Improving the low Mach number steady state convergence of the cascaded lattice Boltzmann method by preconditioning

Hajabdollahi, Farzaneh; Premnath, Kannan N.

doi:10.1016/j.camwa.2016.12.034

Cited by 16 publications

(20 citation statements)

References 38 publications

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“…A modified formulation based on central moments involving relaxation to discrete equilibria rather than continuous Maxwellian equilibria was also proposed [39]. In order to accelerate convergence of steady flows, a preconditioned cascaded LB method was constructed and studied in [40], and whose Galilean invariance properties were significantly improved via corrections to equilibria in [41]. The cascaded LB scheme has recently been extended for simulating flows with heat transfer in 2D [42,43] and in 3D in our recent work [44].…”

Section: Introductionmentioning

confidence: 99%

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

Hajabdollahi

Premnath

Welch

2019

International Journal of Heat and Mass Transfer

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Section: Introductionmentioning

confidence: 99%

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

Hajabdollahi

Premnath

Welch

2019

International Journal of Heat and Mass Transfer

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“…The code is developed based on C++ and runs on a laptop with Intel (R) Core (TM) i7-6500U CPU @ 2.5 GHz and RAM 8.00 GB. The implementation is basic for all the three models, without resorting to any optimization strategies, such as the preconditioning method [39] and the LAPACK library [40]. To be more specific, we use the program structure provided in the Appendix A in Ref.…”

Section: A the Decay Of A Shear Wavementioning

confidence: 99%

“…Moreover, a thermal cascaded LBM (TCLBM) has been proposed by the present authors to simulate low-Mach compressible thermal flows [31], and several different CLBMs have been developed later for incompressible thermal flows [32][33][34][35][36]. Finally, CLBM has also been extended to simulate shallow water equations [37], moving boundary problems [38], as well as stationary flows with a preconditioning method [39].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

Fei

Luo

2018

Phys. Rev. E

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The cascaded or central-moment-based lattice Boltzmann method (CLBM) proposed in [Phys. Rev. E 73, 066705 (2006)] possesses very good numerical stability. However, two constraints exist in three-dimensional (3D) CLBM simulations. First, the conventional implementation for 3D CLBM involves cumbersome operations and requires much higher computational cost compared to the single-relaxation-time (SRT) LBM. Second, it is a challenge to accurately incorporate a general force field into the 3D CLBM. In this paper, we present an improved method to implement CLBM in 3D. The main strategy is to adopt a simplified central moment set and carry out the central-moment-based collision operator based on a general multi-relaxation-time (GMRT) framework. Next, the recently proposed consistent forcing scheme for CLBM [Fei and Luo, Phys. Rev. E 96, 053307 (2017)] is extended to incorporate a general force field into 3D CLBM. Compared with the recently developed nonorthogonal CLBM [Rosis, Phys. Rev. E 95, 013310 (2017)], our implementation is proved to reduce the computational cost significantly. The inconsistency of adopting the discrete equilibrium distribution functions in the nonorthogonal CLBM is analyzed and validated. The 3D CLBM developed here in conjunction with the consistent forcing scheme is verified through numerical simulations of several canonical force-driven flows, highlighting very good properties in terms of accuracy, convergence, and consistency with the nonslip rule. Finally, the techniques developed here for 3D CLBM can be applied to make the implementation and execution of 3D MRT-LBM more efficient.

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“…In order to facilitate the Chapman-Enskog analysis, the central moment LB formulation can be equivalently rewritten in terms of a collision process involving relaxation to a generalized equilibria in the lattice or rest frame of reference [41]. This strategy is considered in this work to further investigate the structure of the cubic velocity non-GI truncation errors for our preconditioned LB method.…”

Section: Chapman-enskog Analysismentioning

confidence: 99%

“…Here, γ is the preconditioning parameter, which can be used to tune the pseudo-sound speed, thereby alleviating the eigenvalue stiffness and improving convergence acceleration (e.g. [41] In order to first identify such truncation errors, we perform a Chapman-Enskog analysis of the preconditioned central moment LB formulation and isolate various cubic-velocity and parameter dependent errors at various moment orders. It will be seen that the anisotropy of the stress tensor depends not just on the cubic-velocity terms (like in the previous studies), but also on the preconditioning parameter γ.…”

Section: Introductionmentioning

confidence: 99%

Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient steady flow simulations

Hajabdollahi

Premnath

2018

Phys. Rev. E

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Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean-invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third-order diagonal moments on the first-order moments for standard lattices, and strategies have recently been introduced to restore Galilean invariance without such errors using a modified collision operator involving corrections to either the relaxation times or the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that can be used to tune the effective sound speed, and thereby alleviating the numerical stiffness. In the present paper, we present a GI formulation of the preconditioned cascaded central-moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice, for steady flows. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Such parameter dependent corrections eliminate the remaining truncation errors arising from the degeneracy of the diagonal third-order moments and fully restore Galilean invariance without cubic defects for the preconditioned LB scheme on a standard lattice. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. The GI preconditioned central-moment LB method is validated for a number of complex flow benchmark problems and its effectiveness to achieve convergence acceleration and improvement in accuracy is demonstrated.

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Improving the low Mach number steady state convergence of the cascaded lattice Boltzmann method by preconditioning

Cited by 16 publications

References 38 publications

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

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

Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient steady flow simulations

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