Advection–diffusion lattice Boltzmann scheme for hierarchical grids

Stiebler, Maik; Tölke, Jonas; Krafczyk, Manfred

doi:10.1016/j.camwa.2007.08.024

Cited by 29 publications

(24 citation statements)

References 18 publications

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“…There are a variety of approaches to this problem of multi-component fluids [22,23,25,29,30,[77][78][79], but arguably the simplest and most commonly-used involves a simple addition of distribution functions corresponding to each extra component in the fluid. The physical assumption underlying this approach is that the additional components are low in concentration such that they do not explicitly influence the fluid flow.…”

Section: Dissolved Chemical Speciesmentioning

confidence: 99%

“…By extension of this logic, further passive scalars can be added. This allows multi-phase and multi-component fluids to be simulated [19][20][21][22]. Versions in recent years have developed yet further and incorporated a range of interactions between these additional components, advancing the LBM into the realm of chemistry [23][24][25][26][27], including thermal chemical problems such as combustion [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

Bartlett

2017

Computation

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Abstract:The lattice Boltzmann method is an efficient computational fluid dynamics technique that can accurately model a broad range of complex systems. As well as single-phase fluids, it can simulate thermohydrodynamic systems and passive scalar advection. In recent years, it also gained attention as a means of simulating chemical phenomena, as interest in self-organization processes increased. This paper will present a widely-used and versatile lattice Boltzmann model that can simultaneously incorporate fluid dynamics, heat transfer, buoyancy-driven convection, passive scalar advection, chemical reactions and enthalpy changes. All of these effects interact in a physically accurate framework that is simple to code and readily parallelizable. As well as a complete description of the model equations, several example systems will be presented in order to demonstrate the accuracy and versatility of the method. New simulations, which analyzed the effect of a reversible reaction on the transport properties of a convecting fluid, will also be described in detail. This extra chemical degree of freedom was utilized by the system to augment its net heat flux. The numerical method outlined in this paper can be readily deployed for a vast range of complex flow problems, spanning a variety of scientific disciplines.

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Section: Dissolved Chemical Speciesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

Bartlett

2017

Computation

View full text Add to dashboard Cite

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“…Overall, the number of volumetric elements required to represent a porous structure with precision h on the boundary scales like h −2 log h −1 , as opposed to h −3 in case of basic regular grids. Certain techniques, such as the immersed boundary method [29] and hierarchical voxel structures [30], allow regular grid based approaches reach the effective storage efficiency similar to that of unstructured meshes. However, they increase the complexity of the fluid simulation method, and the lack of coupling between the nodal positions and the precise location of the solid boundary persists.…”

Section: Evacuation Of Particles Through Advection and Diffusionmentioning

confidence: 99%

Simulating anomalous dispersion in porous media using the unstructured lattice Boltzmann method

et al. 2015

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Flow in porous media is a significant challenge to many computational fluid dynamics methods because of the complex boundaries separating pore fluid and host medium. However, the rapid development of the lattice Boltzmann methods and experimental imaging techniques now allow us to efficiently and robustly simulate flows in the pore space of porous rocks. Here we study the flow and dispersion in the pore space of limestone samples using the unstructured, characteristic based off-lattice Boltzmann method. We use the method to investigate the anomalous dispersion of particles in the pore space. We further show that the complex pore network limits the effectivity by which pollutants in the pore space can be removed by continuous flushing. In the smallest pores, diffusive transport dominates over advective transport and therefore cycles of flushing and no flushing, respectively, might be a more efficient strategy for pollutant removal.

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“…To name a few: [Stiebler et al, 2008], [Shi and Guo, 2009], [Chai and Zhao, 2013], [Yoshida and Nagaoka, 2010] and [Huang and Wu, 2014]. Of these works, Yoshida and Key words and phrases.…”

Section: Introductionmentioning

confidence: 99%

Do Current Lattice Boltzmann Methods for Diffusion and Advection-Diffusion Equations Respect Maximum Principle and the Non-Negative Constraint?

Karimi

Nakshatrala

2016

Commun. Comput. Phys.

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Abstract. The lattice Boltzmann method (LBM) has established itself as a valid numerical method in computational fluid dynamics. Recently, multiple-relaxation-time LBM has been proposed to simulate anisotropic advection-diffusion processes. The governing differential equations of advective-diffusive systems are known to satisfy maximum principles, comparison principles, the non-negative constraint, and the decay property. In this paper, it will be shown that current single-and multiple-relaxation-time lattice Boltzmann methods fail to preserve these mathematical properties for transient diffusion and advection-diffusion equations. It will also be shown that the discretization of Dirichlet boundary conditions will affect the performance of lattice Boltzmann methods in meeting these mathematical principles. A new way of discretizing the Dirichlet boundary conditions is also proposed. Several benchmark problems have been solved to illustrate the performance of lattice Boltzmann methods and the effect of discretization of boundary conditions with respect to the aforementioned mathematical properties.

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Advection–diffusion lattice Boltzmann scheme for hierarchical grids

Cited by 29 publications

References 18 publications

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

Simulating anomalous dispersion in porous media using the unstructured lattice Boltzmann method

Do Current Lattice Boltzmann Methods for Diffusion and Advection-Diffusion Equations Respect Maximum Principle and the Non-Negative Constraint?

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