Least-squares finite-element lattice Boltzmann method

Li, Yusong; LeBoeuf, Eugene J.; Basu, Prodyot K.

doi:10.1103/physreve.69.065701

Cited by 45 publications

(24 citation statements)

References 17 publications

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“…As one of the efforts to extend traditional LBM to non-uniform and unstructured meshes, we developed a LSFE-LBM, which uses a LSFE method (Jiang 1998) in space and a Crank-Nicolson method in time to solve the lattice Boltzmann equation. LSFE-LBM was successfully implemented on unstructured mesh to simulate fluid flow and solute transport in porous media, using fewer grid points and consuming significantly less memory than traditional LBM (Li et al 2004). A brief overview of the LSFE-LBM follows.…”

Section: Lsfe-lbm Simulation Of Fluid and Transport At Pore Scalementioning

confidence: 99%

“…Here, we present a hierarchical modeling approach to solve such a system. At the pore scale, a least-squares finite-element lattice Boltzmann method (LSFE-LBM) (Li et al 2004(Li et al , 2005a was employed to simulate fluid flow and HOCs transport in the pore space. At the particle scale, a finite difference method is employed to address intraorganic diffusion processes.…”

Section: Conceptual Modelmentioning

confidence: 99%

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Investigation of Transport- and Sorption-Related Factors on the Removal of Hydrophobic Organic Compounds in Heterogeneous Soils Using a Hierarchical Modeling Approach

Li¹,

LeBoeuf

2009

Transp Porous Med

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Hydrophobic organic compounds (HOCs) represent a class of generally highly persistent contaminants in groundwater. Factors influencing the transport of HOCs are evaluated through a hierarchical modeling approach, which incorporates particle scale sorption/diffusion with pore scale flow and transport models. The relative contributions of transport-and sorption-related factors on HOCs transport are first elucidated in a simplified single particle system. The comparative roles of different soil organic matter contents and compositions on the fate and transport of HOCs are further investigated by simulation of phenanthrene transport in porous media. This effort represents a proof-of-concept demonstration of bridging comprehensive representations of fluid-flow with mechanistic sorption/desorption processes.

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Section: Lsfe-lbm Simulation Of Fluid and Transport At Pore Scalementioning

confidence: 99%

Section: Conceptual Modelmentioning

confidence: 99%

Investigation of Transport- and Sorption-Related Factors on the Removal of Hydrophobic Organic Compounds in Heterogeneous Soils Using a Hierarchical Modeling Approach

Li¹,

LeBoeuf

2009

Transp Porous Med

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“…For the application in complex geometry, there are three ways so far. The first way is solving LBE by FDM, 2 FVM 3 or FEM 4 The second way is based on the boundary extrapolation on regular mesh. Sometimes they are coupled with mesh refinement.…”

Section: Introductionmentioning

confidence: 99%

An Isoparametric Transformation-Based Interpolation-Supplemented Lattice Boltzmann Method and Its Application

Chen

Chew

2010

Mod. Phys. Lett. B

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Isoparametric transformation was applied to the interpolation-supplemented lattice Boltzmann method (ISLBM). As a result, it can be applied to arbitrarily structural grids and reserve the simple procedure of ISLBM. The simulation of the lid-driven cavity flow and the flow around a cylinder were performed to validate the proposed method. The numerical results agree excellently with the data in the literature.

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“…To get some indication we look back to the last terms in Eqs. (17) and (18) which are regarded as artificial viscosities to reduce the numerical wall-heating phenomena. To simplify the discussion, we choose always ∆x = ∆y.…”

Section: Von Neumann Analysismentioning

confidence: 99%

Lattice Boltzmann Approach to High-Speed Compressible Flows

Pan

Zhang

et al. 2007

Int. J. Mod. Phys. C

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We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara [Phys. Rev. E 69, 056702 (2004)] and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios (1000 : 1) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.

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Least-squares finite-element lattice Boltzmann method

Cited by 45 publications

References 17 publications

Investigation of Transport- and Sorption-Related Factors on the Removal of Hydrophobic Organic Compounds in Heterogeneous Soils Using a Hierarchical Modeling Approach

Investigation of Transport- and Sorption-Related Factors on the Removal of Hydrophobic Organic Compounds in Heterogeneous Soils Using a Hierarchical Modeling Approach

An Isoparametric Transformation-Based Interpolation-Supplemented Lattice Boltzmann Method and Its Application

Lattice Boltzmann Approach to High-Speed Compressible Flows

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