Lattice Boltzmann method for inhomogeneous fluidsS. Melchionna1 and U. Marini Bettolo Marconi2
1 INFM-SOFT, Dipartimento di Fisica, Università di Roma and Istituto Nazionale di Fisica della Materia Piazzale A. Moro 2, 00185, Roma, Italy
2 INFM-SOFT, Dipartimento di Fisica, Università di Camerino and Istituto Nazionale di Fisica della Materia Via Madonna delle Carceri, 62032, Camerino, Italy
received 4 September 2007; accepted in final form 26 November 2007; published February 2008
published online 21 December 2007
We present a lattice-based numerical method to describe the non-equilibrium behavior of a simple fluid under non-uniform spatial conditions. The evolution equation for the one-particle phase-space distribution function is derived starting from a microscopic description of the system. It involves a series of approximations which are similar to those employed in theories of inhomogeneous fluids, such as the density functional theory. Among the merits of the present approach: the possibility to determine the equation of state of the model, the transport coefficients and to provide an efficient method of numerical solution under non-uniform conditions. The algorithm is tested in a particular non-equilibrium situation, namely the steady flow of a hard-sphere fluid across a narrow slit. Pronounced non-hydrodynamic oscillations in the density and velocity profiles are found.
47.11.-j - Computational methods in fluid dynamics.
47.61.-k - Micro- and nano- scale flow phenomena.
61.20.-p - Structure of liquids.
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