zbMATH — the first resource for mathematics

On the stability of multi-step finite-difference-based lattice Boltzmann schemes. (English) Zbl 1404.76202

76M28 Particle methods and lattice-gas methods
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
[1] Abe, T., Derivation of the lattice Boltzmann method by means of the discrete ordinate method for the Boltzmann equation, J. Comput. Phys., 31, 1, 241-246, (1997) · Zbl 0877.76062
[2] Bhatnagar, P. L.; Gross, E. P.; Krook, M., A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94, 3, 511-525, (1954) · Zbl 0055.23609
[3] Biciusca, T.; Horga, A.; Sofonea, V., Simulation of liquidvapor phase separation on GPUs using Lattice Boltzmann models with off-lattice velocity sets, Compt. R. Mecan., 343, 10-11, 580-588, (2015)
[4] Cao, N.; Chen, S.; Jin, S.; Martinez, D., Physical symmetry and lattice symmetry in the lattice Boltzmann method, Phys. Rev. E, 55, 1, R21-R24, (1997)
[5] Chen, S.; Doolen, D., Lattice Boltzmann method for fluid flows, Ann. Rev. Fluid Mech., 30, 329-364, (1998) · Zbl 1398.76180
[6] Cristea, A.; Sofonea, V., Two component lattice Boltzmann model with flux limiters, Cent. Eur. J. Phys., 2, 2, 382-396, (2004)
[7] El-Amin, M. F.; Sun, S.; Salama, A., On the stability of the finite difference based lattice Boltzmann method, Proc. Comput. Sci., 18, 2101-2108, (2013)
[8] Fakhari, A.; Lee, T., Finite-difference lattice Boltzmann method with a block-structured adaptive-mesh-refinement technique, Phys. Rev. E, 89, 033310-1-033310-12, (2014)
[9] Fakhari, A.; Lee, T., Numerics of the lattice Boltzmann method on non-uniform grids: Standard LBM and finite-difference LBM, Comput. Fluids, 107, 205-213, (2015) · Zbl 1390.76710
[10] Guo, Z.; Zhao, T. S., Explicit finite-difference lattice Boltzmann method for curvilinear coordinates, Phys. Rev. E, 67, 066709-1-066709-12, (2003)
[11] Guo, Z.; Zhao, T. S., Finite-difference-based lattice Boltzmann scheme for dense binary mixtures, Phys. Rev. E, 71, 026701-1-026701-12, (2005)
[12] Guo, Z.; Zheng, C.; Zhao, T. S., A lattice BGK scheme for general propagation, J. Sci. Comput., 16, 4, 569-585, (2001) · Zbl 1039.76054
[13] Guzel, G.; Koc, I., Time-accurate flow simulations using a finite-volume based lattice Boltzmann flow solver with dual time stepping scheme, Int. J. Comput. Methods, 13, 6, 1650035-1-1650035-18, (2016) · Zbl 1359.76229
[14] He, X.; Luo, L.-S., Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E, 56, 6, 6811-6817, (1997)
[15] Hejranfar, K.; Ezzatneshan, E., Simulation of two-phase liquid-vapor flows using a high-order compact finite-difference lattice Boltzmann method, Phys. Rev. E, 92, 053305-1-053305-23, (2015)
[16] Huang, J. J.; Huang, H.; Shu, C.; Chew, Y. T.; Wang, S. L., Hybrid multiple-relaxation-time lattice-Boltzmann finite-difference method for axisymmetric multiphase flows, J. Phys. A, Math. Theor., 46, 055501-1-055501-27, (2013) · Zbl 1339.76042
[17] Kandhai, D.; Soll, W.; Chen, S.; Hoekstra, A.; Sloot, P., Finite-difference lattice-BGK methods on nested grids, Comput. Phys. Commun., 129, 100-109, (2000) · Zbl 0976.76067
[18] Kefayati, G. R., FDLBM simulation of magnetic field effect on mixed convection in a two sided lid-driven cavity filled with non-Newtonian nanofluid, Powder Technol., 280, 135-153, (2015)
[19] Krivovichev, G. V., On the finite-element-based lattice Boltzmann scheme, Appl. Math. Sci., 8, 33, 1605-1620, (2014)
[20] Kupershtokh, A. L., Criterion of numerical instability of liquid state in LBE simulations, Comput. Math. Appl., 59, 2235-2245, (2010) · Zbl 1193.76111
[21] Liu, H.; Valocchi, A. J.; Zhang, Y.; Kang, Q., Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows, Phys. Rev. E, 87, 013010-1-013010-13, (2013)
[22] Mei, E.; Shyy, W., On the finite difference-based lattice Boltzmann method in curvilinear coordinates, J. Comput. Phys., 123, 426-448, (1998) · Zbl 0934.76074
[23] Mohammadpourfard, M.; Fallah, M., Optimized free energy-based lattice Boltzmann method for modeling micro drop dynamics, Int. J. Comput. Methods, 10, 3, 1350006-1-1350006-17, (2013) · Zbl 1359.76233
[24] Nejat, A.; Abdollahi, V., A critical study of the compressible lattice Boltzmann methods for Riemann problem, J. Sci. Comput., 54, 1-20, (2013) · Zbl 1426.76610
[25] Niu, X. D.; Shu, C.; Chew, Y. T.; Wang, T. G., Investigation of stability and hydrodynamics of different lattice Boltzmann models, J. Stat. Phys., 117, 3-4, 665-680, (2004) · Zbl 1113.82044
[26] Nourgaliev, R. R.; Dinh, T. N.; Theofanous, T. G.; Joseph, D., The lattice Boltzmann equation method: Theoretical interpretation, numerics and implications, Int. J. Multiphase Flow, 29, 117-169, (2003) · Zbl 1136.76594
[27] Pan, C.; Luo, L. S.; Miller, C. T., An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Comput. Fluids, 35, 8, 898-909, (2006) · Zbl 1177.76323
[28] Reider, M. B.; Sterling, J. D., Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations, Comput. Fluids, 24, 4, 459-467, (1995) · Zbl 0845.76086
[29] Richtmyer, R. D.; Morton, K. W., Difference Methods for Initial-Value Problems, (1994), John Wiley and Sons: John Wiley and Sons, New York · Zbl 0824.65084
[30] Rinaldi, P. R.; Dari, E. A.; Venere, M. J.; Clausse, A., A Lattice-Boltzmann solver for 3D fluid simulation on GPU, Simul. Model. Pract. Theory, 25, 163-171, (2012)
[31] Schreiber, M.; Neumann, P.; Zimmer, S.; Bungartza, H. J., Free-surface lattice-Boltzmann simulation on many-core architectures, Proc. Comput. Sci., 4, 984-993, (2011)
[32] Seta, T.; Takakashi, R., Numerical stability analysis of FDLBM, J. Stat. Phys., 7, 1-2, 557-572, (2002) · Zbl 1007.82009
[33] Shan, X.; Yuan, X.-F.; Chen, H., Kinetic theory representation of hydrodynamics: A way beyond the Navier Stokes equation, J. Fluid Mech., 550, 1, 413-441, (2006) · Zbl 1097.76061
[34] Shi, Y.; Yap, Y. W.; Sader, J. E., Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer, Phys. Rev. E, 92, 013307-1-013307-13, (2015)
[35] Smith, B. T.; Boyle, J. M.; Dongarra, J. J.; Garbow, B. S.; Ikebe, Y.; Klema, V. C.; Moler, C. B., Matrix Eigensystem Routines — EISPACK Guide, Lect. Notes Comput. Sci., 6, 1-123, (1976) · Zbl 0325.65016
[36] Sofonea, V.; Sekerka, R. F., Viscosity of finite difference lattice Boltzmann models, J. Comput. Phys., 184, 422-434, (2003) · Zbl 1062.76556
[37] Sterling, J. D.; Chen, S., Stability analysis of lattice Boltzmann methods, J. Comput. Phys., 123, 196-206, (1996) · Zbl 0840.76078
[38] Ubertini, S.; Bella, G.; Succi, S., Lattice Boltzmann method on unstructured grids: Further developments, Phys. Rev. E, 68, 1, 016701-1-016701-10, (2003)
[39] Ubertini, S.; Succi, S., Recent advances of lattice Boltzmann techniques on unstructured grids, Progr. Comput. Fluid Dyn., 5, 1-2, 85-96, (2004)
[40] Wardle, K. E.; Lee, T., Finite element lattice Boltzmann simulations of free surface flow in a concentric cylinder, Comput. Math. Appl., 65, 230-238, (2013) · Zbl 1268.76051
[41] Watari, M., Finite difference lattice Boltzmann method with arbitrary specific heat ratio applicable to supersonic flow simulations, Phys. A,, 382, 502-522, (2007)
[42] Watari, M.; Tsutahara, M., Supersonic flow simulations by a three-dimensional multispeed thermal model of the finite difference lattice Boltzmann method, Phys. A, 364, 129-144, (2006)
[43] Wei, Y.-K.; Hu, X.-Q., Two-dimensional simulations of turbulent flow past a row of cylinders using lattice Boltzmann method, Int. J. Comput. Methods, 14, 1, 1750002-1-1750002-11, (2017) · Zbl 1404.76213
[44] Worthing, R. A.; Mozer, J.; Seeley, G., Stability of lattice Boltzmann methods in hydrodynamic regimes, Phys. Rev. E,, 56, 2, 2243-1-2243-11, (1997)
[45] Yan, B.; Xu, A.-G.; Zhang, G.-C.; Ying, Y.-J.; Li, H., Lattice Boltzmann model for combustion and detonation, Front. Physics, 8, 1, 94-110, (2013)
[46] Zhang, Y.; Pan, G.; Hung, Q., ICCM2016: The implementation of two-dimensional multi-block lattice Boltzmann method on GPU, Int. J. Comput. Methods, 15, 2, 1840002-1-1840002-16, (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.