×

zbMATH — the first resource for mathematics

Numerical stability of entropic versus positivity-enforcing lattice Boltzmann schemes. (English) Zbl 1116.76068
Summary: A preliminary study of the nonlinear stability properties of entropic schemes versus positivity-enforcing (FIX-UP) schemes is presented for the case of two-dimensional cavity flow. It is shown that, although they operate on fairly distinct schedules, both methods achieve substantial stability enhancements over the standard single-time relaxation Lattice Boltzmann scheme.

MSC:
76M28 Particle methods and lattice-gas methods
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ansumali, S.; Karlin, I.V., Entropy function approach to the lattice Boltzmann method, J. stat. phys., 107, 291, (2002) · Zbl 1007.82019
[2] Ansumali, S.; Karlin, I.V.; Öttinger, H.C., Minimal entropic kinetic models for hydrodynamics, Europhys. lett., 63, 6, 798-804, (2003)
[3] Benzi, R.; Succi, S.; Vergassola, M., The lattice Boltzmann equation: theory and applications, Phys. rep., 222, 145-197, (1992)
[4] Boghosian, B.M.; Yepez, J.; Coveney, P.V.; Wagner, A.J., Entropic lattice Boltzmann methods, Proc. R. soc. lond. A, 457, 717-766, (2001) · Zbl 0984.76069
[5] Chen, S.; Chen, H.; Martinez, D.; Matthaeus, W.H., Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. rev. lett., 67, 3776-3779, (1991)
[6] Chen, H.; Chen, S.; Matthaeus, W.H., Recovery of the navier – stokes equations using a lattice-gas Boltzmann method, Phys. rev. A, 45, 5339-5342, (1992)
[7] Chen, H.; Teixeira, C., H-theorem and origins of instability in thermal lattice Boltzmann models, Comp. phys. commun., 129, 21-31, (2000) · Zbl 0985.76070
[8] d’Humieres, D., Generalized lattice-Boltzmann equation, (), 450-458
[9] Erturk, E.; Corke, T.C.; Gökçöl, C., Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, Int. J. num. methods fluid, 48, 7, 747-774, (2005) · Zbl 1071.76038
[10] Higuera, F.J.; Succi, S.; Benzi, R.; Higuera, F.J.; Jimenez, J., Lattice gas dynamics with enhanced collisions, Europhys. lett., Europhys. lett., 9, 662-667, (1989)
[11] Hou, S.; Zou, Q.; Chen, S.; Doolen, G.; Cogley, A.C., Simulation of cavity flow by the lattice Boltzmann method, J. comp. phys., 11, 329-347, (1995) · Zbl 0821.76060
[12] Karlin, I.V.; Ferrante, A.; Öttinger, H.C., Perfect entropy functions of the lattice Boltzmann method, Europhys. lett., 47, 2, 182-188, (1999)
[13] Karlin, I.V.; Gorban, A.N.; Succi, S.; Boffi, V., Maximum entropy principle for lattice kinetic equations, Phys. rev. lett., 81, 6-9, (1998)
[14] Li, Y.; Shock, R.; Zhang, R.; Chen, H., Numerical study of flow past an impulsively started cylinder by the lattice-Boltzmann method, J. fluid mech., 519, 273-300, (2004) · Zbl 1065.76166
[15] Qian, Y.H.; d’Humieres, D.; Lallemand, P., Lattice BGK models for navier – stokes equation, Europhys. lett., 17, 6, 479-484, (1992) · Zbl 1116.76419
[16] Succi, S., The lattice Boltzmann equation for fluid dynamics and beyond, (2001), Oxford University Press, Claredon Press · Zbl 0990.76001
[17] F. Tosi, S. Ubertini, S. Succi and I. Karlin, Optimization strategies for the entropic lattice Boltzmann method, submitted for publication. · Zbl 1110.76043
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.