메뉴 건너뛰기




Volumn 32, Issue 10, 2008, Pages 2050-2058

A novel lattice Boltzmann model for the Poisson equation

Author keywords

Chapman Enskog expansion; Lattice Boltzmann method; The Poisson equation

Indexed keywords

DIFFUSION; DISTRIBUTION FUNCTIONS; MATHEMATICAL MODELS; NUMERICAL METHODS;

EID: 44649186272     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2007.06.033     Document Type: Article
Times cited : (181)

References (28)
  • 1
    • 0034229896 scopus 로고    scopus 로고
    • Lattice Boltzmann simulation of electrochemical systems
    • He X., and Ling N. Lattice Boltzmann simulation of electrochemical systems. Comput. Phys. Commun. 129 (2000) 158-166
    • (2000) Comput. Phys. Commun. , vol.129 , pp. 158-166
    • He, X.1    Ling, N.2
  • 2
    • 20844448624 scopus 로고    scopus 로고
    • A lattice Boltzmann algorithm for electro-osmotic flows in microfluidic devices
    • Guo Z., Zhao T.S., and Shi Y. A lattice Boltzmann algorithm for electro-osmotic flows in microfluidic devices. J. Chem. Phys. 122 (2005) 144907
    • (2005) J. Chem. Phys. , vol.122 , pp. 144907
    • Guo, Z.1    Zhao, T.S.2    Shi, Y.3
  • 3
    • 33644972098 scopus 로고    scopus 로고
    • Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels
    • Wang J., Wang M., and Li Z. Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels. J. Colloid. Interface Sci. 296 (2006) 729-736
    • (2006) J. Colloid. Interface Sci. , vol.296 , pp. 729-736
    • Wang, J.1    Wang, M.2    Li, Z.3
  • 4
    • 33947136710 scopus 로고    scopus 로고
    • Simulation of electro-osmotic flow in microchannel with lattice Boltzmann method
    • Chai Z., and Shi B. Simulation of electro-osmotic flow in microchannel with lattice Boltzmann method. Phys. Lett. A 364 (2007) 183-188
    • (2007) Phys. Lett. A , vol.364 , pp. 183-188
    • Chai, Z.1    Shi, B.2
  • 5
    • 0035435290 scopus 로고    scopus 로고
    • An accurate solution of the Poisson equation by the finite difference-Chebyshev-Tau method
    • Siyyam H.I. An accurate solution of the Poisson equation by the finite difference-Chebyshev-Tau method. Appl. Math. Mech. 22 8 (2001) 0935-0939
    • (2001) Appl. Math. Mech. , vol.22 , Issue.8 , pp. 0935-0939
    • Siyyam, H.I.1
  • 6
    • 2342454337 scopus 로고    scopus 로고
    • Hybrid boundary element and finite difference method for Solving the Nonlinear Poisson-Boltzmann equation
    • Boschitsch A.H., and Fenley M.O. Hybrid boundary element and finite difference method for Solving the Nonlinear Poisson-Boltzmann equation. J. Comput. Chem. 25 7 (2004) 935-955
    • (2004) J. Comput. Chem. , vol.25 , Issue.7 , pp. 935-955
    • Boschitsch, A.H.1    Fenley, M.O.2
  • 7
    • 33644582740 scopus 로고    scopus 로고
    • A finite element method using singular functions for Poisson equations: mixed boundary conditions
    • Cai Z., Kim S., Kim S., and Kong S. A finite element method using singular functions for Poisson equations: mixed boundary conditions. Comput. Methods Appl. Mech. Engrg. 195 (2006) 2635-2648
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 2635-2648
    • Cai, Z.1    Kim, S.2    Kim, S.3    Kong, S.4
  • 8
    • 33749668582 scopus 로고    scopus 로고
    • Remarks on a posteriori error estimation for finite element solutions
    • Kikuchi F., and Saito H. Remarks on a posteriori error estimation for finite element solutions. J. Comput. Appl. Math. 199 2 (2007) 329-336
    • (2007) J. Comput. Appl. Math. , vol.199 , Issue.2 , pp. 329-336
    • Kikuchi, F.1    Saito, H.2
  • 9
    • 0031652439 scopus 로고    scopus 로고
    • General boundary element method for Poisson equation with spatially varying conductivity
    • Liao S.J. General boundary element method for Poisson equation with spatially varying conductivity. Eng. Anal. Bound. Elem. 21 (1998) 23-38
    • (1998) Eng. Anal. Bound. Elem. , vol.21 , pp. 23-38
    • Liao, S.J.1
  • 10
    • 13844320326 scopus 로고
    • The lattice Boltzmann equation: theory and applications
    • Benzi R., Succi S., and Vergassola M. The lattice Boltzmann equation: theory and applications. Phys. Rep. 222 (1992) 147-197
    • (1992) Phys. Rep. , vol.222 , pp. 147-197
    • Benzi, R.1    Succi, S.2    Vergassola, M.3
  • 11
    • 1542471855 scopus 로고    scopus 로고
    • Lattice Boltzmann method for fluid flows
    • Chen S., and Doolen G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30 (1998) 329-364
    • (1998) Annu. Rev. Fluid Mech. , vol.30 , pp. 329-364
    • Chen, S.1    Doolen, G.D.2
  • 13
    • 35949016104 scopus 로고
    • Lattice-gas automata for the Navier-Stokes equation
    • Frisch U., Hasslacher B., and Pomeau Y. Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56 (1986) 1505-1508
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 1505-1508
    • Frisch, U.1    Hasslacher, B.2    Pomeau, Y.3
  • 14
    • 0001207344 scopus 로고    scopus 로고
    • A priori derivation of the lattice Boltzmann equation
    • He X., and Luo L.S. A priori derivation of the lattice Boltzmann equation. Phys. Rev. E 55 (1997) R6333-R6336
    • (1997) Phys. Rev. E , vol.55
    • He, X.1    Luo, L.S.2
  • 15
    • 0002945795 scopus 로고    scopus 로고
    • Discretization of the velocity space in the solution of Boltzmann equation
    • Shan X., and He X. Discretization of the velocity space in the solution of Boltzmann equation. Phys. Rev. Lett. 80 (1998) 65-68
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 65-68
    • Shan, X.1    He, X.2
  • 16
    • 0033297205 scopus 로고    scopus 로고
    • Fully Lagrangian and lattice Boltzmann methods for the advection-diffusion equation
    • Guo Z.L., Shi B.C., and Wang N.C. Fully Lagrangian and lattice Boltzmann methods for the advection-diffusion equation. J. Sci. Comput. 14 3 (1999) 291-300
    • (1999) J. Sci. Comput. , vol.14 , Issue.3 , pp. 291-300
    • Guo, Z.L.1    Shi, B.C.2    Wang, N.C.3
  • 17
    • 24144467365 scopus 로고    scopus 로고
    • A new lattice Bhatnagar-Gross-Krook model for convection-diffusion equation with a source term
    • Deng B., Shi B.C., and Wang G.C. A new lattice Bhatnagar-Gross-Krook model for convection-diffusion equation with a source term. Chin. Phys. Lett. 22 2 (2005) 267-270
    • (2005) Chin. Phys. Lett. , vol.22 , Issue.2 , pp. 267-270
    • Deng, B.1    Shi, B.C.2    Wang, G.C.3
  • 19
    • 4444377230 scopus 로고    scopus 로고
    • A lattice Boltzmann model and simulation of KdV-Burgers equation
    • Zhang C.Y., Tan H.L., Liu M.R., and Kong L.J. A lattice Boltzmann model and simulation of KdV-Burgers equation. Commun. Theor. Phys. 42 2 (2004) 281-284
    • (2004) Commun. Theor. Phys. , vol.42 , Issue.2 , pp. 281-284
    • Zhang, C.Y.1    Tan, H.L.2    Liu, M.R.3    Kong, L.J.4
  • 20
    • 24644479765 scopus 로고    scopus 로고
    • A new lattice Boltzmann model for KdV-Burgers equation
    • Ma C. A new lattice Boltzmann model for KdV-Burgers equation. Chin. Phys. Lett. 29 9 (2005) 2313-2315
    • (2005) Chin. Phys. Lett. , vol.29 , Issue.9 , pp. 2313-2315
    • Ma, C.1
  • 21
    • 85126489152 scopus 로고    scopus 로고
    • Z. Chai, B. Shi, L. Zheng, A unified lattice Boltzmann model for some nonlinear partial differential equations, Chaos Solitons Fractals, in press, doi:10.1016/j.chaos.2006.07.023.
    • Z. Chai, B. Shi, L. Zheng, A unified lattice Boltzmann model for some nonlinear partial differential equations, Chaos Solitons Fractals, in press, doi:10.1016/j.chaos.2006.07.023.
  • 22
    • 0346478347 scopus 로고    scopus 로고
    • A lattice Boltzmann equation for waves
    • Yan G. A lattice Boltzmann equation for waves. J. Comput. Phys. 161 (2000) 61-69
    • (2000) J. Comput. Phys. , vol.161 , pp. 61-69
    • Yan, G.1
  • 23
    • 0035242937 scopus 로고    scopus 로고
    • The lattice BGK model for the Poisson equation
    • Hirabayashi M., Chen Y., and Ohashi H. The lattice BGK model for the Poisson equation. JSME Int. J. Ser. B 44 1 (2001) 45-52
    • (2001) JSME Int. J. Ser. B , vol.44 , Issue.1 , pp. 45-52
    • Hirabayashi, M.1    Chen, Y.2    Ohashi, H.3
  • 24
    • 0000325356 scopus 로고    scopus 로고
    • Lattice BGK model for incompressible Navier-Stokes equation
    • Guo Z., Shi B., and Wang N. Lattice BGK model for incompressible Navier-Stokes equation. J. Comput. Phys. 165 (2000) 288-306
    • (2000) J. Comput. Phys. , vol.165 , pp. 288-306
    • Guo, Z.1    Shi, B.2    Wang, N.3
  • 25
    • 33645859586 scopus 로고
    • Lattice Boltzmann Computations for reaction-diffusion equations
    • Dawson S.P., Chen S., and Doolen D.G. Lattice Boltzmann Computations for reaction-diffusion equations. J. Chem. Phys. 98 2 (1993) 1514-1523
    • (1993) J. Chem. Phys. , vol.98 , Issue.2 , pp. 1514-1523
    • Dawson, S.P.1    Chen, S.2    Doolen, D.G.3
  • 26
    • 0031321552 scopus 로고    scopus 로고
    • On a fast direct elliptic solver by a modified Fourier method
    • Averbuch A., Vozovoi L., and Israeli M. On a fast direct elliptic solver by a modified Fourier method. Numer. Algorithms 15 (1997) 287-313
    • (1997) Numer. Algorithms , vol.15 , pp. 287-313
    • Averbuch, A.1    Vozovoi, L.2    Israeli, M.3
  • 27
    • 0036334507 scopus 로고    scopus 로고
    • Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method
    • Guo Z.L., Zheng C.G., and Shi B.C. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin. Phys. 11 4 (2002) 366-374
    • (2002) Chin. Phys. , vol.11 , Issue.4 , pp. 366-374
    • Guo, Z.L.1    Zheng, C.G.2    Shi, B.C.3
  • 28
    • 33646777168 scopus 로고    scopus 로고
    • A stability notion for lattice Boltzmann equations
    • Banda M.K., Yong W.A., and Klar A. A stability notion for lattice Boltzmann equations. SIAM J. Sci. Comput. 27 (2006) 2098-2111
    • (2006) SIAM J. Sci. Comput. , vol.27 , pp. 2098-2111
    • Banda, M.K.1    Yong, W.A.2    Klar, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.