Entropy Balance and Dispersive Oscillations in Lattice Boltzmann Models

TL;DR

This paper investigates dispersive oscillations in the entropic lattice-Boltzmann method, finding no regularization benefit over standard methods, but demonstrating regularization via median filtering.

Contribution

It introduces a root finding implementation of ELBM with guaranteed dissipation sign and compares its regularization effects to median filtering in LBGK.

Findings

ELBM shows no regularization benefit over LBGK in shock tube simulations.

Median filtering at a single point per step effectively regularizes LBGK.

The root finding algorithm for ELBM converges rapidly with cubic rate.

Abstract

We conduct an investigation into the dispersive post-shock oscillations in the entropic lattice-Boltzmann method (ELBM). To this end we use a root finding algorithm to implement the ELBM which displays fast cubic convergence and guaranties the proper sign of dissipation. The resulting simulation on the one-dimensional shock tube shows no benefit in terms of regularization from using the ELBM over the standard LBGK method. We also conduct an experiment investigating of the LBGK method using median filtering at a single point per time step. Here we observe that significant regularization can be achieved.