Abstract
There have been contradicting reports in the literature regarding the application of the Entropic LBM to various flow problems. In this paper, we aim to evaluate the various formulations of the Entropic LBM and elaborate on the construction and numerical implementation required for successfully running such simulations. Tests conducted on four different test cases over a large parameter range, along with comparisons with Lattice-BGK results, allows us to comment on the behaviour of four Entropic LBM formulations namely: the iterative Entropic LBM, the 1st and 3rd order Essentially Entropic LBM, and a simplified analytical Entropic LBM approach. The benchmark problems considered are: the athermal shocktube problem, the decay of a Taylor-Green vortex, the square lid driven cavity and, the unsteady flow past a square cylinder. Our simulations reveal the superiority of the iterative and Essentially Entropic LBM over the Lattice-BGK model in terms of numerical stability and operating parameter range at fixed grid sizes. In terms of computational cost, the Lattice-BGK and 1st order Essentially Entropic LBM are comparable, followed by the 3rd order Essentially Entropic LBM and the iterative Entropic LBM. Our results suggest that although the iterative and Essentially Entropic LBM schemes can be used as-is with continuum problems, care is needed for situations where shocks occur. Furthermore, the iterative Entropic LBM model suggests a parametric nature not displayed by the Essentially Entropic LBM schemes. With the simplified Entropic LBM, we find that additional numerical safeguards are needed for typical flow problems.
Published Version
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