Lattice Boltzmann Model in General Curvilinear Coordinates Applied to Exactly Solvable 2D Flow Problems

TL;DR

This paper demonstrates that a Lattice Boltzmann Method formulated in general curvilinear coordinates accurately simulates exactly solvable 2D fluid flows, maintaining minimal numerical diffusion and converging to exact solutions with increased grid resolution.

Contribution

The paper introduces a curvilinear coordinate formulation of the Lattice Boltzmann Method that preserves exact advection and demonstrates its effectiveness on solvable 2D flow problems.

Findings

The curvilinear LBM converges to exact solutions with finer grids.

The method maintains minimal numerical diffusion in complex geometries.

It works effectively for both near and non-equilibrium conditions.

Abstract

Numerical simulation results of basic exactly solvable fluid flows using the previously proposed Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H. Chen, such curvilinear Lattice Boltzmann Method preserves a fundamental one-to-one exact advection feature in producing minimal numerical diffusion, as the Cartesian lattice Boltzmann model. As we numerically show, the new model converges to exact solutions of basic fluid flows with the increase of grid resolution in the presence of both natural curvilinear geometry and/or grid non-uniform contraction, both for near equilibrium and non-equilibrium LBM parameter choices.