Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects

Hajabdollahi, Farzaneh; Premnath, Kannan N.; Welch, Samuel

doi:10.1016/j.ijheatmasstransfer.2018.09.059

Cited by 24 publications

(24 citation statements)

References 68 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The construction of the collision step in the LB formulations using central moments based on the peculiar velocity [29,30] naturally maintains the Galilean invariance of the moments independently supported by the lattice and its advantages have been demonstrated for a variety of fluid dynamical problems (see e.g., [31][32][33][34][35][36]). Based on these considerations, we proposed a 2D central moment rectangular LB scheme recently and demonstrated its superior numerical features for simulating flows at higher Reynolds numbers using relatively small grid aspect ratio when compared to the other existing LB methods based on the rectangular lattice [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Yahia

Schupbach

Premnath

2021

Fluids

Self Cite

View full text Add to dashboard Cite

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

show abstract

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Yahia

Schupbach

Premnath

2021

Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the case of the LBE for computing fluid flow, the symmetry of their moment equilibria to respect the isotropy of the viscous stress tensor limits the dependence of the corresponding non-equilibrium second order moments to only on the symmetric part of the velocity gradient tensor (i.e., the strain rate tensor). However, the construction of the LBE for computing the transport of a passive scalar represented by the CDE does not need to satisfy these restrictive constraints, and the additional degrees of freedom available for the higher order moments can be suitably exploited [57]. Indeed, since the diffusion term of the CDE need only to satisfy a lower degree of isotropy than that of the viscous term of the NSE, the third order moment equilibria for solving the former case can be specifically designed to locally represent the skew-symmetric part of the velocity gradient tensor via the respective off-diagonal non-equilibrium secondorder moment (based on an equation analogous to the sixth equation in the above moment system withκ eq x m y n replaced byη eq x m y n andm…”

Section: Discussionmentioning

confidence: 99%

“…We prescribe the central moment equilibria based on those of the local Maxwellian, by replacing the density with the scalar field φ (see e.g., [54,55,56]). Usually, the third order central moment equilibria then becomeη eq xxy =η eq xyy = 0 and the corresponding raw moment equilibria areη eq xxy = c 2 sφ φu y + φu 2 x u y and η eq xyy = c 2 sφ φu x + φu x u 2 y [54,55,56]. On the other hand, to enable local computation of the vorticity field, our derivation in Secs.…”

Section: Discussionmentioning

confidence: 99%

Local vorticity computation approach in double distribution functions based lattice Boltzmann methods for flow and scalar transport

Hajabdollahi

Premnath

2020

International Journal of Heat and Fluid Flow

Self Cite

View full text Add to dashboard Cite

Computation of vorticity, or the skew-symmetric velocity gradient tensor, in conjunction with the strain rate tensor, plays an important role in fluid mechanics in the flow classification, in vortical structure identification and in the modeling of various complex fluids and flows. For the simulation of flows accompanied by the advection-diffusion transport of a scalar field, double distribution functions (DDF) based lattice Boltzmann (LB) methods, involving a pair of LB schemes are commonly used. We present a new local vorticity computation approach by introducing an intensional anisotropy of the scalar flux in the third order, off-diagonal moment equilibria of the LB scheme for the scalar field, and then combining the second order non-equilibrium components of both the LB methods. As such, any pair of lattice sets in the DDF formulation that can independently support the third order off-diagonal moments would enable local determination of the complete flow kinematics, with the LB methods for the fluid motion and the transport of the passive scalar respectively providing the necessary moment relationships to determine the symmetric and skew-symmetric components of the velocity gradient tensor. Since the resulting formulation is completely local and do not rely on finite difference approximations for velocity derivatives, it is by design naturally suitable for parallel computation. As an illustration of our approach, we formulate a DDF-LB scheme for local vorticity computation using a pair of multiple relaxation times (MRT) based collision approaches on two-dimensional, nine velocity (D2Q9) lattices, where the necessary moment relationships to determine the velocity gradient tensor and the vorticity are established via a Chapman-Enskog analysis. Simulations of various benchmark flows demonstrate good accuracy of the predicted vorticity fields using our approach against available solutions, including numerical results, with a second order convergence. Furthermore, extensions of our formulation for a variety of collision models to enable local vorticity computation are presented.

show abstract

“…In addition to the aforementioned studies many numerical models that use the axisymmetric form of Navier-Stokes equations have been developed, for both compressible (Gokhale and Suresh, 1997; Clain et al , 2010; Musa et al , 2016) and incompressible (Leloudas et al , 2018, 2020; Saiac, 1990; Morsi et al , 1995; Durkish, 2006; Moshkin et al , 2010; Dağtekin and Ünsal, 2011; Lee and Lee, 2011; Semião and Carvalho, 1997) flows, featuring various discretization methods, flux evaluation schemes and turbulence models. Moreover, axisymmetric flow modelling has lately become a highly attractive topic in the context of mesoscopic approaches as well, such as the lattice Boltzmann method (LBM) (Zhang et al , 2019b; Lee et al , 2005; Huang et al , 2007; Liu et al , 2016; Li et al , 2018; Chen et al , 2019; Hajabdollahi et al , 2019; Liu et al , 2019). However, to the authors’ best knowledge, the implementation of an axisymmetric Navier-Stokes solver for swirling flows using the artificial compressibility method (ACM) is not available.…”

Section: Introductionmentioning

confidence: 99%

An artificial compressibility method for axisymmetric swirling flows

Leloudas

Lygidakis

Delis

et al. 2021

View full text Add to dashboard Cite

Purpose This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows. Design/methodology/approach The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure. Findings A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy. Originality/value This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

show abstract

Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects

Cited by 24 publications

References 68 publications

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Local vorticity computation approach in double distribution functions based lattice Boltzmann methods for flow and scalar transport

An artificial compressibility method for axisymmetric swirling flows

Contact Info

Product

Resources

About