Isotropy of three-dimensional quantum lattice Boltzmann schemes

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
P. J. Dellar ◽  
D. Lapitski ◽  
S. Palpacelli ◽  
S. Succi
Keyword(s):  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Quantum Lattice

scholarly journals Convergence of a three-dimensional quantum lattice Boltzmann scheme towards solutions of the Dirac equation

2011 ◽  
Vol 369 (1944) ◽  
pp. 2155-2163 ◽  
Author(s):  
Denis Lapitski ◽  
Paul J. Dellar
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Lattice Boltzmann ◽  
Schrodinger Equation ◽  
Fourier Transforms ◽  
Operator Splitting ◽  
Three Dimensional ◽  
Relativistic Limit ◽  
Quantum Lattice ◽  
Lattice Boltzmann Scheme

We investigate the convergence properties of a three-dimensional quantum lattice Boltzmann scheme for the Dirac equation. These schemes were constructed as discretizations of the Dirac equation based on operator splitting to separate the streaming along the three coordinate axes, but their output has previously only been compared against solutions of the Schrödinger equation. The Schrödinger equation arises as the non-relativistic limit of the Dirac equation, describing solutions that vary slowly compared with the Compton frequency. We demonstrate first-order convergence towards solutions of the Dirac equation obtained by an independent numerical method based on fast Fourier transforms and matrix exponentiation.

Investigation of dimensional accuracy of metal droplet deposition under repulsion using a lattice Boltzmann approach

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yanlin Ren ◽  
Zhaomiao Liu ◽  
Yan Pang ◽  
Xiang Wang ◽  
Shanshan Gao
Keyword(s):  
Lattice Boltzmann ◽  
Moving Boundary ◽  
Three Dimensional ◽  
Metal Droplet ◽  
Dimensional Accuracy ◽  
Longitudinal Section ◽  
Collision Term ◽  
Droplet Deposition ◽  
Content Type ◽  
Deposition Distance

Purpose This paper aims to investigate the influence of droplet infiltration and sliding on the deposition size and make a uniform deposition by controlling the interaction between droplets, using the three-dimensional lattice Boltzmann method (LBM) based on the actual working condition. Design/methodology/approach D3Q19 Shan-Chen LB approach is developed and optimized based on the metal droplet deposition. The Carnahan-Starling equation of state and transition layers are introduced to maintain the greater stability and low pseudo velocities. In addition, an additional collision term is adopted to implement immersed moving boundary scheme to deal with no-slip boundaries on the front of the phase change. Findings The numerical results show that the new¬ incoming droplet wet and slide off the solidified surface and the rejection between droplets are the reasons for the deviation of the actual deposition length. The total length of the longitudinal section negatively correlates with the deposition distance. To improve the dimensional accuracy, the deposition distance and repulsion rate need to be guaranteed. The optimal deposition distance is found to have a negative linear correlation with wettability. Originality/value The numerical model developed in this paper will help predict the continuous metal droplet deposition and provide guidance for the selection of deposition distance.

scholarly journals A coupled lattice Boltzmann and Cosserat rod model method for three-dimensional two-way fluid–structure interactions

AIP Advances ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 075020
Author(s):  
Suguru Ando ◽  
Mitsuru Nishikawa ◽  
Masayuki Kaneda ◽  
Kazuhiko Suga
Keyword(s):  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Model Method ◽  
Cosserat Rod ◽  
Rod Model
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