Abstract
We present a multilevel algorithm to compute steady states oflattice Boltzmann models directly as fixed points of a time-stepper. At the fine scale, we use a Richardson iteration for the fixed point equation, which amounts to time-stepping towards equilibrium. This fine-scale iteration is accelerated by transferring the error to a coarse level. At this coarse level, one directly solves for the density (the zeroth moment of the lattice Boltzmann distributions), for which a coarse-level equation is known in some appropriate limit. The algorithm closely resembles the classical multigrid algorithm in spirit, structure and convergence behaviour. In this paper, we discuss the formulation of this algorithm. We give an intuitive explanation of its convergence behaviour and illustrate with numerical experiments.
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Acknowledgements
This work was supported by the Research Foundation – Flanders through Research Projects G.0130.03 and G.0170.08 and by the Interuniversity Attraction Poles Programme of the Belgian Science Policy Office through grant IUAP/V/22 (GS). The scientific responsibility rests with its authors.
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Samaey, G., Vandekerckhove, C., Vanroose, W. (2011). A Multilevel Algorithm to Compute Steady States of Lattice Boltzmann Models. In: Gorban, A., Roose, D. (eds) Coping with Complexity: Model Reduction and Data Analysis. Lecture Notes in Computational Science and Engineering, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14941-2_8
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DOI: https://doi.org/10.1007/978-3-642-14941-2_8
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