박 유동에 대해서는 CFD 방법만으로는 정확도 측면에서 한계가 있고, DSMC 방법만으로는 효율성 측면에서 제한이 있다. 최근 CFD와 DSMC 사이의 격차를 메우기 위해 대안적인 입자 시뮬레이션 기법들이 제시되고 있다. 가장 활발히 연구되고 있는 대상은 Bhatnagar-Gross-Krook (BGK) 방법과 Fokker-Planck (FP) 방법이 있다. 하지만 수치 방법들의 성능을 일관성 있게 평가하는 비교 연구는 아직 부족한 상황이다. 본 연구에서는 희박기체 유동 해석에 대해 CFD, DSMC, BGK, FP 방법을 적용하고 성능을 분석하였다.

다국어 초록 (Multilingual Abstract)

In practice, Computational Fluid Dynamics (CFD) based on the Navier-Stokes-Fourier equation is applied in the continuum regime, while Direct Simulation Monte Carlo (DSMC) based on the Boltzmann equation is applied in the rarefied regime. However, many aerodynamic engineering problems, such as re-entry vehicles, involve multi-scale rarefied gas flows where the density significantly varies locally. For multi-scale rarefied gas flows, CFD has limitations in terms of accuracy, while DSMC has limitations in terms of efficiency. Recently, alternative particle Monte Carlo methods have been proposed to bridge the gap between CFD and DSMC. These include the Bhatnagar-Gross-Krook (BGK) method and the Fokker-Planck (FP) method. However, there is a scarcity of comprehensive comparative studies to assess their performance. The present paper provides consistent comparison results among CFD, DSMC, BGK, and FP for rarefied gas flows.

참고문헌 (Reference)

• 1 Jenny, P., "solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion" 229 (229): 1077-1098, 2010
• 2 Maxwell, J. C., "VII. On stresses in rarifiedgases arising from inequalities of temperature" 170 : 231-256, 1879
• 3 McDonald, J. G., "Towards realizable hyperbolic moment closures for viscous heat-conducting gas flows based on a maximum-entropy distribution" 25 : 573-603, 2013
• 4 Gallis, M., "The application of the BGK model in particle simulations" 2360-, 2000
• 5 Struchtrup, H., "Regularization of Grad’s 13 moment equations: Derivation and linear analysis" 15 (15): 2668-2680, 2003
• 6 Guo, Z., "Progress of discrete unified gas-kinetic scheme for multiscale flows" 3 : 1-42, 2021
• 7 Pfeiffer, M., "Particle-based fluid dynamics:Comparison of different Bhatnagar-Gross-Krook models and the direct simulation Monte Carlo method for hypersonic flows" 30 (30): 2018
• 8 Lebowitz, J. L., "Nonequilibrium distribution functions in a fluid" 3 (3): 325-338, 1960
• 9 Cai, Z., "Moment method as a numerical solver : Challenge from shock structure problems" 444 : 110593-, 2021
• 10 Bird, G. A., "Molecular Gas Dynamics and the Direct Simulation of Gas Flows" Clarendon Press 1994
• 11 "Manual, UDF., ANSYS FLUENT 12.0, Theory Guide"
• 12 Struchtrup, H., "Macroscopic transport equations for rarefied gas flows" Springer 2005
• 13 Holway, L. H., "Kinetic theory of shock structure using an ellipsoidal distribution function" 1 : 193-, 1965
• 14 Kennard, E. H., "Kinetic theory of gases" McGraw-hill 1938
• 15 Xu, K, "Gas-kinetic finite volume methods, flux-vector splitting, and artificial diffusion" 120 (120): 48-65, 1995
• 16 Yao, S., "Extension of the Shakhov Bhatnagar–Gross–Krook model for nonequilibrium gas flows" 35 (35): 2023
• 17 Plimpton, S. J., "Direct simulation Monte Carlo on petaflop supercomputers and beyond" 31 (31): 2019
• 18 Jun, E., "Cubic Fokker–Planck method for rarefied monatomic gas flow through a slit and an orifice" 175 : 199-213, 2018
• 19 Jun, E., "Cubic Fokker-Planck-DSMC hybrid method for diatomic rarefied gas flow through a slit and an orifice" 159 : 125-133, 2019
• 20 Jun, E., "Cubic Fokker-Planck-DSMC hybrid method for diatomic gas flow through a slit" 2132 (2132): 2019
• 21 Kim, S., "Critical assessment of various particle Fokker–Planck models for monatomic rarefied gas flows" 35 (35): 2023
• 22 Jun, E., "Comparative study between cubic and ellipsoidal Fokker–Planck kinetic models" 57 (57): 2524-2533, 2019
• 23 Jun, E., "Assessment of the cubic Fokker–Planck–DSMC hybrid method for hypersonic rarefied flows past a cylinder" 168 : 1-13, 2018
• 24 Jun, E., "Assessment of the LD-DSMC hybrid method for hypersonic rarefied flow" 166 : 123-138, 2018
• 25 Jun, E., "Assessment of an all-particle hybrid method for hypersonic rarefied flow" 1203-, 2013
• 26 Kim, C., "Analysis and implementation of the gas-kinetic BGK scheme for computational gas dynamics" 25 (25): 21-49, 1997
• 27 Jun, E., "All-Particle Multiscale Computation of Hypersonic Rarefied Flow for Mars Entry" 1333 (1333): 557-562, 2011
• 28 Jun, E., "All-Particle Multiscale Computation of Hypersonic Rarefied Flow for Mars Entry" 822-, 2010
• 29 Kim, S., "A stochastic particle Fokker–Planck method with nonlinear production terms for a variable hard-sphere gas" 34 (34): 2022
• 30 Bhatnagar, P. L., "A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems" 94 (94): 511-, 1954
• 31 Wagner, W., "A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation" 66 : 1011-1044, 1992
• 32 Fei, F., "A benchmark study of kinetic models for shock waves" 58 (58): 2596-2608, 2020
• 33 Mathiaud, J., "A Fokker–Planck model of the Boltzmann equation with correct Prandtl number" 162 : 397-414, 2016