Recent advances of Lattice Boltzmann techniques on unstructured grids

Ubertini, Stefano; Succi, Sauro

doi:10.1504/pcfd.2005.005820

Cited by 86 publications

(64 citation statements)

References 28 publications

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“…Refs. [43,44]. The second method, the one we will adopt in the following, consists of transferring off-grid distributions into grid locations through (bilinear) interpolation.…”

Section: Collisionmentioning

confidence: 99%

Fully relativistic lattice Boltzmann algorithm

2011

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Starting from the Maxwell-Jüttner equilibrium distribution, we develop a relativistic lattice Boltzmann (LB) algorithm capable of handling ultrarelativistic systems with flat, but expanding, spacetimes. The algorithm is validated through simulations of quark-gluon plasma, yielding excellent agreement with hydrodynamic simulations. The present scheme opens the possibility of transferring the recognized computational advantages of lattice kinetic theory to the context of both weakly and ultra-relativistic systems.PACS numbers: 47.75.+f, 47.11.-j Keywords: Relativistic fluid dynamics, Quark-gluon plasmas, Lattice Boltzmann I. MOTIVATIONThe great success of the Relativistic Heavy-Ion Collider (RHIC) experimental program [1][2][3][4] has provided the motivation to come up with realistic and quantitative simulations of heavy-ion collisions.Since the bulk of particles produced in relativistic heavy-ion collisions is described by fluid dynamics [5], the center-piece of any complete simulation attempt will involve a viscous fluid dynamics algorithm. The majority of presently available fluid dynamics codes is able to handle smooth initial conditions in 2+1 dimensions in the presence of shear viscosity [6][7][8][9][10]. However, it has by now been understood that the presence of event-by-event fluctuations in the initial state can lead to significantly different quantitative results with respect to smooth initial conditions [11], and may in some cases even explain qualitatively new phenomena. To be more specific, the presence of event-by-event fluctuations is the source of the non-vanishing elliptic flow found in RHIC experiments at central collisions, the source of hydrodynamic flow-fluctuations, and may (through the presence of socalled triangular flow v 3 ) naturally explain the presence of the 'ridge phenomenon' found in experiments [12][13][14][15]. Thus, it is probably fair to say that without including the effect of event-by-event fluctuations, a description of the medium created in heavy-ion collisions cannot be regarded as realistic. This provides the motivation to develop a fully relativistic and computationally efficient viscous fluid dynamics algorithm that can handle initial state fluctuations. Also, such an algorithm can be used Further motivation is provided by other systems where relativistic viscous fluid flows are of interest, such as astrophysical systems and condensed matter systems such as graphene [17]. One particular question that arises in all this different systems is when relativistic fluid flow becomes turbulent, which involves a determination of the critical Reynolds number and the turbulent spectrum [18,19]. II. LATTICE KINETIC APPROACH TO HYDRODYNAMICSFluid turbulence, both classical and relativistic, sets one of the most compelling challenges in modern computational physics. This motivates a relentless search for new and ever more efficient methods for solving the hydrodynamic equations of motion in the high-Reynolds turbulent regimes. In the last two decades, a new computational paradigm has...

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“…Refs. [43,44]. The second method, the one we will adopt in the following, consists of transferring off-grid distributions into grid locations through (bilinear) interpolation.…”

Section: Collisionmentioning

confidence: 99%

Fully relativistic lattice Boltzmann algorithm

2011

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“…One of the advantages of the LBM is that the shear tensor can be computed locally, with no need of taking space derivatives of the velocity field [14].…”

Section: Introductionmentioning

confidence: 99%

A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method

Yoshino

Hotta

Hirozane

et al. 2007

Journal of Non-Newtonian Fluid Mechanics

117

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A new numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method (LBM) is proposed. The essence of the present method lies in the determination of shear-dependent viscosity of the fluid by using a variable parameter related to the local shear rate. Also, the relaxation time in the BGK collision term is kept at unity taking account of numerical stability. The method is applied to two representative test case problems, power-law fluid flows in a reentrant corner geometry and non-Newtonian fluid flows in a three-dimensional porous structure. These simulations indicate that the method can be useful for practical non-Newtonian fluid flows, such as shear-thickening (dilatant) and shearthinning (pseudoplastic) fluid flows.

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“…In Fig. 8, the primary flow reattachment length (the distance at which the velocity field on the bottom wall becomes directed towards the outlet) is compared with the results of the simulations of the incompressible Navier-Stokes equation by various numerical techniques [24,28], with the recent two-dimensional lattice Boltzmann simulation on a nonuniform grid [40], as well as with the experimental data of Armaly et al [9], and was found to be in excellent agreement. We stress that the accuracy and stability achieved with the new outlet boundary condition allowed us to use a small step size of only ten grid points, much less than it would be required with different boundary conditions.…”

Section: Application: Outflow Condition In Lattice Boltzmann Simulationsmentioning

confidence: 58%

“…Because specification of pressure at the outlet has no significance in long pipes, one relies on interpolation schemes (see, e.g. [40]). Interpolation often becomes a major source of inaccuracy in the simulations.…”

Section: Application: Outflow Condition In Lattice Boltzmann Simulationsmentioning

confidence: 99%

“…Before reporting the results, it should be pointed out that the same threedimensional lattice Boltzmann model with the outlet boundary conditions based on a simple second-order interpolation formula for the missing populations (see, e. g. [40]) failed at Reynolds number Re < 50. The reason for such a poor performance is the errors which start at the outlet and propagate upstream.…”

Section: Application: Outflow Condition In Lattice Boltzmann Simulationsmentioning

confidence: 99%

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Lattice Boltzmann Method and Kinetic Theory

Ansumali

Frouzakis

Karlin

et al.

Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

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Summary.One of the classical questions of non-equilibrium thermodynamics is the validity of various closure approximations in nontrivial flows. We study this question for a lid-driven cavity flow using a minimal molecular model derived from the Boltzmann equation. In this nontrivial flow, we quantify the model as a superset of the Grad moment approximation and visualize the quality of the Chapman-Enskog and Grad closure approximations. It is found that the Grad closure approximation is strikingly more robust than the Chapman-Enskog approximation at all Knudsen numbers studied. Grad's approximation is used to formulate a novel outflow boundary condition for lattice Boltzmann simulations.

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Recent advances of Lattice Boltzmann techniques on unstructured grids

Cited by 86 publications

References 28 publications

Fully relativistic lattice Boltzmann algorithm

Fully relativistic lattice Boltzmann algorithm

A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method

Lattice Boltzmann Method and Kinetic Theory

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