Gaussian Lattice Boltzmann method and its applications to rarefied flows

Ilyin, Oleg

doi:10.1063/1.5126306

Cited by 14 publications

(7 citation statements)

References 85 publications

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“…The lattice Boltzmann method (LBM) has been recognized as a powerful mesoscopic numerical method and alternative technique to macroscopic numerical approaches for simulation of different complex fluid flow, heat, and transfer problems. [50][51][52][53][54][55][56][57][58] The main benefits of LBM are the nature of the parallel algorithm, the simple and straightforward programming and implementation, and strong ability for complex geometries. In contrast to the common macroscopic numerical methods (e.g., the finite element method) which discretizes continuum equations, LBM utilizes mesoscopic kinetic equations which satisfy the macroscopic averaged properties.…”

Section: The Numerical Methodsmentioning

confidence: 99%

A mesoscopic model for thermal–solutal problems of power-law fluids through porous media

et al. 2021

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A mesoscopic method based on the lattice Boltzmann method for thermal-solutal incompressible non-Newtonian power-law fluids through porous media is introduced. The macroscopic equations of different representative element volume (REV) models of porous media are presented, and the equations of power-law fluids through porous media for various REV models reported. The general mesoscopic model for two-and three-dimensional cases are presented, and their derivations shown. To demonstrate the ability of the proposed method, natural convection and double-diffusive natural convection of Newtonian and power-law fluids in porous cavities are studied, and the results are validated against previous findings. Finally, double-diffusive natural convection in a porous cubic cavity filled with a non-Newtonian power-law fluid is simulated by the proposed method.

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Section: The Numerical Methodsmentioning

confidence: 99%

A mesoscopic model for thermal–solutal problems of power-law fluids through porous media

et al. 2021

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“…In the applications, the discretization of these equations in the velocity (and physical) space is usually performed. One of the most popular discretization approaches is the Lattice-Boltzmann (LB) method [2][3][4][5] which was initially developed as an alternative to the continuum fluid methods like Navier-Stokes equations [6]; furthermore, the method has been extended to the rarefied flows modeling [7][8][9][10][11][12][13][14][15][16][17][18][19]. The conventional LB model has the following form…”

Section: Introductionmentioning

confidence: 99%

Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics

Ilyin

2021

Mathematics

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In this paper, we consider the development of the two-dimensional discrete velocity Boltzmann model on a nine-velocity lattice. Compared to the conventional lattice Boltzmann approach for the present model, the collision rules for the interacting particles are formulated explicitly. The collisions are tailored in such a way that mass, momentum and energy are conserved and the H-theorem is fulfilled. By applying the Chapman–Enskog expansion, we show that the model recovers quasi-incompressible hydrodynamic equations for small Mach number limit and we derive the closed expression for the viscosity, depending on the collision cross-sections. In addition, the numerical implementation of the model with the on-lattice streaming and local collision step is proposed. As test problems, the shear wave decay and Taylor–Green vortex are considered, and a comparison of the numerical simulations with the analytical solutions is presented.

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“…In addition, the computational time and cost is significantly lower than for macroscopic methods, which makes it attractive in various fields, especially heat and fluid flow problems. [30][31][32][33][34][35][36][37][38][39] Xuan and Yao 40 developed and introduced an LBM for simulating nanofluids by considering a series of acting forces including one which represented the Brownian motion. However, the model did not include the Thermophoresis and Brownian terms in the energy equation.…”

Section: Introductionmentioning

confidence: 99%

A lattice Boltzmann method for single- and two-phase models of nanofluids: Newtonian and non-Newtonian nanofluids

Kefayati

Bassom

2021

Physics of Fluids

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Nanofluids play an important role in many different industries for an improvement of heat transfer. The modeling and simulation of such fluids is developing continuously. Two important models for studying nanofluids are mixture (or single-phase) and two-phase (or Buongiorno) forms, which have been examined in various ways. Non-Newtonian behavior of nanofluids (shear-thinning and viscoplasticity) has been observed in experimental tests and simulated in several studies. However, a lattice Boltzmann method (LBM), which can employ either model depending on the particular non-Newtonian constitutive equation, has not been considered to date within the suite of available numerical methods. Here, we propose a comprehensive LBM to simulate both Newtonian and non-Newtonian nanofluids. The approach has the potential to incorporate any format of extra tensor directly and is independent to the relaxation time; the upshot is that our method is appropriate for studying non-Newtonian nanofluids. The derivations for both models are presented and discussed in some detail. To evaluate the proposed method, it was compared with previous studies into a benchmark problem, natural convection in a square enclosure filled with Newtonian nanofluids and non-Newtonian fluids. Then, the applied macroscopic and LBM equations, using the power-law and viscoplastic models, for the benchmark are derived and the results are presented.

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Gaussian Lattice Boltzmann method and its applications to rarefied flows

Cited by 14 publications

References 85 publications

A mesoscopic model for thermal–solutal problems of power-law fluids through porous media

A mesoscopic model for thermal–solutal problems of power-law fluids through porous media

Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics

A lattice Boltzmann method for single- and two-phase models of nanofluids: Newtonian and non-Newtonian nanofluids

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