scholarly journals Modelling thermal fluctuations in non-ideal fluids with the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2274-2282 ◽  
Author(s):  
M. Gross ◽  
R. Adhikari ◽  
M. E. Cates ◽  
F. Varnik
Keyword(s):  
Ideal Fluid ◽  
Lattice Boltzmann ◽  
Exact Result ◽  
Thermal Fluctuations ◽  
Ideal Gas ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Wide Range ◽  
Ideal Fluids ◽  
Boltzmann Method

Recently, we proposed a theoretical framework to include thermal fluctuations into the Lattice Boltzmann (LB) method for non-ideal fluids. Here, we apply a variant thereof to a certain class of force-based non-ideal fluid LB models. We find that ideal-gas-like noise is an exact result of the fluctuation–dissipation theorem in the hydrodynamic regime. It is shown that satisfactory equilibration of the density and fluid momentum can be obtained in a simulation over a wide range of length scales.

SIMULATION OF AN AXISYMMETRIC RISING BUBBLE BY A MULTIPLE RELAXATION TIME LATTICE BOLTZMANN METHOD

2009 ◽  
Vol 23 (24) ◽  
pp. 4907-4932 ◽  
Author(s):  
ABBAS FAKHARI ◽  
MOHAMMAD HASSAN RAHIMIAN
Keyword(s):  
Free Surface ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rise Velocity ◽  
Rising Bubble ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Multiple Relaxation Time ◽  
Bubble Rising ◽  
Boltzmann Method

In this paper, the lattice Boltzmann method is employed to simulate buoyancy-driven motion of a single bubble. First, an axisymmetric bubble motion under buoyancy force in an enclosed duct is investigated for some range of Eötvös number and a wide range of Archimedes and Morton numbers. Numerical results are compared with experimental data and theoretical predictions, and satisfactory agreement is shown. It is seen that increase of Eötvös or Archimedes number increases the rate of deformation of the bubble. At a high enough Archimedes value and low Morton numbers breakup of the bubble is observed. Then, a bubble rising and finally bursting at a free surface is simulated. It is seen that at higher Archimedes numbers the rise velocity of the bubble is greater and the center of the free interface rises further. On the other hand, at high Eötvös values the bubble deforms more and becomes more stretched in the radial direction, which in turn results in lower rise velocity and, hence, lower elevations for the center of the free surface.

scholarly journals A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 148
Author(s):  
Seyed Amin Nabavizadeh ◽  
Himel Barua ◽  
Mohsen Eshraghi ◽  
Sergio D. Felicelli
Keyword(s):  
Natural Convection ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Bgk Model ◽  
Flow Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Boltzmann Method ◽  
Benchmark Solutions

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.

scholarly journals Molecular machines operating on the nanoscale: from classical to quantum

2016 ◽  
Vol 7 ◽  
pp. 328-350 ◽  
Author(s):  
Igor Goychuk
Keyword(s):  
Molecular Motors ◽  
High Performance ◽  
Molecular Machines ◽  
Thermal Fluctuations ◽  
Maximum Power ◽  
Thermodynamic Efficiency ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Physical Features

The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation–dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.

Parallelization of the Lattice Boltzmann Method in Simulating Buoyancy-Driven Convection Heat Transfer

2004 ◽  
Author(s):  
Anoosheh Niavarani-Kheirier ◽  
Masoud Darbandi ◽  
Gerry E. Schneider
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Message Passing ◽  
Large Scale ◽  
Message Passing Interface ◽  
Parallel Machines ◽  
Convection Heat Transfer ◽  
Wide Range ◽  
Buoyancy Driven Convection ◽  
Boltzmann Method

The main objective of the current work is to utilize Lattice Boltzmann Method (LBM) for simulating buoyancy-driven flow considering the hybrid thermal lattice Boltzmann equation (HTLBE). After deriving the required formulations, they are validated against a wide range of Rayleigh numbers in buoyancy-driven square cavity problem. The performance of the method is investigated on parallel machines using Message Passing Interface (MPI) library and implementing domain decomposition technique to solve problems with large order of computations. The achieved results show that the code is highly efficient to solve large scale problems with excellent speedup.

LBM Simulation of Flow Around an Oscillating Cylinder and a Stationary Cylinder in Side-by-Side Arrangement

2018 ◽  
Author(s):  
Yang Zhang ◽  
Li Sheng ◽  
Jinlong Duan ◽  
Ke Chen ◽  
Yunxiang You
Keyword(s):  
Lattice Boltzmann ◽  
Forced Oscillation ◽  
Power Spectra ◽  
Circular Cylinders ◽  
Wide Range ◽  
Pitch Ratio ◽  
Response State ◽  
Boltzmann Method ◽  
Different Characteristics ◽  
Flow Interference

Flow interference between two identical circular cylinders in side-by-side arrangement with one stationary and the other forced to oscillate in the transverse direction are studied. Direct numerical simulations are performed by Lattice Boltzmann Method (LBM) with a constant Reynolds number of 100. We consider four representative pitch ratios, T/D, ranging from 1.2 to 4, corresponding to four distinct flow patterns for two stationary side-by-side cylinders. The forced oscillation is fixed at a constant small amplitude of A/D = 0.1. A wide range of dimensionless oscillating frequency (fe/fs = [0.5, 2]) is examined. The results show that the response state of flow around two side-by-side cylinders when one cylinder is forced to vibrate is quite different from that of the corresponding stationary system. Four response states are identified according to the different characteristics on the power spectra and phase portrait of lift forces on cylinders. In addition, hydrodynamic forces on the cylinders are analyzed in terms of root-mean-square and time-averaged quantities. It is found that the pitch ratio, oscillating frequency and response state play different roles in determining the force quantities.

Simulation of High Knudsen Number Gas Flows in Nanochannels via the Lattice Boltzmann Method

2011 ◽  
Vol 403-408 ◽  
pp. 5318-5323
Author(s):  
A.H. Meghdadi Isfahani ◽  
A. Soleimani ◽  
A. Homayoon
Keyword(s):  
Lattice Boltzmann Method ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Numerical Data ◽  
Gas Flows ◽  
Wide Range ◽  
Flow Through ◽  
Boltzmann Method ◽  
Slip Transition ◽  
Pressure Driven Flow

Using a modified Lattice Boltzmann Method (LBM), pressure driven flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen number, Kn, covering the slip, transition and to some extend the free molecular regimes. The results agree very well with exiting empirical and numerical data.

Study of flapping filaments using the immersed boundary-lattice Boltzmann method

2018 ◽  
Vol 89 (15) ◽  
pp. 3127-3136
Author(s):  
Zhengdao Wang ◽  
Yi Kun Wei ◽  
Yuehong Qian
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Resonance Phenomenon ◽  
Discrete Equation ◽  
Immersed Boundary ◽  
Modified Method ◽  
Wide Range ◽  
Motion Characteristics ◽  
Boltzmann Method

In this study, flow over a flexible filament under a wide range of parameters is simulated using the immersed boundary-lattice Boltzmann method (IB-LBM). The leading end of the filament is fixed in the flow field and the trailing end is free to flap. To execute the simulation, we combine the IB-LBM and a semi-implicit discrete equation of force on the filament to better satisfy the boundary condition. After some numerical simulations validating the modified method, the motion of flexible filaments is examined with different dimensionless bending coefficients ([Formula: see text]) and Reynolds numbers ([Formula: see text]). From the trajectory of the flapping filament, different flapping modes are found. When the parameter is between that of two modes, the anti-resonance phenomenon is observed. Numerical results show that the dimensionless bending coefficient and Reynolds number both affect the flapping motion, but in different ways. The dimensionless bending coefficient mainly affects the mode of the flapping, while the Reynolds number mainly affects the perturbation to the filament motion, which is related to the motivation of this system. Some other motion characteristics, for example, the function of amplitude and perturbation propagation, are also discussed in this work.

scholarly journals Scrutinizing GW-Based Methods Using the Hubbard Dimer

2021 ◽  
Vol 9 ◽  
Author(s):  
S. Di Sabatino ◽  
P.-F. Loos ◽  
P. Romaniello
Keyword(s):  
Excitation Spectrum ◽  
Trace Formula ◽  
Electron Interaction ◽  
Excitation Energies ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Wide Range ◽  
Self Consistent ◽  
Approximate Nature ◽  
Self Consistency

Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.

scholarly journals Lattice Boltzmann simulation of Rayleigh-Benard convection in enclosures filled with Al2O3-water nanofluid

2018 ◽  
Vol 22 (Suppl. 2) ◽  
pp. 535-545
Author(s):  
Weihua Cai ◽  
Zhifeng Zheng ◽  
Changye Huang ◽  
Yue Wang ◽  
Xin Zheng ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Lattice Boltzmann ◽  
Convection Heat Transfer ◽  
Bénard Convection ◽  
Lattice Boltzmann Simulation ◽  
Benard Convection ◽  
Wide Range ◽  
Boltzmann Method ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In order to clarify the controversies for the role of nanoparticles on heat transfer in natural convection, lattice Boltzmann method is used to investigate Rayleigh-Benard convection heat transfer in differentially-heated enclosures filled with Al2O3-water nanofluids. The results for streamline and isotherm contours, vertical velocity, and temperature profiles as well as the local and average Nusselt number are discussed for a wide range of Rayleigh numbers and nanoparticle volume fractions (0 ? ? ? 5%). The results show that with the increase of Rayleigh number and nanoparticles loading, Nuave increases. It is suggested that the addition of nanoparticles can enhance the heat transfer in Rayleigh-Benard convection.

Sign in / Sign up

Export Citation Format

Share Document