Cascaded collision lattice Boltzmann model (CLBM) for simulating fluid and heat transport in porous media

Shah, Nimit; Dhar, Purbarun; Chinige, Sampath Kumar; Geier, Martin; Pattamatta, Arvind

doi:10.1080/10407790.2017.1377530

Cited by 15 publications

(8 citation statements)

References 17 publications

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“…An important assumption on the cascaded LBM is to use an orthogonal basis of central moments that relax to the equilibrium state of the continuous Maxwellian distribution [12]. Building on this work, many other efforts demonstrated that this model can largely enhance the stability of the LBM [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], even if it may lead to cumbersome analytical formulations and practical implementations, especially in three dimensions [32].…”

Section: Introductionmentioning

confidence: 99%

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

Rosis

Luo

2019

Phys. Rev. E

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The cascaded lattice Boltzmann method decomposes the collision stage on a basis of central moments on which the equilibrium state is assumed equal to that of the continuous Maxwellian distribution. Such a relaxation process is usually considered as an assumption, which is then justified a posteriori by showing the enhanced Galilean invariance of the resultant algorithm. An alternative method is to relax central moments to the equilibrium state of the discrete second-order truncated distribution. In this paper, we demonstrate that relaxation to the continuous Maxwellian distribution is equivalent to the discrete counterpart if higher-order (up to sixth) Hermite polynomials are used to construct the equilibrium when the D3Q27 lattice velocity space is considered. Therefore, a theoretical a priori justification of the choice of the continuous distribution is formally provided for the first time.

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Section: Introductionmentioning

confidence: 99%

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

Rosis

Luo

2019

Phys. Rev. E

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“…They further extended the model with an improved forcing scheme for large density ratio multiphase flows at high Reynolds and Weber numbers [30]. 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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“…Originally, an orthogonal basis of central moments, which relaxes to the equilibrium state of the continuous Maxwellian distribution is assumed for the cascaded LBM. In spite of overwhelming analytical formulation and practical implementation specifically in threedimensional cases 36 , this method leads to a considerable stability enhancement in many cases 35,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] . Recently, De Rosis developed a new LBM framework based on the central moments, which is different from the cascaded scheme in two aspects.…”

Section: Introductionmentioning

confidence: 99%

Central-Moments-Based Lattice Boltzmann for Associating Fluids: A New Integrated Approach

2020

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Dynamic and thermodynamic behavior of associating fluids play a crucial role in a variety of engineering and science disciplines. Cubic plus association equation of state (CPA EOS) is implemented in a central-moments-based lattice Boltzmann method (LBM) in order to mimic the thermodynamic behavior of associating fluids. The pseudopotential approach is selected to model the multiphase thermodynamic characteristics such as reduced density of associating fluids. The priority of central moments-based approach over multiple-relaxation-time collision operator is shown by performing double shear layers. The integration of central-moments-based LBM and CPA EOS is useful to simulate associating fluids at high flow rate conditions, which is extended to high-density ratio scenarios by increasing the anisotropy order of gradient operator. In order to increase the stability of the model, a higher anisotropy order of the gradient operator is implemented; about 34 present reduction in spurious velocities is noticed in some cases. The type of gradient operator considerably affects the model thermodynamic consistency. Finally, the model is validated by observing a straight line in the Laplace law test. Prediction of thermodynamic behaviours of associating fluids is of significance in biological processes as well as fluid flow in porous media.

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Cascaded collision lattice Boltzmann model (CLBM) for simulating fluid and heat transport in porous media

Cited by 15 publications

References 17 publications

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

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

Central-Moments-Based Lattice Boltzmann for Associating Fluids: A New Integrated Approach

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