Bernsdorf, J.; Durst, F.; Schäfer, M. Comparison of cellular automata and finite volume techniques for simulation of incompressible flows in complex geometries. (English) Zbl 0940.76067 Int. J. Numer. Methods Fluids 29, No. 3, 251-264 (1999). Summary: A cellular automata method for the prediction of incompressible fluid flows is presented and its practical relevance is investigated by comparing it with a standard finite volume solver. The cellular automata approach is based on an advanced lattice Boltzmann technique for a discrete microscopic description of the fluid flow. The finite volume solution procedure solves the macroscopic Navier-Stokes equations by means of an advanced multigrid pressure-correction technique on block-structured grids. Advantages and disadvantages of the cellular automata technique are discussed and quantitative comparative results related to accuracy, convergence properties and computing times are given for test cases with varying geometrical complexity. As a practical application of the method, results for the numerical simulation of the flow in porous sedimentary layer are given. Cited in 11 Documents MSC: 76M28 Particle methods and lattice-gas methods 76M12 Finite volume methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:cellular automata method; finite volume solver; advanced lattice Boltzmann technique; Navier-Stokes equations; multigrid pressure-correction technique; block-structured grids; porous sedimentary layer PDFBibTeX XMLCite \textit{J. Bernsdorf} et al., Int. J. Numer. Methods Fluids 29, No. 3, 251--264 (1999; Zbl 0940.76067) Full Text: DOI References: [1] Eggels, Int. J. Heat Fluid Flow 17 pp 307– (1996) [2] Durst, Int. J. Numer. Method Fluids 22 pp 549– (1996) [3] Noble, Int. J. Numer. Methods Fluids 23 pp 1– (1996) [4] Satofuka, XIXth Int. Cong. of Theoretical and Applied Mechanics pp 25– (1996) [5] Higuera, Europhys. Lett. 9 pp 663– (1989) [6] Kingdon, J. Phys. Math. 25 pp 3559– (1992) [7] Succi, Physica D 47 pp 219– (1991) [8] Patankar, Int. J. Heat Mass Transf. 15 pp 1787– (1972) [9] Bückle, J. Mater. Proc. Manuf. Sci. 4 pp 69– (1995) [10] Durst, J. Cryst. Growth 125 pp 612– (1992) [11] Hortmann, Comput. Fluid Mech. 2 pp 65– (1994) [12] Hortmann, Int. J. Numer. Methods in Fluids 11 pp 189– (1990) [13] Frisch, Complex Syst. 1 pp 649– (1987) [14] Qian, Europhys. Lett. 17 pp 479– (1992) [15] Kohring, J. Phys. II 1 pp 87– (1991) [16] ’Limitations of a finite mean free path for simulating flows in porous media’, UniversïtaKöln, April 1991. [17] Lavallée, Physica D 47 pp 233– (1991) [18] Inamuro, Phys. Fluids 7 pp 2928– (1995) [19] Ziegler, J. Stat. Phys. 71 pp 1171– (1993) [20] Skordos, Phys. Rev. E 48 pp 4823– (1993) [21] Noble, Phys. Fluids 7 pp 203– (1995) [22] and , ’Recent advances in lattice Boltzmann computing’, In: (ed.) Annual Reviews of Computational Physics III 1995, p. 209. [23] Kropp, Diplomarbeit (1992) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.