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Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows

Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich, Switzerland
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These authors contributed equally to this work.
Entropy 2020, 22(3), 370; https://doi.org/10.3390/e22030370
Received: 21 February 2020 / Revised: 19 March 2020 / Accepted: 19 March 2020 / Published: 24 March 2020
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
The entropic lattice Boltzmann method for the simulation of compressible flows is studied in detail and new opportunities for extending operating range are explored. We address limitations on the maximum Mach number and temperature range allowed for a given lattice. Solutions to both these problems are presented by modifying the original lattices without increasing the number of discrete velocities and without altering the numerical algorithm. In order to increase the Mach number, we employ shifted lattices while the magnitude of lattice speeds is increased in order to extend the temperature range. Accuracy and efficiency of the shifted lattices are demonstrated with simulations of the supersonic flow field around a diamond-shaped and NACA0012 airfoil, the subsonic, transonic, and supersonic flow field around the Busemann biplane, and the interaction of vortices with a planar shock wave. For the lattices with extended temperature range, the model is validated with the simulation of the Richtmyer–Meshkov instability. We also discuss some key ideas of how to reduce the number of discrete speeds in three-dimensional simulations by pruning of the higher-order lattices, and introduce a new construction of the corresponding guided equilibrium by entropy minimization. View Full-Text
Keywords: entropy; lattice Boltzmann method; compressible flow; nonlinear acoustics; shock waves entropy; lattice Boltzmann method; compressible flow; nonlinear acoustics; shock waves
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Frapolli, N.; Chikatamarla, S.; Karlin, I. Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows. Entropy 2020, 22, 370.

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