A Multiple-Relaxation-Time Lattice Boltzmann Model for General Nonlinear Anisotropic Convection–Diffusion Equations
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Chen, S., Doolen, G.: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364 (1998)
Guo, Z., Shu, C.: Lattice Boltzmann Method and Its Applications in Engineering. World Scientific, Singapore (2013)
Huber, C., Chopard, B., Manga, M.: A lattice Boltzmann model for coupled diffusion. J. Comput. Phys. 229, 7956–7976 (2010)
Yu, X.M., Shi, B.C.: A lattice Bhatnagar–Gross–Krook model for a class of the generalized Burgers equations. Chin. Phys. 15, 1441–1449 (2006)
Succi, S.: A note on the lattice Boltzmann versus finite-difference methods for the numerical solution of the Fisher’s equation. Int. J. Mod. Phys. C 25, 1340015 (2014)
Chai, Z., Shi, B.: A novel lattice Boltzmann model for the Poisson equation. Appl. Math. Model. 32, 2050–2058 (2008)
Dawson, S.P., Chen, S., Doolen, G.D.: Lattice Boltzmann computations for reaction–diffusion equations. J. Chem. Phys. 98, 1514–1523 (1993)
Guo, Z.L., Shi, B.C., Wang, N.C.: Fully lagrangian and lattice Boltzmann methods for the advection–diffusion equation. J. Sci. Comput. 14, 291–300 (1999)
van der Sman, R.G.M., Ernst, M.H.: Convection–diffusion lattice Boltzmann scheme for irregular lattices. J. Comput. Phys. 160, 766–782 (2000)
He, X., Li, N., Goldstein, B.: Lattice Boltzmann simulation of diffusion–convection systems with surface chemical reaction. Mol. Simul. 25, 145–156 (2000)
Deng, B., Shi, B.C., Wang, G.C.: A new lattice Bhatnagar–Gross–Krook Model for the convection–diffusion equation with a source term. Chin. Phys. Lett. 22, 267–270 (2005)
Zheng, H.W., Shu, C., Chew, Y.T.: A lattice Boltzmann model for multiphase flows with large density ratio. J. Comput. Phys. 218, 353–371 (2006)
Shi, B.C., Deng, B., Du, R., Chen, X.W.: A new scheme for source term in LBGK model for convection–diffusion equation. Comput. Math. Appl. 55, 1568–1575 (2008)
Chopard, B., Falcone, J.L., Latt, J.: The lattice Boltzmann advection–diffusion model revisited. Eur. Phys. J. Spec. Top. 171, 245–249 (2009)
Huang, H.-B., Lu, X.-Y., Sukop, M.C.: Numerical study of lattice Boltzmann methods for a convection–diffusion equation coupled with Navier–Stokes equations. J. Phys. A 44, 055001 (2011)
Chai, Z., Zhao, T.S.: Lattice Boltzmann model for the convection–diffusion equation. Phys. Rev. E 87, 063309 (2013)
Perko, J., Patel, R.A.: Single-relaxation-time lattice Boltzmann scheme for advection–diffusion problems with large diffusion-coefficient heterogentities and high-advection transport. Phys. Rev. E 89, 053309 (2014)
Yoshida, H., Nagaoka, M.: Lattice Boltzmann method for the convection–diffusion equation in curvilinear coordinate systems. J. Comput. Phys. 257, 884–900 (2014)
Chai, Z., Zhao, T.S.: Nonequilibrium scheme for computing the flux of the convection–diffusion equation in the framework of the lattice Boltzmann method. Phys. Rev. E 90, 013305 (2014)
Liang, H., Shi, B.C., Guo, Z.L., Chai, Z.H.: Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows. Phys. Rev. E 89, 053320 (2014)
Huang, R., Wu, H.: Lattice Boltzmann model for the correct convection–diffusion equation with divergence-free velocity field. Phys. Rev. E 91, 033302 (2015)
Li, Q., Chai, Z., Shi, B.: Lattice Boltzmann model for a class of convection–diffusion equations with variable coefficients. Comput. Math. Appl. 70, 548–561 (2015)
Huang, J., Yong, W.-A.: Boundary conditions of the lattice Boltzmann method for convection–diffusion equations. J. Comput. Phys. 300, 70–91 (2015)
Zhang, X., Bengough, A.G., Crawford, J.W., Young, I.M.: A lattice BGK model for advection and anisotropic dispersion equation. Adv. Water Resour. 25, 1–8 (2002)
Suga, S.: Stability and accuracy of lattice Boltzmann schemes for anisotropic advection–diffusion equations. Int. J. Mod. Phys. C 20, 633–650 (2009)
Servan-Camas, B., Tsai, F.T.-C.: Lattice Boltzmann method with two relaxation times for advection–diffusion equation: third order analysis and stability analysis. Adv. Water Resour. 31, 1113–1126 (2008)
Rasin, I., Succi, S., Miller, W.: A multi-relaxation lattice kinetic method for passive scalar diffusion. J. Comput. Phys. 206, 453–462 (2005)
Yoshida, H., Nagaoka, M.: Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation. J. Comput. Phys. 229, 7774–7795 (2010)
Li, L., Mei, R., Klausner, J.F.: Multiple-relaxation-time lattice Boltzmann model for the axisymmetric convection diffusion equation. Int. J. Heat Mass Transf. 67, 338–351 (2013)
Li, L., Chen, C., Mei, R., Klausner, J.F.: Conjugate heat and mass transfer in the lattice Boltzmann equation method. Phys. Rev. E 89, 043308 (2014)
Huang, R., Wu, H.: A modified multiple-relaxation-time lattice Boltzmann model for convection–diffusion equation. J. Comput. Phys. 274, 50–63 (2014)
Shi, B., Guo, Z.: Lattice Boltzmann model for nonlinear convection–diffusion equations. Phys. Rev. E 79, 016701 (2009)
Shi, B., Guo, Z.: Lattice Boltzmann simulation of some nonlinear convection–diffusion equations. Comput. Math. Appl. 61, 3443–3452 (2011)
Ginzburg, I.: Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Adv. Water Resour. 28, 1171–1195 (2005)
Ginzburg, I.: Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations. Adv. Water Resour. 28, 1196–1216 (2005)
Ginzburg, I.: Lattice Boltzmann modeling with discontinuous collision components: hydrodynmic and advection-diffusion equations. J. Stat. Phys. 126, 157–206 (2007)
Ginzburg, I.: Truncation errors, exact and heuristic stability analysis of two-relaxation-times lattice Boltzmann schemes for anisotropic advection–diffusion equation. Commun. Comput. Phys. 11, 1439–1502 (2012)
Ginzburg, I.: Multiple anisotropic collison for advection–diffusion lattice Boltzmann schemes. Adv. Water Res. 51, 381–404 (2013)
Lallemand, P., Luo, L.S.: Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61, 6546–6562 (2000)
Qian, Y.H., d’Humières, D., Lallemand, P.: Lattice BGK models for Navier–Stokes equation. Europhys. Lett. 17, 479–484 (1992)
Ansumali, S., Karlin, I.V., Öttinger, H.C.: Minimal entropic kinetic models for hydrodynamics. Europhys. Lett. 63, 798–804 (2003)
Ginzburg, I., Verhaeghe, F., d’Humières, D.: Two-relaxation-time lattice Boltzmann scheme: about parametrization, velocity, pressure and mixed boundary conditions. Commun. Comput. Phys. 3, 427–478 (2008)
d’Humières, D.: Generalized lattice-Boltzmann equations. In: Shizgal, B.D., Weave, D.P. (eds.) Rarefied Gas Dynamics: Theory and Simulations, vol. 159, pp. 450–458. AIAA, Washington, DC (1992)
Luo, L.-S., Liao, W., Chen, X., Peng, Y., Zhang, W.: Numerics of the lattice Boltzmann method: effects of collision models on the lattice Boltzmann simulations. Phys. Rev. E 83, 056710 (2011)
Chai, Z., Chai, T.S.: Effect of the forcing term in the multiple-relaxation-time lattice Boltzmann equation on the shear stress or the strain rate tensor. Phys. Rev. E 86, 016705 (2012)
He, X., Chen, S., Doolen, G.D.: A novel thermal model for the lattice Boltzmann method in incompressible limit. J. Comput. Phys. 146, 282–300 (1998)
Guo, Z.-L., Zheng, C.-G., Shi, B.-C.: Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin. Phys. 11, 366–374 (2002)
Zhang, T., Shi, B., Guo, Z., Chai, Z., Lu, J.: General bounce-back scheme for concentration boundary condition in the lattice-Boltzmann method. Phys. Rev. E 85, 016701 (2012)
Wazwaz, A.-M.: The tanh method for generalized forms of nonliner heat conduction and Burgers–Fisher equations. Appl. Math. Comput. 169, 321–338 (2005)
Karlsen, K.H., Brusdal, K., Dahle, H.K., Evje, S., Lie, K.-A.: The corrected operator splitting approach applied to a nonlinear advection–diffusion problem. Comput. Methods Appl. Mech. Eng. 167, 239–260 (1998)
Kurganov, A., Tadmor, E.: New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. J. Comput. Phys. 160, 241–282 (2000)
He, X., Zou, Q., Luo, L.-S., Dembo, M.: Analytic solutions and analysis on non-slip boundary condition for the lattice Boltzmann BGK model. J. Stat. Phys. 87, 115–136 (1997)
Ginzburg, I., Adler, P.M.: Boundary flow condition analysis for the three-dimesional lattice Boltzmann model. J. Phys. II France 4, 191–214 (1994)