Essentially entropic lattice Boltzmann model: Theory and simulations

TL;DR

This paper introduces an exact analytical solution for the entropic lattice Boltzmann model that ensures unconditional stability, simplifies computations, and extends applicability to heat transfer without Prandtl number limitations.

Contribution

It provides a closed-form analytical solution to the entropic lattice Boltzmann model, reducing computational complexity and extending the model's applicability to heat transfer problems.

Findings

Exact solution matches iterative solutions near equilibrium.

The analytical solution simplifies computations and removes overhead.

Extension to ES-BGK model removes Prandtl number limitations.

Abstract

We present a detailed description of the essentially entropic lattice Boltzmann model. The entropic lattice Boltzmann model guarantees unconditional numerical stability by iteratively solving the nonlinear entropy evolution equation. In this paper we explain the construction of closed-form analytic solutions to this equation. We demonstrate that near equilibrium this exact solution reduces to the standard lattice Boltzmann model. We consider a few test cases to show that the exact solution does not exhibit any significant deviation from the iterative solution. We also extend the analytical solution for the ES-BGK model to remove the limitation on the Prandtl number for heat transfer problems. The simplicity of the exact solution removes the computational overhead and algorithmic complexity associated with the entropic lattice Boltzmann models.