Top

Journal of Scientific Computing

Published in:

01-11-2014

An Efficient Lattice Boltzmann Model for Steady Convection–Diffusion Equation

Authors: Qianhuan Li, Zhenhua Chai, Baochang Shi

Published in: Journal of Scientific Computing | Issue 2/2014

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, an efficient lattice Boltzmann model for n-dimensional steady convection–diffusion equation with variable coefficients is proposed through modifying the equilibrium distribution function properly, and the Chapman–Enskog analysis shows that the steady convection–diffusion equation with variable coefficients can be recovered exactly. Detailed simulations are performed to test the model, and the results show that the accuracy and efficiency of the present model are better than previous models.

previous article A Framework for Hyperbolic Conservation Laws

next article Numerical Anisotropy Study of a Class of Compact Schemes

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Deolmi, G., Marcuzzi, F., Morandi Cecchi, M.: The best-approximation weighted-residuals method for the steady convection–diffusion–reaction problem. Math. Comput. Simul. 82, 144–162 (2011)MathSciNetCrossRefMATH

Brill, S., Smith, E.: Analytical upstream collocation solution of a quadratically forced steady-state convection–diffusion equation. Int. J. Numer. Method. H. 22(4), 436–457 (2012)CrossRef

Galligani, E.: A nonlinearity lagging for the solution of nonlinear steady state reaction diffusion problems. Int. J. Nonlinear Sci. Num. 18, 567–583 (2013)MathSciNetCrossRefMATH

Angelini, O., Brenner, K., Hilhorst, D.: A finite volume method on general meshes for a degenerate parabolic convection–reaction–diffusion equation. Numer. Math. 123, 219–257 (2013)MathSciNetCrossRefMATH

Bause, M., Schwegler, K.: Higher order finite element approximation of systems of convection–diffusion–reaction equations with small diffusion. J. Comput. Appl. Math. 246, 52–64 (2013)MathSciNetCrossRefMATH

Codina, R.: Comparison of some finite element methods for solving the diffusion–convection–reaction equation. Comput. Method. Appl. M. 156, 185–210 (1998)MathSciNetCrossRefMATH

Egger, H., Schoberl, J.: A hybrid mixed discontinuous galerkin finite-element method for convection–diffusion problems. IMA. J. Numer. Anal. 30, 1206–1234 (2010)MathSciNetCrossRefMATH

Benzi, R., Succi, S., Vergassola, M.: The lattice Boltzmann equation: theory and applications. Phys. Rep. 222, 145–197 (1992)CrossRef

Chen, S.Y., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364 (1998)MathSciNetCrossRef

10.

Qian, Y.H., Succi, S., Orszag, S.A.: Lattice BGK models for Navier–Stokes equation. Annu. Rev. Comput. Phys. 3, 195–242 (1995)MathSciNetCrossRef

11.

Wang, M., Wang, J.K., Pan, N.: Three-dimensional effect on the effective thermal conductivity of porous media. J. Phys. D. Appl. Phys. 40, 260–265 (2007)CrossRef

12.

Dou, Z., Zhou, Z.F.: Numerical study of non-uniqueness of the factors influencing relative permeability in heterogeneous porous media by lattice Boltzmann method. Int. J. Heat Fluid FL. 42, 23–32 (2013)CrossRef

13.

Guo, Z.L., Shi, B.C., Zheng, C.G.: Chequerboard effects on spurious currents in the lattice Boltzmann equation for two-phase flows. Phil. Trans. R. Soc. A 369, 2283–2291 (2011)MathSciNetCrossRefMATH

14.

Dellar, P.J.: Electromagnetic waves in lattice Boltzmann magnetohydrodynamics. Europhys. Lett. 90, 50002 (2010)CrossRef

15.

Chai, Z.H., Shi, B.C.: Simulation of electro-osmotic flow in microchannel with lattice Boltzmann method. Phys. Lett. A 364, 183–188 (2007)CrossRefMATH

16.

Wang, J.K., Wang, M.R., Li, Z.X.: Lattice Poisson–Boltzmann simulations of electro-osmotic flows in microchannels. J. Colloid Interface Sci. 296, 729–736 (2006)CrossRef

17.

Mendoza, M., Boghosian, B.M., Herrmann, H.J., Succi, S.: Fast lattice Boltzmann solver for relativistic hydrodynamics. Phys. Rev. Lett. 105, 014502 (2010)CrossRef

18.

Hupp, D., Mendoza, M., Bouras, I., Succi, S.: Relativistic lattice Boltzmann method for quark-gluon plasma simulations. Phys. Rev. D 84, 125015 (2011)CrossRef

19.

Ashrafizaadeh, M., Bakhshaei, H.: A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations. Comput. Math. Appl. 58, 1045–1054 (2009)MathSciNetCrossRefMATH

20.

Joshi, A.S., Sun, Y.: Multiphase lattice Boltzmann method for particle suspensions. Phys. Rev. E 79, 066703 (2009)CrossRef

21.

He, X.Y., Li, N.: Lattice Boltzmann simulation of electrochemical systems. Comput. Phys. Commun. 129, 158–166 (2000)CrossRefMATH

22.

Li, Q.J., Zheng, Z.S., Wang, S., Liu, J.K.: A multilevel finite difference scheme for one-dimensional Burgers equation derived from the lattice Boltzmann method. J. Appl. Math. 2012, 925920 (2012)

23.

Yermakou, V., Succi, S.: A fluctuating lattice Boltzmann scheme for the one-dimensional KPZ equation. Physica. A 391, 4557–4563 (2012)CrossRef

24.

Blaak, R., Sloot, P.M.: Lattice dependence of reaction-diffusion in lattice Boltzmann modeling. Comput. Phys. Commun. 129, 256–266 (2000)MathSciNetCrossRefMATH

25.

Chai, Z.H., Shi, B.C.: A novel lattice Boltzmann model for the Poisson equation. Appl. Math. Model. 32, 2050–2058 (2008)MathSciNetCrossRefMATH

26.

Feng, H.Y., Zhang, X.Q., Peng, Y.H.: A lattice Boltzmann model for elliptic equations with variable coefficient. Appl. Math. Comput. 219, 2798–2807 (2012)MathSciNetCrossRef

27.

Shi, B.C., Guo, Z.L.: Lattice Boltzmann model for nonlinear convection–diffusion equations. Phys. Rev. E 79, 016701 (2009)CrossRef

28.

Chai, Z.H., Zhao, T.S.: Lattice Boltzmann model for the convection–diffusion equation. Phys. Rev. E 87, 063309 (2013)CrossRef

29.

Yoshida, H., Nagaoka, M.: Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation. J. Comput. Phys. 229, 7774–7795 (2010)MathSciNetCrossRefMATH

30.

van der Sman, R.G.M., Ernst, M.H.: Convection–diffusion lattice Boltzmann scheme for irregular lattice. J. Comput. Phys. 160, 766–782 (2000)MathSciNetCrossRefMATH

31.

Ginzburg, I.: Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Adv. Water Resour. 28, 1171–1195 (2005)CrossRef

32.

Xiang, X.Q., Wang, Z.H., Shi, B.C.: Modified lattice Boltzmann scheme for nonlinear convection diffusion equations. Int. J. Nonlinear Sci. Num. 17, 2415–2425 (2012)MathSciNetCrossRefMATH

33.

Guo, Z.L., Zheng, C.G., Shi, B.C.: Non-equilibrium extrapolation methodfor velocity and pressure boundary conditionsin the lattice Boltzmann method. Chin. Phys. 11, 366–374 (2002)CrossRef

34.

Gao, Z., Shen, Y.Q.: Analysis and application of high resolution numerical perturbation algorithm for convective–diffusion equation. Chin. Phys. Lett. 29, 104702 (2012)MathSciNetCrossRef

Title: An Efficient Lattice Boltzmann Model for Steady Convection–Diffusion Equation
Authors: Qianhuan Li
Zhenhua Chai
Baochang Shi
Publication date: 01-11-2014
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2014
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9827-z

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 2/2014

A Scalable Approach for Variational Data Assimilation

An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Triangular Elements

Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids

Parallel Domain Decomposition Methods with Mixed Order Discretization for Fully Implicit Solution of Tracer Transport Problems on the Cubed-Sphere

Variational Space–Time Methods for the Wave Equation

High-Order Flux Correction for Viscous Flows on Arbitrary Unstructured Grids

Premium Partner