Assessment of the two relaxation time Lattice‐Boltzmann scheme to simulate Stokes flow in porous media

Talon, Laurent; Bauer, Daniela; Gland, N.; Youssef, S.; Auradou, Harold; Ginzburg, Irina

doi:10.1029/2011wr011385

Cited by 97 publications

(82 citation statements)

References 42 publications

(48 reference statements)

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“…We have employed the two relaxation time collision (TRT) operator [19,25], which is a special case of a multi relaxation time collision operator (MRT, [26]), most commonly used in the lattice Boltzmann studies of porous flow due to its improved treatment of the solid boundary conditions in comparison to the standard, single relaxation time BhatnagarGross-Krook (BGK) operator [19].…”

Section: Unstructured Lattice Boltzmann Methodsmentioning

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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Section: Unstructured Lattice Boltzmann Methodsmentioning

confidence: 99%

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

et al. 2015

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“…However, several issues arising in the use of LBM remain unsolved. Such an issue is the limitations that comes in applying boundary conditions, that may lead to difficulties for computations in confined structures [84]. Another issue is the question of stability and the optimal choice of the parameters in order to minimize numerical diffusion while maintaining the robustness.…”

Section: Navier-stokes Equations and High Performance Computingmentioning

confidence: 99%

Second-order entropy satisfying BGK-FVS schemes for incompressible Navier-Stokes equations

Bouchut¹,

Jobic²,

Natalini³

et al. 2018

The SMAI Journal of Computational Mathematics

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Abstract. Kinetic BGK numerical schemes for the approximation of incompressible Navier-Stokes equations are derived via classical discrete velocity vector BGK approximations, but applied to an inviscid compressible gas dynamics system with small Mach number parameter, according to the approach of Carfora and Natalini (2008). As the Mach number, the grid size and the timestep tend to zero, the low Mach number limit and the time-space convergence of the scheme are achieved simultaneously, and the numerical viscosity tends to the physical viscosity of the Navier-Stokes system. The method is analyzed and formulated as an explicit finite volume/difference flux vector splitting (FVS) scheme over a Cartesian mesh. It is close in spirit to lattice Boltzmann schemes, but it has several advantages. The first is that the scheme is expressed only in terms of momentum and mass compressible variables. It is therefore very easy to implement, and several types of boundary conditions are straightforward to apply. The second advantage is that the scheme satisfies a discrete entropy inequality, under a CFL condition of parabolic type and a subcharacteristic stability condition involving a cell Reynolds number that ensures that diffusion dominates advection at the level of the grid size. This ensures the robustness of the method, with explicit uniform bounds on the approximate solution. Moreover the scheme is proved to be second-order accurate in space if the parameters are well chosen, this is the case in particular for the Lax-Friedrichs scheme with Mach number proportional to the grid size. The scheme falls then into the class of artificial compressibility methods, the novelty being its exceptionally good theoretical properties. We show the efficiency of the method in terms of accuracy and robustness on a variety of classical two-dimensional benchmark tests. The method is finally applied in three dimensions to compute the permeability of a porous medium defined by a complex idealized Kelvin-like cell. Relations between our scheme and compressible low Mach number schemes are discussed.

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“…I is the identity matrix, and F is the force term. We use here the two relaxation time formulations in which symmetric and antisymmetric moments are relaxed with different rates (Talon et al 2012). The two relaxation rates are specified according to the recommendation of d 'Humières and Ginzburg (2009) and are shown to lead to viscosityindependent non-slip boundary solutions with the bounce-back boundary method (Pan et al 2006).…”

Section: Numerical Flow Simulationsmentioning

confidence: 99%

High-Resolution 3D FIB-SEM Image Analysis and Validation of Numerical Simulations of Nanometre-Scale Porous Ceramic with Comparisons to Experimental Results

Welch

Gray

Butcher³

et al. 2017

Transp Porous Med

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The development of focused ion beam-scanning electron microscopy (FIB-SEM) techniques has allowed high-resolution 3D imaging of nanometre-scale porous materials. These systems are of important interest to the oil and gas sector, as well as for the safe long-term storage of carbon and nuclear waste. This work focuses on validating the accurate representation of sample pore space in FIB-SEM-reconstructed volumes and the predicted permeability of these systems from subsequent single-phase flow simulations using a highly homogeneous nanometre-scale, mesoporous (2-50 nm) to macroporous (>50 nm), porous ceramic in initial developments for digital rock physics. The limited volume of investigation available from FIB-SEM has precluded direct quantitative validation of petrophysical parameters estimated from such studies on rock samples due to sample heterogeneity, large variations in recorded sample pore sizes and lack of pore connectivity. By using homogeneous synthetic ceramic samples we have shown that lattice-Boltzmann flow simulations using processed FIB-SEM images are capable of predicting the permeability of a homogeneous material dominated by 10-100 nanometre-scale pores (similar, albeit simpler, to those in natural samples) at the much larger scale where permeability measurements become practical. This result shows the LB flow simulations can be used with confidence in pores at this scale allowing future work to focus on sample preparation techniques for samples sensitive to drying and multiple FIB-SEM site selection for the population of larger-scale models for heterogeneous systems.

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Assessment of the two relaxation time Lattice‐Boltzmann scheme to simulate Stokes flow in porous media

Cited by 97 publications

References 42 publications

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

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

Second-order entropy satisfying BGK-FVS schemes for incompressible Navier-Stokes equations

High-Resolution 3D FIB-SEM Image Analysis and Validation of Numerical Simulations of Nanometre-Scale Porous Ceramic with Comparisons to Experimental Results

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