Solving incompressible fluid flows on unstructured meshes with the lattice Boltzmann flux solver

Nicolas Pellerin,Sébastien Leclaire,Marcelo Reggio

doi:10.1080/19942060.2017.1292410

Nicolas Pellerin, Sébastien Leclaire + Show 1 more

Open Access

https://doi.org/10.1080/19942060.2017.1292410

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Abstract

ABSTRACTAn application of the recently developed lattice Boltzmann flux solver (LBFS) is proposed to solve incompressible flows using unstructured meshes with high aspect ratio triangular cells. The capability to solve turbulent flows is also introduced by coupling the method with a turbulence model, for which the viscosity transport equation is solved on the same mesh. The proposed computational approach is validated for the classical lid-driven cavity flow, the flow over a circular cylinder, and the turbulent flow around a NACA0012 airfoil. Overall, the results obtained agree well with reference data, and demonstrate the validity of using the LBFS on directionally refined meshes, providing the advantage of limiting the number of vertices required in boundary layer regions of the fluid flow. An alternate flux construction method derived from a lattice Boltzmann boundary condition model based on equilibrium distribution streaming is also presented.

Highlights

The lattice Boltzmann method (LBM) for fluids is a flow-solving approach which treats fluids as a probabilistic ensemble of interacting particles, rather than as a continuum, as in Navier-Stokes solvers
For flows with high Reynolds numbers, in a turbulent regime, the LBM needs to be supplemented with turbulence models
Imamura et al (2005) use an orthogonal grid system that conforms to the airfoil geometry, in conjunction with coordinate transformation that allows the LBM to be applied on a non-Cartesian mesh

Summary

Introduction

The lattice Boltzmann method (LBM) for fluids is a flow-solving approach which treats fluids as a probabilistic ensemble of interacting particles, rather than as a continuum, as in Navier-Stokes solvers. Regardless of the approach, fast flows require mesh spacing near walls to be small enough to capture the fluid dynamics within the boundary layers Both commercial packages use regular lattices and multi-domain mesh refinement strategies in order to provide adequate lattice spacing near walls, while limiting the total number of lattice sites. In previous work (Pellerin et al, 2015), the current authors elected to use the multi-domain approach, and coupled it to a finite-difference implementation of the Spalart-Allmaras turbulence model They identified mesh refinement near the airfoil’s leading edge as a key element in obtaining accurate solutions. They report a stable solution for the lid-driven cavity flow with a Reynolds number of 10000, using a non-uniform orthogonal grid of 121 × 121 with near-wall refinement This suggests that the LBFS may have interesting stability properties that could be useful for higher Reynolds number flows. The usual collide-and-stream process of the standard LBM is by nature an upwind operator in the lattice speed directions, and the LBFS, by the way it is constructed, takes advantage of this

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