Two‐dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

Abstract

SUMMARY In this article, an extension to the total variation diminishing finite volume formulation of the lattice Boltzmann equation method on unstructured meshes was presented. The quadratic least squares procedure is used for the estimation of first‐order and second‐order spatial gradients of the particle distribution functions. The distribution functions were extrapolated quadratically to the virtual upwind node. The time integration was performed using the fourth‐order Runge–Kutta procedure. A grid convergence study was performed in order to demonstrate the order of accuracy of the present scheme. The formulation was validated for the benchmark two‐dimensional, laminar, and unsteady flow past a single circular cylinder. These computations were then investigated for the low Mach number simulations. Further validation was performed for flow past two circular cylinders arranged in tandem and side‐by‐side. Results of these simulations were extensively compared with the previous numerical data. Copyright © 2011 John Wiley & Sons, Ltd.

A simplified finite volume lattice Boltzmann method for simulations of fluid flows from laminar to turbulent regime, Part I: Numerical framework and its application to laminar flow simulation

“…The same results can be found in Ref. [24,46,47]. At this spacing, the gap flow between two cylinders is upward or downward biased and the shedding pattern of vortexes from two cylinders is asymmetric.…”

“…First, the same test in Ref. [24] with Re = 100 is adopted to validate the present method can apply to unsteady flow. The computational domain is 70d × 50d and the cylinder is set into the center location of domain, where the d is the cylinder diameter.…”

“…Patil et al introduce the Roe's flux-difference splitting scheme and the limiters to the unstructured grid [16]. The main problem of this work is that the numerical diffusion is larger, which causes the results are not present an improved scheme for unsteady flow and have more accuracy results compared with their originated work [24]. The main defect of this work is that the stencil for calculation the gradient of distribution function is not compact, so the computational efficiency is lower for parallel computing.…”

Performance evaluation of the general characteristics based off-lattice Boltzmann scheme and DUGKS for low speed continuum flows

“…However, a straightforward implementation of the CFD techniques usually leads to the loss of the advantages of standard LBM, especially the low dissipation property and stability at large time step. For example, in many of the schemes [4,7,8,10,11], the time step is limited by the relaxation time to get an accurate solution, even as the collision term is computed implicitly [7]. This drawback makes these OLB schemes very computational expensive when simulating high Reynolds number flows.…”

The Effect of the Addition of Inlet Disturbance Body (IDB) to Flow Resistance Through the Square Cylinders Arranged in Tandem

“…Patil and Lakshmisha [18] used quadratic least squares (QLS) procedure to extract the first-order derivatives of distribution functions up to the second-order accuracy. The numerical results showed better agreement with the previous findings for a flow through a single circular cylinder.…”