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Semi-Lagrangian lattice Boltzmann method for compressible flows [article]

Dominik Wilde, Andreas Krämer, Dirk Reith, Holger Foysi
2020 arXiv   pre-print
The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction  ...  Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance.  ...  This work was supported by the German Ministry of Education and Research and the Ministry for Culture and Science North Rhine-Westfalia (research grant 13FH156IN6). D.  ... 
arXiv:1910.13918v3 fatcat:d6ylxe6h3rbtfb55mecidv2ifq

Semi-Lagrangian lattice Boltzmann method for compressible flows

Dominik Wilde, Andreas Krämer, Dirk Reith, Holger Foysi
2020 Physical review. E  
The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem, and a shock-vortex interaction  ...  Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance.  ...  ACKNOWLEDGMENTS The authors would like to thank Ilya V. Karlin  ... 
doi:10.1103/physreve.101.053306 pmid:32575305 fatcat:qlu4zimdgzekrmdxv6mrbfjv2e

Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices

Hui-Hai Zhao, Zhi-Yuan Xie, Tao Xiang, Masatoshi Imada
2016 Physical review B  
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices.  ...  We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate  ...  Later, Xie et al 11 proposed the HOTRG to study two and three dimensional lattice models based on the HOSVD of local tensors.  ... 
doi:10.1103/physrevb.93.125115 fatcat:awiwbfattjecvdabyrjnjjl6oa

Discrete Rotational Symmetry, Moment Isotropy, and Higher Order Lattice Boltzmann Models

Hudong Chen, Isaac Goldhirsch, Steven A. Orszag
2007 Journal of Scientific Computing  
In this paper, we present some basic results on moment isotropy and its relationship to the rotational symmetry of a generating discrete vector set.  ...  The analysis provides a geometric understanding for popular lattice Boltzmann models, while offering a systematic procedure to construct higher-order models.  ...  Acknowledgments: We are grateful to Raoyang Zhang, Xiaowen Shan, and Ilya Staroselsky for important discussions. This work is supported in part by National Science Foundation.  ... 
doi:10.1007/s10915-007-9159-3 fatcat:2bjynp7lizdr7hacm2j3qqluoy

An improved lattice Boltzmann D3Q19 method based on an alternative equilibrium discretization [article]

Martin Bauer, Ulrich Rüde
2018 arXiv   pre-print
Lattice Boltzmann simulations of three-dimensional, isothermal hydrodynamics often use either the D3Q19 or the D3Q27 velocity sets.  ...  While both models correctly approximate Navier-Stokes in the continuum limit, the D3Q19 model is computationally less expensive but has some known deficiencies regarding Galilean invariance, especially  ...  However, a lack of rotational invariance has been shown for the D3Q19 model in certain simulation setups.  ... 
arXiv:1803.04937v2 fatcat:g43rxh3wyze2lauba5plnt7oie

String breaking in four dimensional lattice QCD

A. Duncan, E. Eichten, H. Thacker
2001 Physical Review D, Particles and fields  
For unquenched four dimensional lattice QCD, this (so far elusive) phenomenon is studied using the recently developed truncated determinant algorithm (TDA).  ...  Virtual quark pair screening leads to breaking of the string between fundamental representation quarks in QCD.  ...  The analysis of dynamical two-flavor configurations on large coarse lattices obtained by the truncated determinant simulation method provides evidence for string breaking in zero temperature 4-dimensional  ... 
doi:10.1103/physrevd.63.111501 fatcat:pnr42rj3ebhhbowrk6i6rly5z4

Lattice Boltzmann model for elastic thin plate with small deflection

Guangwu Yan, Tingting Li, Xianli Yin
2012 Computers and Mathematics with Applications  
In order to recover the Sophie-Germain equation for elastic thin plate by lattice Boltzmann method, we transform the equation into a set of Poisson equations.  ...  In this paper, a lattice Boltzmann model for solving problems of elastic thin plate with small deflection is proposed.  ...  load. (3) It is useful to develop a three-dimensional lattice Boltzmann model for the elastic dynamical equations.  ... 
doi:10.1016/j.camwa.2012.01.015 fatcat:uqemzej4ovgqbpqiwuk42zznau

Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows

N. Frapolli, S. S. Chikatamarla, I. V. Karlin
2020 Entropy  
The entropic lattice Boltzmann method for the simulation of compressible flows is studied in detail and new opportunities for extending operating range are explored.  ...  We also discuss some key ideas of how to reduce the number of discrete speeds in three-dimensional simulations by pruning of the higher-order lattices, and introduce a new construction of the corresponding  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e22030370 pmid:33286144 pmcid:PMC7516843 fatcat:m47jgv6yhvbilhd7z7y47pk5t4

Lattice Boltzmann Method on Curvilinear Coordinates System: Flow around a Circular Cylinder

Xiaoyi He, Gary Doolen
1997 Journal of Computational Physics  
the lattice Boltzmann method is tems.  ...  The grid Compared with previous lattice Boltzmann simulations of the same in previous LB models has been limited to triangular, problem, our new approach greatly enhances the computational square, or cubic  ...  This enhancement will be even greater for simulations of three-dimensional flows.  ... 
doi:10.1006/jcph.1997.5709 fatcat:oh5fnrinu5drlljrtk5u2yabtq

Three-dimensional central-moments-based lattice Boltzmann method with external forcing: A consistent, concise and universal formulation [article]

Alessandro De Rosis, Rongzong Huang, Christophe Coreixas
2019 arXiv   pre-print
The cascaded or central-moments-based lattice Boltzmann method (CM-LBM) is a robust alternative to the more conventional BGK-LBM for the simulation of high-Reynolds number flows.  ...  Knowing the original model also relies on central moments that are derived in an adhoc manner, i.e., by mimicking those of the Maxwell-Boltzmann distribution to ensure their Galilean invariance a posteriori  ...  It should be noted that this paper delivers the first tangible solution of the three-dimensional high-Reynolds Orszag-Tang vortex within the framework of the lattice Boltzmann method.  ... 
arXiv:1905.10182v3 fatcat:vhgry5cxong55eozri3bsm2kdq

A Review on the Application of the Lattice Boltzmann Method for Turbulent Flow Simulation

Leila Jahanshaloo, Emad Pouryazdanpanah, Nor Azwadi Che Sidik
2013 Numerical Heat Transfer, Part A Applications  
The Lattice Boltzmann Method (LBM) is a potent numerical technique based on kinetic theory, which has been effectively employed in various complicated physical, chemical, and fluid mechanics problems.  ...  Recent extensions of this method are categorized based on three main groups of turbulence simulation: DNS, LES and RANS methods.  ...  It was remarked that the D3Q27 lattice model could achieve the rotational invariance in terms of turbulence statistics and produced the comparable results to the DNS data, while the D3Q19 lattice model  ... 
doi:10.1080/10407782.2013.807690 fatcat:lhi7mpmkyzg2ho3ngkpmre7uiy

Algorithms for tensor network renormalization

G. Evenbly
2017 Physical review B  
The efficacy of the TNR approach is then benchmarked for the 2D classical statistical and 1D quantum Ising models; in particular the ability of TNR to maintain a high level of accuracy over sustained coarse-graining  ...  We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems.  ...  (a) Comparison between TRG and TNR of the truncation error ε, as defined in Eq.11, as a function of RG step s in the 2D classical Ising model at critical temperature Tc.While increasing the bond dimension  ... 
doi:10.1103/physrevb.95.045117 fatcat:4qxw5r7rznbmnazn5ha3irmcka

Extended Lattice Boltzmann Model

Mohammad Hossein Saadat, Benedikt Dorschner, Ilya Karlin
2021 Entropy  
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the  ...  The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer  ...  Introduction The lattice Boltzmann method (LBM) solves a Boltzmann-type kinetic equation on a discrete velocity set, forming the links of a space-filling lattice.  ... 
doi:10.3390/e23040475 pmid:33920499 pmcid:PMC8073312 fatcat:ahxrg76o5zfznghmq3x4qlmchu

A Coupled lattice Boltzmann-Multiparticle collision method for multi-resolution hydrodynamics [article]

Andrea Montessori, Adriano Tiribocchi, Marco Lauricella, Sauro Succi
2020 arXiv   pre-print
In this work we discuss the coupling of two mesoscopic approaches for fluid dynamics, namely the lattice Boltzmann method (LB) and the multiparticle collision dynamics (MPCD) to design a new class of flexible  ...  lattice Boltzmann alone falls short of providing the correct physical information due to a lack of resolution, as it occurs for example in thin films between interacting bubbles or droplets in microfluidic  ...  Methods Lattice Boltzmann method The lattice Boltzmann method [4] (LB) is based on a minimal version of the time-honored Bathnagar-Gross-Krook equation, in which the computational molecules, namely  ... 
arXiv:2004.00304v1 fatcat:5w3jw5w4h5aotadusxfzjrprxq

One-Step Aeroacoustics Simulation Using Lattice Boltzmann Method

X. M. Li, R. C. K. Leung, R. M. C. So
2006 AIAA Journal  
The lattice Boltzmann method (LBM) is a numerical simplification of the Boltzmann equation of the kinetic theory of gases that describes fluid motions by tracking the evolution of the particle velocity  ...  The modified LBM model is solved using a two-dimensional 9-discretized and a twodimensional 13-discretized velocity lattices.  ...  Acknowledgment Support given by the Research Grants Council of the Government of the Hong Kong Special Administrative Region under Grants PolyU5174/02E, PolyU5303/03E, and PolyU1/02C is gratefully acknowledged  ... 
doi:10.2514/1.15993 fatcat:dh2wevxvlrge7e7lmhg6q6zv5u
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