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Pair interaction lattice gas simulations: Flow past obstacles in two and three dimensions

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Abstract

Apart from the FCHC (face-centered hypercube), Nasilowski's pair interaction lattice gas (PI) is the only known lattice gas automaton for three-dimensional hydrodynamic simulations. Unfortunately, the viscosity of PI is not isotropic. In order to determine the degree anisotropy, we derive fluid dynamic equations for the regime of compressible viscid flow. From relaxation measurements of waves propagating in various directions we compute the physically relevant dissipation coefficients and compare our results with theoretical predictions. Although PI shows a high degree of anisotropy, we define the mean value of the dissipation tensor as effective shear viscosity. Using this value of v 2Deff =0.35, two-dimensional simulations of flow past a cylinder yield drag coefficients in quantitative agreement with wind tunnel measurements over a range of Reynolds numbers of 5–50. Three-dimensional simulations of flow past a sphere yield qualitative agreement with various references. A fit of the results to a semi-empirical curve provides an effective value of v 2Deff =0.21 for a range of Reynolds numbers from 0.19 to 40. In order to check for finite-size effects, we measured the mean free pathλ and computed the Knudsen numbers. We obtainedλ≈ 1 lattice unit, corresponding to Kn=0.01 (2D) and Kn=0.1 (3D). We found no significant finite-size effects.

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  1. Alfred-Wegener-Institute for Polar and Marine Research, D-2850, Bremerhaven, Germany

    Armin Vogeler & Dieter A. Wolf-Gladrow

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  1. Armin Vogeler
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  2. Dieter A. Wolf-Gladrow
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Vogeler, A., Wolf-Gladrow, D.A. Pair interaction lattice gas simulations: Flow past obstacles in two and three dimensions. J Stat Phys 71, 163–190 (1993). https://doi.org/10.1007/BF01048093

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