Stabilization of the Lattice Boltzmann Method Using Information Theory
Tyler L Wilson, Mary Pugh, Francis Dawson
TL;DR
This paper introduces a new Lattice Boltzmann method based on information theory principles, specifically the Minimum Cross Entropy, to enhance stability and accuracy in fluid flow simulations.
Contribution
It develops a novel Lattice Boltzmann method using the MinxEnt principle and Kullback-Leibler Divergence, improving stability and accuracy over existing methods.
Findings
MinxEnt-LBM shows improved stability in shock tube simulations.
Enhanced accuracy demonstrated in lid-driven cavity flow.
Outperforms traditional LBM methods in tested scenarios.
Abstract
A novel Lattice Boltzmann method is derived using the Principle of Minimum Cross Entropy (MinxEnt) via the minimization of Kullback-Leibler Divergence (KLD). By carrying out the actual single step Newton-Raphson minimization (MinxEnt-LBM) a more accurate and stable Lattice Boltzmann Method can be implemented. To demonstrate this, 1D shock tube and 2D lid-driven cavity flow simulations are carried out and compared to Single Relaxation Time LBM, Two Relaxation Time LBM, Multiple Relaxation Time LBM and Eherenfest Step LBM.
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Taxonomy
TopicsLattice Boltzmann Simulation Studies · Image and Signal Denoising Methods · Generative Adversarial Networks and Image Synthesis