메뉴 건너뛰기




Volumn 223, Issue 2, 2007, Pages 589-608

Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement

Author keywords

Adaptive mesh and algorithm refinement; Boltzmann kinetic equation; Hybrid methods; Rarefied gas dynamics; Unified flow solver

Indexed keywords

BOLTZMANN EQUATION; COMPUTATIONAL EFFICIENCY; COMPUTATIONAL FLUID DYNAMICS; CONTINUUM MECHANICS; DOMAIN DECOMPOSITION METHODS; FLOW SIMULATION; INTEGRAL EQUATIONS; KINETIC THEORY; KINETICS; TRANSPORT PROPERTIES;

EID: 33947143699     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.09.021     Document Type: Article
Times cited : (258)

References (66)
  • 1
    • 24144458425 scopus 로고    scopus 로고
    • A discussion of hybrid atomistic-continuum methods for multiscale hydrodynamics
    • Wijesinghe H.S., and Hadjiconstantinou N.G. A discussion of hybrid atomistic-continuum methods for multiscale hydrodynamics. Int. J. Multiscale Comput. Eng. 2 (2004) 189
    • (2004) Int. J. Multiscale Comput. Eng. , vol.2 , pp. 189
    • Wijesinghe, H.S.1    Hadjiconstantinou, N.G.2
  • 3
    • 0011150327 scopus 로고
    • Development of a hybrid scheme and its application to a flat plate flow
    • Harvey J., and Lord G. (Eds), Oxford University Press, Oxford
    • Eggers J., and Beylich A.E. Development of a hybrid scheme and its application to a flat plate flow. In: Harvey J., and Lord G. (Eds). Proceedings of the 19th International Symposium on Rarefied Gas Dynamics vol. 2 (1995), Oxford University Press, Oxford 1216-1222
    • (1995) Proceedings of the 19th International Symposium on Rarefied Gas Dynamics , vol.2 , pp. 1216-1222
    • Eggers, J.1    Beylich, A.E.2
  • 4
    • 0030240034 scopus 로고    scopus 로고
    • Coupling Boltzmann and Navier-Stokes equations by friction
    • Bourgat J.F., Le Tallec P., and Tidriri M.D. Coupling Boltzmann and Navier-Stokes equations by friction. J. Comput. Phys. 127 (1996) 227
    • (1996) J. Comput. Phys. , vol.127 , pp. 227
    • Bourgat, J.F.1    Le Tallec, P.2    Tidriri, M.D.3
  • 5
    • 85190801756 scopus 로고    scopus 로고
    • D.C. Wadsworth, D.A. Erwin, Two-dimensional hybrid continuum/particle approach for rarefied flows, AIAA paper 92-2975, 1992.
  • 6
    • 0032540143 scopus 로고    scopus 로고
    • An adaptive domain decomposition procedure for Boltzmann and Euler equations
    • Tiwari S., and Klar A. An adaptive domain decomposition procedure for Boltzmann and Euler equations. J. Comput. Appl. Math. 90 (1998) 223
    • (1998) J. Comput. Appl. Math. , vol.90 , pp. 223
    • Tiwari, S.1    Klar, A.2
  • 7
    • 0031236545 scopus 로고    scopus 로고
    • Coupling Boltzmann and Navier-Stokes equations by half fluxes
    • Le Tallec P., and Mallinger F. Coupling Boltzmann and Navier-Stokes equations by half fluxes. J. Comput. Phys. 136 (1997) 51
    • (1997) J. Comput. Phys. , vol.136 , pp. 51
    • Le Tallec, P.1    Mallinger, F.2
  • 8
    • 0000399532 scopus 로고    scopus 로고
    • Coupling of the Boltzmann and Euler equations with automatic domain decomposition
    • Tiwari S. Coupling of the Boltzmann and Euler equations with automatic domain decomposition. J. Comput. Phys. 144 (1998) 710
    • (1998) J. Comput. Phys. , vol.144 , pp. 710
    • Tiwari, S.1
  • 9
    • 85190779307 scopus 로고    scopus 로고
    • T.Ohsawa, T.Ohwada, Deterministic hybrid computation of rarefied gas flows, RGD23, in: Andrew D. Ketsdever, E.P. Munz (Eds.), Rarefied Gas Dynamics: 23rd International Symposium, AIP Conference Proceedings, vol. 663, 2003, pp. 931-938.
  • 10
    • 85190794502 scopus 로고    scopus 로고
    • H.A. Carlson, R.Roveda, I.D. Boyd, G.V. Candler, A hybrid CFD-DSMC method of modeling continuum-rarefied flows, AIAA paper 2004-1180.
  • 11
    • 11144347132 scopus 로고    scopus 로고
    • Three-dimensional hybrid continuum-atomistic simulations for multiscale hydrodynamics
    • Wijesinghe H.S., Hornung R., Garsia A.L., and Hadjiconstantinou H.N. Three-dimensional hybrid continuum-atomistic simulations for multiscale hydrodynamics. J. Fluids Eng. 126 (2004) 768-777
    • (2004) J. Fluids Eng. , vol.126 , pp. 768-777
    • Wijesinghe, H.S.1    Hornung, R.2    Garsia, A.L.3    Hadjiconstantinou, H.N.4
  • 12
    • 33947186128 scopus 로고    scopus 로고
    • Numerical simulation for gas microflows using Boltzmann equation
    • Morinishi K. Numerical simulation for gas microflows using Boltzmann equation. Comput. Fluids 70 (2005) 303
    • (2005) Comput. Fluids , vol.70 , pp. 303
    • Morinishi, K.1
  • 13
    • 4544253987 scopus 로고    scopus 로고
    • A hybrid kinetic/fluid models for solving the gas dynamics Boltzmann-BGK equation
    • Crouseilles N., Degond P., and Lemou M. A hybrid kinetic/fluid models for solving the gas dynamics Boltzmann-BGK equation. J. Comput. Phys. 199 (2004) 776
    • (2004) J. Comput. Phys. , vol.199 , pp. 776
    • Crouseilles, N.1    Degond, P.2    Lemou, M.3
  • 14
    • 0034045486 scopus 로고    scopus 로고
    • Solving the kinetic equation for all Knudsen numbers
    • Beylich A.E. Solving the kinetic equation for all Knudsen numbers. Phys. Fluids 12 (2000) 444
    • (2000) Phys. Fluids , vol.12 , pp. 444
    • Beylich, A.E.1
  • 15
    • 0036675590 scopus 로고    scopus 로고
    • Kinetics of thermalization in shock waves
    • Beylich A.E. Kinetics of thermalization in shock waves. Phys. Fluids 14 (2002) 2683
    • (2002) Phys. Fluids , vol.14 , pp. 2683
    • Beylich, A.E.1
  • 16
    • 0000383154 scopus 로고    scopus 로고
    • Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
    • Garsia A.L., B Bell J., Crutchfield W.Y., and Alder B.J. Adaptive mesh and algorithm refinement using direct simulation Monte Carlo. J. Comput. Phys. 54 (1999) 134
    • (1999) J. Comput. Phys. , vol.54 , pp. 134
    • Garsia, A.L.1    B Bell, J.2    Crutchfield, W.Y.3    Alder, B.J.4
  • 17
    • 85190771297 scopus 로고    scopus 로고
    • D.B. Hash, H.A. Hassan, Two-dimensional coupling issues of hybrid DSMC/Navier-Stokes solvers, AIAA paper 97-2507, 1997.
  • 18
    • 85190800792 scopus 로고    scopus 로고
    • H.A. Carlson, R.Roveda, I.D. Boyd, G.V. Candler, A hybrid CFD-DSMC method of modeling continuum-rarefied flows, AIAA paper 2004-1180, 2004.
  • 19
    • 85190770199 scopus 로고    scopus 로고
    • V.V. Aristov, A.A. Frolova, S.A. Zabelok, V.I. Kolobov, S.A. Bayyuk, R.R. Arslanbekov, Coupling direct Boltzmann and continuum flow solvers, in: M.Capitelli (Ed.), Rarefied Gas Dynamics, AIP Conference Proceedings, vol. 762, NY, 2005, pp. 96-101.
  • 21
    • 85190790071 scopus 로고    scopus 로고
    • F.G. Tcheremissine, Direct numerical solution of the Boltzmann equation, in: M. Capitelli (Ed.), Rarefied Gas Dynamics, AIP Conference Proceedings, NY, vol. 762, 2005, pp. 677-685.
  • 22
    • 85190808585 scopus 로고    scopus 로고
    • S.P. Popov, F.G. Tcheremissine, Method of joint solution of the Boltzmann and Navier-Stokes equations, in: M. Capitelli (Ed.), Rarefied Gas Dynamics, AIP Conference Proceedings, NY, vol. 762, 2005, pp. 82-87.
  • 23
    • 0001445852 scopus 로고    scopus 로고
    • A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method
    • Xu K. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method. J. Comput. Phys. 171 (2001) 289-335
    • (2001) J. Comput. Phys. , vol.171 , pp. 289-335
    • Xu, K.1
  • 24
    • 26944487244 scopus 로고    scopus 로고
    • Simple derivation of high-resolution schemes for compressible flows by kinetic approach
    • Ohwada T., and Fukata S. Simple derivation of high-resolution schemes for compressible flows by kinetic approach. J. Comput. Phys. 211 (2006) 424
    • (2006) J. Comput. Phys. , vol.211 , pp. 424
    • Ohwada, T.1    Fukata, S.2
  • 25
    • 0141515637 scopus 로고    scopus 로고
    • Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
    • Popinet S. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190 (2003) 572
    • (2003) J. Comput. Phys. , vol.190 , pp. 572
    • Popinet, S.1
  • 27
    • 2142703427 scopus 로고    scopus 로고
    • A conservative method for solving the Boltzmann equation with centrally symmetric interaction potentials
    • Popov S.P., and Cheremisin F.G. A conservative method for solving the Boltzmann equation with centrally symmetric interaction potentials. Comput. Math. Math. Phys. 39 (1999) 156
    • (1999) Comput. Math. Math. Phys. , vol.39 , pp. 156
    • Popov, S.P.1    Cheremisin, F.G.2
  • 29
    • 85190775610 scopus 로고    scopus 로고
    • D.B. Goldstein, B. Sturtevant, J.E. Broadwell, Investigation of the motion of the discrete velocity gases, in: E.P. Muntz et al. (Eds.), Proceedings of the16th International Symposium on RGD, in Series: Progress in Astronautics and Aeronautics 118, 1989, p. 100.
  • 30
    • 0030547664 scopus 로고    scopus 로고
    • A discrete velocity scheme for the Boltzmann operator of rarefied gas dynamics
    • Buet C. A discrete velocity scheme for the Boltzmann operator of rarefied gas dynamics. Trans. Theo. Stat. Phys. 25 (1996) 33
    • (1996) Trans. Theo. Stat. Phys. , vol.25 , pp. 33
    • Buet, C.1
  • 31
    • 0040347813 scopus 로고
    • A direct method for solving Boltzmann equation
    • Rogier F., and Schneider J.A. A direct method for solving Boltzmann equation. Trans. Theo. Stat. Phys. 23 1-3 (1994) 313-338
    • (1994) Trans. Theo. Stat. Phys. , vol.23 , Issue.1-3 , pp. 313-338
    • Rogier, F.1    Schneider, J.A.2
  • 32
    • 0008519617 scopus 로고
    • The Δ-ε method for the Boltzmann equation
    • Tan Z., and Varghese P.L. The Δ-ε method for the Boltzmann equation. J. Comput. Phys. 110 (1994) 327
    • (1994) J. Comput. Phys. , vol.110 , pp. 327
    • Tan, Z.1    Varghese, P.L.2
  • 33
    • 33746058205 scopus 로고    scopus 로고
    • Solution to the Boltzmann kinetic equation for high-speed flows
    • Tcheremissine F.G. Solution to the Boltzmann kinetic equation for high-speed flows. Comput. Math. Math. Phys. 46 (2006) 315
    • (2006) Comput. Math. Math. Phys. , vol.46 , pp. 315
    • Tcheremissine, F.G.1
  • 35
    • 85190802291 scopus 로고    scopus 로고
    • N.M. Korobov, Theoretico-Numerical Methods in Approximate Analysis, Moscow, 2004 (in Russian).
  • 36
    • 82455181714 scopus 로고    scopus 로고
    • Degond P., Pareschi L., and Russo G. (Eds), Birkhauser, Boston
    • In: Degond P., Pareschi L., and Russo G. (Eds). Modeling and Computational methods for Kinetic Equations (2004), Birkhauser, Boston 356
    • (2004) Modeling and Computational methods for Kinetic Equations , pp. 356
  • 39
    • 0036001598 scopus 로고    scopus 로고
    • Generalized discrete velocity models
    • Gorsch D. Generalized discrete velocity models. Math. Models Meth. Appl. Sci. 12 (2002) 49
    • (2002) Math. Models Meth. Appl. Sci. , vol.12 , pp. 49
    • Gorsch, D.1
  • 40
    • 33947099781 scopus 로고
    • Shock wave structure in monatomic gas at power potentials
    • Aristov V.V., and Tcheremissine F.G. Shock wave structure in monatomic gas at power potentials. Fluid Dyn. 2 (1982) 179-183
    • (1982) Fluid Dyn. , Issue.2 , pp. 179-183
    • Aristov, V.V.1    Tcheremissine, F.G.2
  • 41
    • 36449006713 scopus 로고
    • Structure of normal shock waves on the basis of the Boltzmann equation for hard-spheres molecules
    • Ohwada T. Structure of normal shock waves on the basis of the Boltzmann equation for hard-spheres molecules. Phys. Fluids A5 (1993) 217-234
    • (1993) Phys. Fluids , vol.A5 , pp. 217-234
    • Ohwada, T.1
  • 42
    • 33749020864 scopus 로고    scopus 로고
    • Testing continuum and non-continuum descriptions in high speed flows
    • Josyula E., Xu K., and Wadsworth D.C. Testing continuum and non-continuum descriptions in high speed flows. AIP Conf. Proc. 762 (2004) 1217
    • (2004) AIP Conf. Proc. , vol.762 , pp. 1217
    • Josyula, E.1    Xu, K.2    Wadsworth, D.C.3
  • 43
    • 0017299920 scopus 로고
    • Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam
    • Alsmeyer H. Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam. J. Fluid. Mech. 74 (1976) 497
    • (1976) J. Fluid. Mech. , vol.74 , pp. 497
    • Alsmeyer, H.1
  • 44
    • 0014579611 scopus 로고
    • Molecular velocity distribution function measurement in a normal shock wave
    • Muntz E.P., and Harnett L.N. Molecular velocity distribution function measurement in a normal shock wave. Phys. Fluids 12 (1969) 2027-2035
    • (1969) Phys. Fluids , vol.12 , pp. 2027-2035
    • Muntz, E.P.1    Harnett, L.N.2
  • 46
    • 0018964750 scopus 로고
    • Direct simulation methods for compressible inviscid ideal gas flow
    • Pullin D.I. Direct simulation methods for compressible inviscid ideal gas flow. J. Comput. Phys. 34 (1980) 231
    • (1980) J. Comput. Phys. , vol.34 , pp. 231
    • Pullin, D.I.1
  • 47
    • 0001099263 scopus 로고
    • One dimensional compressible gas dynamics calculations using the Boltzmann equations
    • Reitz R.D. One dimensional compressible gas dynamics calculations using the Boltzmann equations. J. Comput. Phys. 42 (1981) 108
    • (1981) J. Comput. Phys. , vol.42 , pp. 108
    • Reitz, R.D.1
  • 48
    • 24144444029 scopus 로고
    • Solving the Euler and Navier-Stokes equations on the basis of the operator splitting of the kinetic equations
    • Aristov V.V., and Tcheremissine F.G. Solving the Euler and Navier-Stokes equations on the basis of the operator splitting of the kinetic equations. Doklady USSR Acad. Sci. 272 (1983) 555
    • (1983) Doklady USSR Acad. Sci. , vol.272 , pp. 555
    • Aristov, V.V.1    Tcheremissine, F.G.2
  • 49
    • 2942617811 scopus 로고
    • The kinetic numerical method for rarefied and continuum gas flows
    • Belotserkovskii O.M., et al. (Ed), Plenum Press, NY
    • Aristov V.V., and Tcheremissine F.G. The kinetic numerical method for rarefied and continuum gas flows. In: Belotserkovskii O.M., et al. (Ed). Rarefied Gas Dynamics, vol. 1 (1985), Plenum Press, NY 269
    • (1985) Rarefied Gas Dynamics, vol. 1 , pp. 269
    • Aristov, V.V.1    Tcheremissine, F.G.2
  • 50
    • 33749017680 scopus 로고
    • A kinetic scheme for gas-dynamic equations in Lagrange coordinates
    • Potkin V.V. A kinetic scheme for gas-dynamic equations in Lagrange coordinates. J. Comp. Math. Math. Phys. 15 (1975) 227
    • (1975) J. Comp. Math. Math. Phys. , vol.15 , pp. 227
    • Potkin, V.V.1
  • 51
    • 0028374191 scopus 로고
    • Kinetic flux vector splitting for Euler equations
    • Mandal J.C., and Deshpande S.M. Kinetic flux vector splitting for Euler equations. Comput. Fluids 23 (1994) 447
    • (1994) Comput. Fluids , vol.23 , pp. 447
    • Mandal, J.C.1    Deshpande, S.M.2
  • 52
    • 0031568155 scopus 로고    scopus 로고
    • Kinetic flux-vector splitting for the Navier-Stokes equations
    • Chou S.Y., and Baganoff D. Kinetic flux-vector splitting for the Navier-Stokes equations. J. Comput. Phys. 130 (1997) 217
    • (1997) J. Comput. Phys. , vol.130 , pp. 217
    • Chou, S.Y.1    Baganoff, D.2
  • 53
    • 0037139655 scopus 로고    scopus 로고
    • On the construction of kinetic schemes
    • Ohwada T. On the construction of kinetic schemes. J. Comput. Phys. 177 (2002) 156
    • (2002) J. Comput. Phys. , vol.177 , pp. 156
    • Ohwada, T.1
  • 54
    • 2942590404 scopus 로고    scopus 로고
    • Management of discontinuous reconstruction in kinetic schemes
    • Ohwada T., and Kobayashi S. Management of discontinuous reconstruction in kinetic schemes. J. Comput. Phys. 197 (2004) 116
    • (2004) J. Comput. Phys. , vol.197 , pp. 116
    • Ohwada, T.1    Kobayashi, S.2
  • 55
    • 0008992250 scopus 로고    scopus 로고
    • A robust and accurate LED-BGK solver on unstructured adaptive meshes
    • Kim C., and Jameson A. A robust and accurate LED-BGK solver on unstructured adaptive meshes. J. Comput. Phys. 143 (1998) 598
    • (1998) J. Comput. Phys. , vol.143 , pp. 598
    • Kim, C.1    Jameson, A.2
  • 56
    • 15944388262 scopus 로고    scopus 로고
    • A compressible Navier-Stokes flow solver with scalar transport
    • Li Q., Fu S., and Xu K. A compressible Navier-Stokes flow solver with scalar transport. J. Comput. Phys. 204 (2005) 692
    • (2005) J. Comput. Phys. , vol.204 , pp. 692
    • Li, Q.1    Fu, S.2    Xu, K.3
  • 57
    • 85190768270 scopus 로고    scopus 로고
    • G. May, B. Srinivasan, A. Jameson, An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow, J. Comput. Phys., 2006, doi:10.1016/j.jcp.2006.05.027.
  • 58
    • 85190794415 scopus 로고    scopus 로고
    • I.D. Boyd, Predicting breakdown of the continuum equations under rarefied flow conditions, in: Andrew D. Ketsdever, E.P. Munz (Eds.), Rarefied Gas Dynamics: 23rd International Symposium, AIP Conference Proceedings 663, 2003, pp. 899-906.
  • 59
    • 0034314854 scopus 로고    scopus 로고
    • Hybrid Euler/direct simulation Monte Carlo calculation of unsteady slit flow
    • Roveda R., Goldstein D.B., and Varghese P.L. Hybrid Euler/direct simulation Monte Carlo calculation of unsteady slit flow. J. Spacecraft Rockets 37 (2000) 753
    • (2000) J. Spacecraft Rockets , vol.37 , pp. 753
    • Roveda, R.1    Goldstein, D.B.2    Varghese, P.L.3
  • 60
    • 85190818550 scopus 로고    scopus 로고
    • W.J. Coirier, An adaptively refined Euler and Navier-Stokes solution on an unstructured quadtree-based grid, Ph.D. thesis, Aerospace Engineering Department, The University of Michigan, 1994.
  • 61
    • 85190780900 scopus 로고    scopus 로고
    • W.J. Coirier, A. Cartesian, Cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations, NASA TM 106786 and AIAA-95-0566.
  • 62
    • 0036647769 scopus 로고    scopus 로고
    • A cartesian grid method with transient anisotropic adaptation
    • Ham F.E., Lien F.S., and Strong A.B. A cartesian grid method with transient anisotropic adaptation. J. Comput. Phys. 179 (2002) 469
    • (2002) J. Comput. Phys. , vol.179 , pp. 469
    • Ham, F.E.1    Lien, F.S.2    Strong, A.B.3
  • 63
    • 0037582806 scopus 로고
    • Cylinder drag in the transition from continuum to free-molecule flow
    • Maslach G.J., and Schaaf S.A. Cylinder drag in the transition from continuum to free-molecule flow. Phys. Fluids 6 3 (1963) 315-321
    • (1963) Phys. Fluids , vol.6 , Issue.3 , pp. 315-321
    • Maslach, G.J.1    Schaaf, S.A.2
  • 64
    • 4344664277 scopus 로고    scopus 로고
    • Microchannel flow in the slip regime: gas-kinetic BGK-Burnett solutions
    • Xu K., and Li Z. Microchannel flow in the slip regime: gas-kinetic BGK-Burnett solutions. J. Fluid Mech. 513 (2004) 87
    • (2004) J. Fluid Mech. , vol.513 , pp. 87
    • Xu, K.1    Li, Z.2
  • 65
    • 85190776902 scopus 로고    scopus 로고
    • R.L. Bayt, Analysis, fabrication and testing of a MEMS-based micropropulsion system, PhD thesis, MIT 1999.
  • 66
    • 85190761690 scopus 로고    scopus 로고
    • J.N. Moss, C.E. Glass, B.R. Hollis, J.W. van Norman, Low-density aerodynamics of the inflatable reentry vehicle experiment (IRVE), AIAA paper 2006-1189.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.