Aplicación del método de la ecuación de Boltzmann en redes para la simulación bidimensional de un problema típico de mecánica de fluidos
DOI:
https://doi.org/10.24054/rcta.v1i25.430Keywords:
Couette flow, numerical simulation, fluids mechanicsAbstract
Existen diversos problemas de flujos de fluidos que cuentan con soluciones analíticas y que pueden ser utilizados como referencia para la validación de soluciones obtenidas a partir de métodos experimentales y numéricos. El flujo de Couette es uno de estos flujos, por lo tanto es utilizado en el presente trabajo para validar el uso de un método numérico relativamente nuevo. Conceptualmente, la configuración más sencilla y la utilizada en el presente trabajo es la de un fluido entre dos placas infinitas, paralelas y separadas entre sí una cierta distancia, y en la que uno de los platos, como en la mayoría de los casos, el superior se traslada con velocidad constante U0. En el presente trabajo se simula, mediante el método de la ecuación de Boltzmann en redes (LBEM), dicho flujo de Couette imponiendo un gradiente de presión aguas abajo y sin dicho gradiente. Los resultados son comparados con las soluciones analíticas existentes (ecuaciones de Navier-Stokes), los cuales demuestran la efectividad del método y del código computacional desarrollado por los autores para la simulación de este tipo de flujo.
References
Las Bhatnagar, P.L., Gross, E.P., Krook. M. (1954), “A model for collision processes in gases. I Small amplitude processes in charged and neutral one-component system”, Phys. Rev., Vol. 94, pp. 511-525.
Chen S. and Martinez D., Mei R. (1996), “On boundary conditions in lattice Boltzmann methods”, Phys. Fluids, Vol. 8 (9), pp.2527- 36.
Dieter A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models, Bremerhaven-Germany, Springer (1ra. Ed), 2000, pp. 40-65
Frisch U., Hasslacher B., and Pomeau Y. (1986), “Lattice-gas automata for the Navier–Stokes equation”, Phys. Rev. Lett., Vol. 56, pp. 1505- 1515
Harris S., An Introduction to the Theory of the Boltzmann Equation, Holt, Rinehart and Winston, New York, 1971.
He X., Luo L-S. (1997), “Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation”. Phys. Rev. E, Vol. 56 (6), pp. 6811-6817.
He X., Zuo Q., Luo L-S and Dembo M. (1997), “Analytic solutions of simple flow and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model”, Journal of Statistic Physics, Vol. 87 (1-2) pp.115-136.
Lallemand P., Luo L-S, (1999), “Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability”. Phys. Rev. E., Vol. 61 (6), pp. 6546-6562.
Maxwell B. J., Lattice Boltzmann methods in Interfacial Wave Modelling. Ph. D. Tesis. Edinburgh's University. 1997. P. 326
Moyers-Gonzalez, Miguel; Frigaard Ian (2010) “The critical wall velocity for stabilization of plane Couette–Poiseuille flow of viscoelastic fluids” Journal of Non-Newtonian Fluids Mechanics, vol. 165, pp. 441-447
Skordos P. A. (1993), “Inicial and boundary conditions for the lattice Boltzmann method”, Phys. Rev E. Vol. 48 (6), pp.4823-42.
Sterling, J. D., Chen, S. (1996), “Stability analysis of lattice Boltzmann methods”, J. Comp. Phys. Vol. 123, pp. 196-206.
Zou Q., He X. (1997), “On pressure and velocity boundary conditions for the lattice Boltzman BGK model”, Phys. Fluids, Vol. 9 (6), pp. 1591-98.
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