메뉴 건너뛰기




Volumn 227, Issue 8, 2008, Pages 3781-3803

Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics

Author keywords

Asymptotic preserving schemes; BGK equation; Boltzmann equation; Chapman Enskog expansion; Compressible Navier Stokes equations; Micro macro decomposition

Indexed keywords

INTEGRAL EQUATIONS; KINETIC THEORY; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; PHASE SPACE METHODS;

EID: 40249113010     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.11.032     Document Type: Article
Times cited : (185)

References (29)
  • 1
    • 0001076950 scopus 로고
    • Fluid dynamic limits of kinetic equations. I. Formal derivations
    • C. Bardos F. Golse D. Levermore Fluid dynamic limits of kinetic equations. I. Formal derivations J. Statist. Phys. 63 1–2 1991 323 344
    • (1991) J. Statist. Phys. , vol.63 , Issue.1–2 , pp. 323-344
    • Bardos, C.1    Golse, F.2    Levermore, D.3
  • 2
    • 85190397816 scopus 로고    scopus 로고
    • M. Bennoune, M. Lemou, L. Mieussens, in preparation.
  • 3
    • 0001407297 scopus 로고    scopus 로고
    • Uniformly accurate schemes for hyperbolic systems with relaxation
    • R.-E. Caflisch S. Jin G. Russo Uniformly accurate schemes for hyperbolic systems with relaxation SIAM J. Numer. Anal. 34 1 1997 246 281
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.1 , pp. 246-281
    • Caflisch, R.-E.1    Jin, S.2    Russo, G.3
  • 4
    • 0003483213 scopus 로고
    • The Boltzmann equation and its applications
    • C. Cercignani The Boltzmann equation and its applications Applied Mathematical Sciences vol. 67 1988 Springer-Verlag New York
    • (1988)
    • Cercignani, C.1
  • 5
    • 85190397406 scopus 로고    scopus 로고
    • C. Cercignani Rarefied gas dynamics Cambridge Texts in Applied Mathematics 2000 Cambridge University Press Cambridge (from basic concepts to actual calculations)
    • (2000)
    • Cercignani, C.1
  • 6
    • 85190399498 scopus 로고
    • S. Chapman T.-G. Cowling The Mathematical Theory of Non-uniform Gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases third ed. 1970 Cambridge University Press London prepared in co-operation with D. Burnett
    • (1970)
    • Chapman, S.1    Cowling, T.-G.2
  • 7
    • 0000198178 scopus 로고    scopus 로고
    • The reconstruction of upwind fluxes for conservation laws: its behavior in dynamic and steady state calculations
    • H. Choi J.-G. Liu The reconstruction of upwind fluxes for conservation laws: its behavior in dynamic and steady state calculations J. Comput. Phys. 144 2 1998 237 256
    • (1998) J. Comput. Phys. , vol.144 , Issue.2 , pp. 237-256
    • Choi, H.1    Liu, J.-G.2
  • 8
    • 0026106517 scopus 로고
    • Numerical passage from kinetic to fluid equations
    • F. Coron B. Perthame Numerical passage from kinetic to fluid equations SIAM J. Numer. Anal. 28 1 1991 26 42
    • (1991) SIAM J. Numer. Anal. , vol.28 , Issue.1 , pp. 26-42
    • Coron, F.1    Perthame, B.2
  • 9
    • 4544253987 scopus 로고    scopus 로고
    • A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation
    • N. Crouseilles P. Degond M. Lemou A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation J. Comput. Phys. 199 2 2004 776 808
    • (2004) J. Comput. Phys. , vol.199 , Issue.2 , pp. 776-808
    • Crouseilles, N.1    Degond, P.2    Lemou, M.3
  • 10
    • 21444459486 scopus 로고    scopus 로고
    • A smooth transition model between kinetic and diffusion equations
    • P. Degond S. Jin A smooth transition model between kinetic and diffusion equations SIAM J. Numer. Anal. 42 6 2005 2671 2687 electronic
    • (2005) SIAM J. Numer. Anal. , vol.42 , Issue.6 , pp. 2671-2687
    • Degond, P.1    Jin, S.2
  • 11
    • 21444454938 scopus 로고    scopus 로고
    • A smooth transition model between kinetic and hydrodynamic equations
    • P. Degond S. Jin L. Mieussens A smooth transition model between kinetic and hydrodynamic equations J. Comput. Phys. 209 2 2005 665 694
    • (2005) J. Comput. Phys. , vol.209 , Issue.2 , pp. 665-694
    • Degond, P.1    Jin, S.2    Mieussens, L.3
  • 12
    • 0035276778 scopus 로고    scopus 로고
    • On the viscosity and thermal conduction of fluids with multivalued internal energy
    • P. Degond M. Lemou On the viscosity and thermal conduction of fluids with multivalued internal energy Eur. J. Mech. B Fluids 20 2 2001 303 327
    • (2001) Eur. J. Mech. B Fluids , vol.20 , Issue.2 , pp. 303-327
    • Degond, P.1    Lemou, M.2
  • 13
    • 34548537653 scopus 로고    scopus 로고
    • Macroscopic fluid models with localized kinetic upscaling effects
    • P. Degond J.-G. Liu L. Mieussens Macroscopic fluid models with localized kinetic upscaling effects Multiscale Model. Simulat. 5 3 2006 940 979 electronic
    • (2006) Multiscale Model. Simulat. , vol.5 , Issue.3 , pp. 940-979
    • Degond, P.1    Liu, J.-G.2    Mieussens, L.3
  • 14
    • 0000677613 scopus 로고    scopus 로고
    • Relaxation schemes for nonlinear kinetic equations
    • E. Gabetta L. Pareschi G. Toscani Relaxation schemes for nonlinear kinetic equations SIAM J. Numer. Anal. 34 6 1997 2168 2194
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.6 , pp. 2168-2194
    • Gabetta, E.1    Pareschi, L.2    Toscani, G.3
  • 15
    • 0033295423 scopus 로고    scopus 로고
    • Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations
    • S. Jin Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations SIAM J. Sci. Comput. 21 2 1999 441 454 electronic
    • (1999) SIAM J. Sci. Comput. , vol.21 , Issue.2 , pp. 441-454
    • Jin, S.1
  • 16
    • 0030194392 scopus 로고    scopus 로고
    • Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
    • S. Jin C.-D. Levermore Numerical schemes for hyperbolic conservation laws with stiff relaxation terms J. Comput. Phys. 126 2 1996 449 467
    • (1996) J. Comput. Phys. , vol.126 , Issue.2 , pp. 449-467
    • Jin, S.1    Levermore, C.-D.2
  • 17
    • 0010663847 scopus 로고    scopus 로고
    • Discretization of the multiscale semiconductor Boltzmann equation by diffusive relaxation schemes
    • S. Jin L. Pareschi Discretization of the multiscale semiconductor Boltzmann equation by diffusive relaxation schemes J. Comput. Phys. 161 1 2000 312 330
    • (2000) J. Comput. Phys. , vol.161 , Issue.1 , pp. 312-330
    • Jin, S.1    Pareschi, L.2
  • 18
    • 85190397946 scopus 로고    scopus 로고
    • S. Jin, L. Pareschi, Asymptotic-preserving (AP) schemes for multiscale kinetic equations: a unified approach, in: Hyperbolic Problems: Theory, Numerics, Applications, vols. I and II (Magdeburg, 2000), vol. 141, Int. Ser. Numer. Math., vol. 140, Birkhäuser, Basel, 2001, pp. 573–582.
  • 19
    • 0000557853 scopus 로고    scopus 로고
    • An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit
    • A. Klar An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit SIAM J. Numer. Anal. 35 3 1998 1073 1094 electronic
    • (1998) SIAM J. Numer. Anal. , vol.35 , Issue.3 , pp. 1073-1094
    • Klar, A.1
  • 20
    • 0005435230 scopus 로고    scopus 로고
    • An asymptotic preserving numerical scheme for kinetic equations in the low Mach number limit
    • A. Klar An asymptotic preserving numerical scheme for kinetic equations in the low Mach number limit SIAM J. Numer. Anal. 36 5 1999 1507 1527 electronic
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.5 , pp. 1507-1527
    • Klar, A.1
  • 21
    • 0033296722 scopus 로고    scopus 로고
    • A numerical method for kinetic semiconductor equations in the drift-diffusion limit
    • A. Klar A numerical method for kinetic semiconductor equations in the drift-diffusion limit SIAM J. Sci. Comput. 20 5 1999 1696 1712 electronic
    • (1999) SIAM J. Sci. Comput. , vol.20 , Issue.5 , pp. 1696-1712
    • Klar, A.1
  • 22
    • 0035612482 scopus 로고    scopus 로고
    • Numerical passage from radiative heat transfer to nonlinear diffusion models
    • A. Klar C. Schmeiser Numerical passage from radiative heat transfer to nonlinear diffusion models Math. Models Methods Appl. Sci. 11 5 2001 749 767
    • (2001) Math. Models Methods Appl. Sci. , vol.11 , Issue.5 , pp. 749-767
    • Klar, A.1    Schmeiser, C.2
  • 23
    • 0031236545 scopus 로고    scopus 로고
    • Coupling Boltzmann and Navier–Stokes equations by half fluxes
    • P. Le Tallec F. Mallinger Coupling Boltzmann and Navier–Stokes equations by half fluxes J. Comput. Phys. 136 1 1997 51 67
    • (1997) J. Comput. Phys. , vol.136 , Issue.1 , pp. 51-67
    • Le Tallec, P.1    Mallinger, F.2
  • 24
    • 85190397887 scopus 로고    scopus 로고
    • M. Lemou, L. Mieussens, A new asymptotic preserving scheme based on micro–macro decomposition for linear kinetic equations in the diffusion limit, SIAM J. Sci. Comput., in press.
  • 25
    • 1842591085 scopus 로고    scopus 로고
    • Boltzmann equation: micro–macro decompositions and positivity of shock profiles
    • T.-P. Liu S.-H. Yu Boltzmann equation: micro–macro decompositions and positivity of shock profiles Comm. Math. Phys. 246 1 2004 133 179
    • (2004) Comm. Math. Phys. , vol.246 , Issue.1 , pp. 133-179
    • Liu, T.-P.1    Yu, S.-H.2
  • 26
    • 0028374191 scopus 로고
    • Kinetic flux vector splitting for Euler equations
    • J.-C. Mandal S.-M. Deshpande Kinetic flux vector splitting for Euler equations Comput. Fluids 23 2 1994 447 478
    • (1994) Comput. Fluids , vol.23 , Issue.2 , pp. 447-478
    • Mandal, J.-C.1    Deshpande, S.-M.2
  • 27
    • 0010662626 scopus 로고    scopus 로고
    • Numerical schemes for kinetic equations in diffusive regimes
    • G. Naldi L. Pareschi Numerical schemes for kinetic equations in diffusive regimes Appl. Math. Lett. 11 2 1998 29 35
    • (1998) Appl. Math. Lett. , vol.11 , Issue.2 , pp. 29-35
    • Naldi, G.1    Pareschi, L.2
  • 28
    • 0001140574 scopus 로고    scopus 로고
    • An implicit Monte Carlo method for rarefied gas dynamics. I. The space homogeneous case
    • L. Pareschi R.-E. Caflisch An implicit Monte Carlo method for rarefied gas dynamics. I. The space homogeneous case J. Comput. Phys. 154 1 1999 90 116
    • (1999) J. Comput. Phys. , vol.154 , Issue.1 , pp. 90-116
    • Pareschi, L.1    Caflisch, R.-E.2
  • 29
    • 0036341659 scopus 로고    scopus 로고
    • Time relaxed Monte Carlo methods for the Boltzmann equation
    • L. Pareschi G. Russo Time relaxed Monte Carlo methods for the Boltzmann equation SIAM J. Sci. Comput. 23 4 2001 1253 1273 electronic
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.4 , pp. 1253-1273
    • Pareschi, L.1    Russo, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.