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Coupling a Lattice Boltzmann and a Finite Difference Scheme [chapter]

Paul Albuquerque, Davide Alemani, Bastien Chopard, Pierre Leone
2004 Lecture Notes in Computer Science  
accessible (after a linear interpolation). • The gradients are obtained from finite differences.  ...  Computation of the new velocities according to the finite difference scheme. ' & $ % A grid cell for the FD model Staggered arrangement of the unknowns (prevents pressure oscillations):  ... 
doi:10.1007/978-3-540-25944-2_70 fatcat:kefbslnqcfg3xo7ngm7jqk5oea

Comparison of Simulations of Convective Flows

Pierre Lallemand, François Dubois
2015 Communications in Computational Physics  
AbstractWe show that a single particle distribution for the "energy-conserving" D2Q13 lattice Boltzmann scheme can simulate coupled effects involving advection and diffusion of velocity and temperature  ...  Our results are compared with the coupled D2Q9-D2Q5 lattice Boltzmann approach for the Boussinesq system and with an elementary finite differences solver for the compressible Navier-Stokes equations.  ...  Many thanks also to the "LaBS project" (Lattice Boltzmann Solver, www.labs-project.org), funded by the French FUI8 research program, for supporting this contribution.  ... 
doi:10.4208/cicp.2014.m400 fatcat:oqkcmtldw5at5ii5wt4luh6fa4

Properties of the SU(Nc) Gluon Plasma [article]

Saumen Datta, Sourendu Gupta
2009 arXiv   pre-print
A detailed lattice study of SU(4) and SU(6) gauge theories are conducted, and finite volume and cutoff effects on thermodynamic observables are studied.  ...  We do not find any evidence of a strongly coupled, conformal phase in these theories.  ...  The renormalized couplings in different schemes are obtained from plaquette data, and converted to aΛ using the two-loop RGE.  ... 
arXiv:0910.2889v1 fatcat:gnn5qj6vifglve7xs27pmm6cny

A Coupled Approach for Fluid Dynamic Problems Using the PDE Framework Peano

Philipp Neumann, Hans-Joachim Bungartz, Miriam Mehl, Tobias Neckel, Tobias Weinzierl
2012 Communications in Computational Physics  
AbstractWe couple different flow models, i.e. a finite element solver for the Navier-Stokes equations and a Lattice Boltzmann automaton, using the framework Peano as a common base.  ...  In addition, the test scenarios show an improved stability of the coupled method compared to pure Lattice Boltzmann simulations.  ...  It is particularly the work presented in [12] where the coupling between a finite difference Navier-Stokes solver and a Lattice Boltzmann automaton is established and validated.  ... 
doi:10.4208/cicp.210910.200611a fatcat:aalyckl2lnexjjlrjrti6gylui

Multispeed models in off-lattice Boltzmann simulations

André Bardow, Iliya V. Karlin, Andrei A. Gusev
2008 Physical Review E  
The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models ͓S. Chikatamarla et al., Phys.  ...  The approach is based on the general characteristic-based algorithm for off-lattice Boltzmann simulations that preserves all appealing properties of the standard lattice Boltzmann method while extending  ...  To analyze the improvement beyond the specific discretization method, a simple central finite-difference scheme is also employed for spatial discretization.  ... 
doi:10.1103/physreve.77.025701 pmid:18352083 fatcat:utx66gvnq5fmtnmlevzp4ae5ky

Chapman-Enskog Analysis of Finite Volume Lattice Boltzmann Schemes [article]

Nima H. Siboni, Dierk Raabe, Fathollah Varnik
2014 arXiv   pre-print
In this paper, we provide a systematic analysis of some finite volume lattice Boltzmann schemes in two dimensions.  ...  As an important result of this analysis, the relation between the lattice Boltzmann relaxation time and the kinematic viscosity of the fluid is derived for each approximate flux evaluation scheme.  ...  Generally speaking, regarding the accuracy, some finite difference schemes and finite volume schemes will result in the same set of discrete equations in the limit of a uniform lattice.  ... 
arXiv:1407.5266v1 fatcat:azzdqpsde5dy3k3vnikpsx6sd4

A lattice Boltzmann model for coupled diffusion

Christian Huber, Bastien Chopard, Michael Manga
2010 Journal of Computational Physics  
We present a new lattice Boltzmann model to account for the diffusive coupling between different chemical species.  ...  The model is tested on a simple diffusion problem with two coupled components and is in excellent agreement with the results obtained through a finite difference method.  ...  Acknowledgements We would like to thank three anonymous reviewers and the editor for insightful reviews. C.H. and M.M. were funded by NSF EAR 0608885.  ... 
doi:10.1016/j.jcp.2010.07.002 fatcat:phqdfn6kcnfkfh5cdacycx2ulm

Page 2130 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Here, a method based on solving the Navier-Stokes equations by a finite difference/front tracking technique that allows the inclusion of fully deformable interfaces and surface tension, in addition to  ...  ) ; Hianel, Dieter (D-DUIS-GS; Duisburg) Multiscale lattice Boltzmann schemes for low Mach number flows.  ... 

A NUMERICAL MODEL FOR BINARY FLUID MIXTURES

A. TIRIBOCCHI, N. STELLA, G. GONNELLA, A. LAMURA
2009 Applied and Industrial Mathematics in Italy III  
A lattice Boltzmann algorithm for the continuity and the Navier-Stokes equations is coupled to a finite-difference scheme for the convection-diffusion equation.  ...  Spurious velocities are reduced by using a general stencil scheme for discretizing spatial derivatives.  ...  To solve numerically these equations, we use a mixed technique that consists of a lattice Boltzmann scheme for Equations (6) and (7) and a finite-difference scheme for Equation (8).  ... 
doi:10.1142/9789814280303_0050 fatcat:3a7xqvuvjbbjzikz4rkz4fff2m

Accuracy of Hybrid Lattice Boltzmann/Finite Difference Schemes for Reaction-Diffusion Systems

Pieter Van Leemput, Christophe Vandekerckhove, Wim Vanroose, Dirk Roose
2007 Multiscale Modeling & simulation  
In this article we construct a hybrid model by spatially coupling a lattice Boltzmann model (LBM) to a finite difference discretization of the partial differential equation (PDE) for reaction-diffusion  ...  Abstract In this article we construct a hybrid model by spatially coupling a lattice Boltzmann model (LBM) to a finite difference discretization of the partial differential equation (PDE) for reaction-diffusion  ...  Acknowledgements The research in this paper is funded by projects G.0130.03 and G.0365.06 (PVL) of the Fund for Scientific Research -Flanders and by project OT/03/04 (CV) of the Research Fund of the K.U.Leuven  ... 
doi:10.1137/060675113 fatcat:ccqauz7cs5cqbfjx6hapff2k2e

Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions

Pierre Lallemand, Li-Shi Luo
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We find that the numerical stability of the lattice Boltzmann scheme improves drastically once the spurious mode coupling is removed.  ...  This spurious mode coupling is highly anisotropic and may occur at small values of wave number k along certain directions, and it is a direct consequence of the following key features of the lattice Boltzmann  ...  Specifically, Appendix G and significant part of Appendix A are the results based on Professor Vahala's con-structive suggestions. L.S.L. would also like to thank Dr. Z. L. Guo and Dr. R.  ... 
doi:10.1103/physreve.68.036706 pmid:14524925 fatcat:tkq4n2wmn5anxfaknxg3jbgvsm

Page 10434 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
We find that the numerical stability of the lattice Boltzmann scheme improves drastically once the spu- rious mode coupling is removed.  ...  To eliminate the spurious mode coupling, we propose a hybrid thermal lattice Boltzmann equa- tion (HTLBE) in which the mass and momentum conservation equations are solved by using the multiple-relaxation-time  ... 

Finite Difference formulation of any lattice Boltzmann scheme [article]

Thomas Bellotti, Benjamin Graille, Marc Massot
2022 arXiv   pre-print
In order to alleviate these shortages and introduce a rigorous framework, we demonstrate that any lattice Boltzmann scheme can be rewritten as a corresponding multi-step Finite Difference scheme on the  ...  More generally, the usual tools for the analysis of Finite Difference schemes are now readily available to study lattice Boltzmann schemes.  ...  Le Calvez, A. Louvet, M. Piquerez and D. Stantejsky for the useful discussions on algebra. This author is supported by a PhD funding (year 2019) from the Ecole polytechnique.  ... 
arXiv:2201.05354v1 fatcat:qjyrasoodndnvmge2fmxin2gbu

Least-squares finite-element lattice Boltzmann method

Yusong Li, Eugene J. LeBoeuf, P. K. Basu
2004 Physical Review E  
A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented.  ...  For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.  ... 
doi:10.1103/physreve.69.065701 pmid:15244659 fatcat:ba4t5wfefzf3jeaw7gkkgbbw4e

Lattice-Boltzmann-Langevin simulations of binary mixtures

Sumesh P. Thampi, Ignacio Pagonabarraga, R. Adhikari
2011 Physical Review E  
Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation.  ...  The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved  ...  Finite difference scheme (a) and finite volume scheme (b) have been used to carry out simulations on a 32 × 32 × 32 lattice with A = 0.065, B = 0, K = 0.04 and M = 0.095 with an initial equilibrium distribution  ... 
doi:10.1103/physreve.84.046709 pmid:22181309 fatcat:uftc7jzuebfqxidtu7rspk5hqy
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