Numerical Modeling of Fluid Flow in Porous Media and in Driven Colloidal Suspensions

Harting, Jens; Zauner, Thomas; Weeber, Rudolf; Hilfer, R.

doi:10.1007/978-3-540-88303-6_25

Cited by 3 publications

(4 citation statements)

References 9 publications

(9 reference statements)

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“…The underlying physical properties of lattice Boltzmann schemes are determined via the hydrodynamic moments of the equilibrium distribution functions. The moments of the distribution functions should satisfy [86] (38) where P is the pressure tensor, and is a coefficient which controls the phase interface diffusion and is related to the mobility M of the fluid as follows [86,129],…”

Section: Free-energy Modelmentioning

confidence: 99%

“…Furthermore, in the LBM all computations involve, only local variables enabling highly efficient parallel implementations based on simple domain decomposition [37]. With more powerful computers becoming available, it was possible to perform detailed simulations of flow in artificially generated geometries [5,[38][39][40], tomographic reconstructions of sandstone samples [29,[41][42][43][44], or fibrous sheets of paper [45].…”

Section: Introductionmentioning

confidence: 99%

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Multiphase lattice Boltzmann simulations for porous media applications

et al. 2015

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Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article, we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

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Section: Free-energy Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiphase lattice Boltzmann simulations for porous media applications

et al. 2015

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“…Moreover, DDFT can be tested by comparing its predictions to experiments. This was done for, e.g., active particles [348], Brownian hard disks [204], charging processes [349], colloids in a DNA solution [304,305,350], crystals [207,208], diffusion and hydrodynamic interactions [315], dynamic mode locking [313], ion channels [351,352], nonequilibrium sedimentation of colloids [133,337], particles in confinement [194], phase separation [353], Poisson-Nernst-Planck (PNP) theory [354], protein adsorption [355,356], protein-polyelectrolyte interaction [333], resistance nonadditivity [357], the van Hove function [358,359], and wetting [208]. Not discussed here due to lack of space is the large body of work that applies polymer DDFT (see Section 3.2.3) to experimental results and employs it in technological applications.…”

Section: Tests Of Ddftmentioning

confidence: 99%

Classical dynamical density functional theory: from fundamentals to applications

Vrugt

Löwen

Wittkowski

2020

Advances in Physics

181

220

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Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems. Originally developed for the treatment of simple and complex fluids, DDFT is now applied in fields as diverse as hydrodynamics, materials science, chemistry, biology, and plasma physics. In this review, we give a broad overview over classical DDFT. We explain its theoretical foundations and the ways in which it can be derived. The relations between the different forms of deterministic and stochastic DDFT as well as between DDFT and related theories, such as quantum-mechanical time-dependent DFT, mode coupling theory, and phase field crystal models, are clarified. Moreover, we discuss the wide spectrum of extensions of DDFT, which covers methods with additional order parameters (like extended DDFT), exact approaches (like power functional theory), and systems with more complex dynamics (like active matter). Finally, the large variety of applications, ranging from fluid mechanics and polymer physics to solidification, pattern formation, biophysics, and electrochemistry, is presented.

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“…Numerous numerical models have been utilized to model flow in porous media, exhibiting strengths in different areas [7][8][9]13]. While finite element methods (FEM) allow for a very efficient calculation of certain systems, the incorporation of complex boundary conditions may become very tedious.…”

Section: Introductionmentioning

confidence: 99%

Multi Relaxation Time Lattice Boltzmann Simulations of Multiple Component Fluid Flows in Porous Media

Schmieschek

Narváez

Harting

2012

High Performance Computing in Science and Engineering ‘12

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The flow of fluid mixtures in complex geometries is of practical interest in many fields, ranging from oil recovery to freeze-dried food products. Due to its inherent locality the lattice Boltzmann method allows for straightforward implementation of complex boundaries and excellently scaling parallel computations. The widely applied Bhatnagar Gross Krook (BGK) scheme, used to model the contribution of particle collisions to the velocity field, does however suffer from limitiations in precision that become more prominent with increasing surface to volume ratio. To increase the accuracy of simulations of mixtures in porous media, we integrated a so-called multi relaxation time (MRT) collision scheme with a pseudo-potential method for fluids with multiple components. We describe some optimisation details of the implementation and present test results verifying the physical accuracy as well as benchmarks obtained on the XC2 Opteron cluster at the Scientific Supercomputing Centre Karlsruhe (SSCK).

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Numerical Modeling of Fluid Flow in Porous Media and in Driven Colloidal Suspensions

Cited by 3 publications

References 9 publications

Multiphase lattice Boltzmann simulations for porous media applications

Multiphase lattice Boltzmann simulations for porous media applications

Classical dynamical density functional theory: from fundamentals to applications

Multi Relaxation Time Lattice Boltzmann Simulations of Multiple Component Fluid Flows in Porous Media

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