메뉴 건너뛰기




Volumn 12, Issue 3, 2012, Pages 662-690

A unified gas-kinetic scheme for continuum and rarefied flows II: Multi-dimensional cases

Author keywords

Navier Stokes solution; Non equilibrium flow; Unified scheme

Indexed keywords


EID: 84863229215     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.030511.220911a     Document Type: Article
Times cited : (197)

References (34)
  • 3
    • 40249113010 scopus 로고    scopus 로고
    • Uniformly stable numerical schemes for the boltzmann equation preserving the compressible navier-stokes asymptotics
    • M. Bennoune, M. Lemou, and L. Mieussens, Uniformly Stable Numerical Schemes for the Boltzmann Equation Preserving the Compressible Navier-Stokes Asymptotics, J. Comput. Phys. 227 (2008), pp. 3781-3803.
    • (2008) J. Comput. Phys. , vol.227 , pp. 3781-3803
    • Bennoune, M.1    Lemou, M.2    Mieussens, L.3
  • 4
    • 26344468007 scopus 로고
    • A model for collision processes in gases i: Small amplitude processes in charged and neutral one-component systems
    • P. L. Bhatnagar, E. P. Gross, and M. Krook, A Model for Collision Processes in Gases I: Small Amplitude Processes in Charged and Neutral One-Component Systems, Phys. Rev. 94 (1954), pp. 511-525.
    • (1954) Phys. Rev. , vol.94 , pp. 511-525
    • Bhatnagar, P.L.1    Gross, E.P.2    Krook, M.3
  • 7
    • 0002854033 scopus 로고
    • Kinetic-theoretic description of the formation of a shock wave
    • C. K. Chu, Kinetic-Theoretic Description of the Formation of a Shock Wave, Phys. Fluids 8 (1965),pp. 12-22.
    • (1965) Phys. Fluids , vol.8 , pp. 12-22
    • Chu, C.K.1
  • 8
    • 34548537653 scopus 로고    scopus 로고
    • Macroscopic fluid models with localized kinetic upscaling effects
    • DOI 10.1137/060651574
    • P. Degond, J. G. Liu, and L. Mieussens, Macroscopic Fluid Models with Localized Kinetic Upscale Effects, Multiscale Model. Simul. 5 (2006), pp. 940-979. (Pubitemid 47381817)
    • (2006) Multiscale Modeling and Simulation , vol.5 , Issue.3 , pp. 940-979
    • Degond, P.1    Liu, J.-G.2    Mieussens, L.3
  • 9
    • 77955511586 scopus 로고    scopus 로고
    • A Class of Asymptotic Preserving Schemes for Kinetic Equations and related problems with stiff sources
    • F. Filbet and S. Jin, A Class of Asymptotic Preserving Schemes for Kinetic Equations and related problems with stiff sources, J. Comput. Phys. 229 (2010), pp. 7625-7648.
    • (2010) J. Comput. Phys. , vol.229 , pp. 7625-7648
    • Filbet, F.1    Jin, S.2
  • 10
    • 49049143188 scopus 로고
    • High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
    • U. Ghia, K. N. Ghia, and C. T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys. 48 (1982), pp. 387-411.
    • (1982) J Comput. Phys. , vol.48 , pp. 387-411
    • Ghia, U.1    Ghia, K.N.2    Shin, C.T.3
  • 11
    • 41249103695 scopus 로고    scopus 로고
    • A comparative study of the LBM and GKS methods for 2D near incompressible flows
    • Z. L. Guo, H. W. Liu, L. S. Luo, and K. Xu, A comparative study of the LBM and GKS methods for 2D near incompressible flows, J. Comput. Phys. 227 (2008), pp. 4955-4976.
    • (2008) J. Comput. Phys. , vol.227 , pp. 4955-4976
    • Guo, Z.L.1    Liu, H.W.2    Luo, L.S.3    Xu, K.4
  • 12
    • 79954616401 scopus 로고    scopus 로고
    • Effects of incomplete surface accommodation on non- equilibrium heat transfer in cavity flow: A parallel DSMC study
    • B. John, X. J. Gu, and D. R. Emerson, Effects of incomplete surface accommodation on non- equilibrium heat transfer in cavity flow: A parallel DSMC study, Comput. Fluids 45 (2011), pp. 197-201.
    • (2011) Comput Fluids , vol.45 , pp. 197-201
    • John, B.1    Gu, X.J.2    Emerson, D.R.3
  • 14
    • 33947143699 scopus 로고    scopus 로고
    • Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement
    • V. I. Kolobov, R. R. Arslanbekov, V. V. Aristov, A. A. Frolova, and S. A. Zabelok, Unified Solver for Rarefied and Continuum Flows with Adaptive Mesh and Algorithm Refinement, J. Comput. Phys. 223; 2007: 589-608.
    • (2007) J. Comput. Phys , vol.223 , pp. 589-608
    • Kolobov, V.I.1    Arslanbekov, R.R.2    Aristov, V.V.3    Frolova, A.A.4    Zabelok, S.A.5
  • 15
    • 79955670511 scopus 로고    scopus 로고
    • Comparison of the generalized Riemann solver and the gas- kinetic scheme for inviscid compressible flow simulations
    • J. Q. Li, Q. B. Li, and K. Xu, Comparison of the generalized Riemann solver and the gas- kinetic scheme for inviscid compressible flow simulations, J. Comput. Phys. 230 (2011), pp. 5080-5099.
    • (2011) J. Comput. Phys. , vol.230 , pp. 5080-5099
    • Li, J.Q.1    Li, Q.B.2    Xu, K.3
  • 16
    • 33750984215 scopus 로고    scopus 로고
    • On the multidimensional gas-kinetic BGK scheme
    • DOI 10.1016/j.jcp.2006.07.010, PII S0021999106003469
    • Q. B. Li and S. Fu, On the Multidimensional Gas-Kinetic BGK Scheme, J. Comput. Phys. 220 (2006), pp. 532-548. (Pubitemid 44742745)
    • (2006) Journal of Computational Physics , vol.220 , Issue.1 , pp. 532-548
    • Li, Q.1    Fu, S.2
  • 17
    • 77955277481 scopus 로고    scopus 로고
    • A high-order gas-kinetic navier-stokes solver
    • Q. B. Li, K. Xu, and S. Fu, A High-Order Gas-Kinetic Navier-Stokes Solver, J. Comput. Phys. 229 (2010), pp. 6715-6731.
    • (2010) J. Comput Phys. , vol.229 , pp. 6715-6731
    • Li, Q.B.1    Xu, K.2    Fu, S.3
  • 18
    • 58149156387 scopus 로고    scopus 로고
    • Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry
    • Z. H. Li and H. X. Zhang, Gas-Kinetic Numerical Studies of Three-Dimensional Complex Flows on Spacecraft Re-Entry, J. Comput. Phys. 228 (2009), pp. 1116-1138.
    • (2009) J Comput. Phys. , vol.228 , pp. 1116-1138
    • Li, Z.H.1    Zhang, H.X.2
  • 19
    • 0037582806 scopus 로고
    • Cylinder drag in the transition from continuum to free- molecule flow
    • G. J. Maslach, and S. A. Schaaf, Cylinder Drag in the Transition from Continuum to Free- Molecule Flow, Phys. Fluids 6 (3) (1963), pp. 315-321.
    • (1963) Phys Fluids , vol.6 , Issue.3 , pp. 315-321
    • Maslach, G.J.1    Schaaf, S.A.2
  • 21
    • 0037812320 scopus 로고    scopus 로고
    • Discrete-velocity models and numerical schemes for the boltzmann-bgk equtaion in plane and axisymmetric geometries
    • L. Mieussens, Discrete-Velocity Models and Numerical Schemes for the Boltzmann-BGK Equtaion in Plane and Axisymmetric Geometries, J. Comput. Phys. 162 (2000), pp. 429-466.
    • (2000) J. Comput. Phys. , vol.162 , pp. 429-466
    • Mieussens, L.1
  • 22
    • 34347248072 scopus 로고    scopus 로고
    • Implicit-explicit schemes for BGK kinetic equations
    • DOI 10.1007/s10915-006-9116-6
    • S. Pieraccini and G. Puppo, Implicit-Explicit Schemes for BGK Kinetic Equations, J. Scientific Computing 32 (2007), pp. 1-28. (Pubitemid 46994619)
    • (2007) Journal of Scientific Computing , vol.32 , Issue.1 , pp. 1-28
    • Pieraccini, S.1    Puppo, G.2
  • 23
    • 28144457666 scopus 로고
    • Numerical hydrodynamics from gas-kinetic theory
    • K. H. Prendergast and K. Xu, Numerical Hydrodynamics from Gas-Kinetic Theory J. Comput. Phys. 109 (1993), pp. 53-66.
    • (1993) J. Comput. Phys. , vol.109 , pp. 53-66
    • Prendergast, K.H.1    Xu, K.2
  • 24
    • 34250475794 scopus 로고
    • Generalization of the Krook kinetic Equation
    • E.M. Shakhov, Generalization of the Krook kinetic Equation, Fluid Dyn. 3,95 (1968).
    • (1968) Fluid Dyn. , vol.3 , pp. 95
    • Shakhov, E.M.1
  • 25
    • 0002597072 scopus 로고    scopus 로고
    • Low-speed flow simulation by the gas-kinetic scheme
    • M. D. Su, K. Xu, and M. S. Ghidaoui, Low-Speed Flow Simulation by the Gas-Kinetic Scheme, J. Comput. Phys. 150 (1999), pp. 17-39.
    • (1999) J Comput. Phys. , vol.150 , pp. 17-39
    • Su, M.D.1    Xu, K.2    Ghidaoui, M.S.3
  • 27
    • 0001445852 scopus 로고    scopus 로고
    • A gas-kinetic bgk scheme for the navier-stokes equations and its connection with artificial dissipation and godunov method
    • DOI 10.1006/jcph.2001.6790
    • K. Xu, A Gas-Kinetic BGK Scheme for the Navier-Stokes Equations and Its Connection with Artificial Dissipation and Godunov Method, J. Comput. Phys. 171 (2001), pp. 289-335. (Pubitemid 33667120)
    • (2001) Journal of Computational Physics , vol.171 , Issue.1 , pp. 289-335
    • Xu, K.1
  • 28
    • 0041856299 scopus 로고    scopus 로고
    • Lattice boltzmann method and gas-kinetic bgk scheme in the low- mach number viscous flow simulations
    • K. Xu, and X. Y. He, Lattice Boltzmann Method and Gas-Kinetic BGK Scheme in the Low- Mach Number Viscous Flow Simulations, J. Comput. Phys. 190 (1) (2003), pp.100-117.
    • (2003) J Comput. Phys. , vol.190 , Issue.1 , pp. 100-117
    • Xu, K.1    He, X.Y.2
  • 29
    • 13644273552 scopus 로고    scopus 로고
    • A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow
    • DOI 10.1016/j.jcp.2004.09.001, PII S0021999104003845
    • K. Xu, M. L. Mao, and L. Tang, A Multidimensional Gas-Kinetic BGK Scheme for Hypersonic Viscous Flow, J. Comput. Phys. 203 (2005), pp. 405-421. (Pubitemid 40233510)
    • (2005) Journal of Computational Physics , vol.203 , Issue.2 , pp. 405-421
    • Xu, K.1    Mao, M.2    Tang, L.3
  • 30
    • 77955514180 scopus 로고    scopus 로고
    • A unified gas-kinetic scheme for continuum and rarefied flows
    • K. Xu and J. C. Huang, A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows J. Comput. Phys. 229 (2010), pp. 7747-7764.
    • (2010) J. Comput. Phys. , vol.229 , pp. 7747-7764
    • Xu, K.1    Huang, J.C.2
  • 31
    • 80053245968 scopus 로고    scopus 로고
    • An improved unified gas-kinetic scheme and the study of shock structures
    • K. Xu and J. C. Huang, An Improved Unified Gas-Kinetic Scheme and the Study of Shock Structures, IMA J. Appl. Math. 76 (2011), pp. 698-711.
    • (2011) IMA J. Appl. Math. , vol.76 , pp. 698-711
    • Xu, K.1    Huang, J.C.2
  • 32
    • 0003067035 scopus 로고
    • Gas-kinetic finite volume methods, flux-vector split- ting and artificial diffusion
    • K. Xu, L. Martinelli, and A. Jameson, Gas-kinetic Finite Volume Methods, Flux-Vector Split- ting and Artificial Diffusion, J. Comput. Phys. 120 (1995), pp. 48-65.
    • (1995) J Comput. Phys. , vol.120 , pp. 48-65
    • Xu, K.1    Martinelli, L.2    Jameson, A.3
  • 33
    • 0003159177 scopus 로고
    • Numerical navier-stokes solutions from gas kinetic theory
    • DOI 10.1006/jcph.1994.1145
    • K. Xu and K. Prendergast, Numerical Navier-Stokes Solutions from Gas-Kinetic Theory, J. Comput. Phys. 114 (1994), pp. 9-17. (Pubitemid 124013468)
    • (1994) Journal of Computational Physics , vol.114 , Issue.1 , pp. 9-17
    • Xu, K.1
  • 34
    • 0011008052 scopus 로고
    • Rarefied flow computations using nonlinear model boltzmann equations
    • J. Y. Yang and J. C. Huang, Rarefied Flow Computations Using Nonlinear Model Boltzmann Equations, J. Comput. Phys. 120 (1995), pp. 323-339.
    • (1995) J Comput. Phys. , vol.120 , pp. 323-339
    • Yang, J.Y.1    Huang, J.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.