Low and highorder accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes
Abstract
The present contribution focuses on the accuracy of reflectiontype boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the tworelaxationtime (TRT) collision and the Brinkmanforce based scheme (BF), called BFTRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BFTRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocityproportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in latticealigned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the noslip wall condition supported by traditional LBM boundary schemes, such as the bounceback rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition atmore »
 Authors:
 Irstea, Antony Regional Centre, HBAN, 1 rue PierreGilles de Gennes CS 10030, 92761 Antony cedex (France)
 CNRS (UMR 7608), Laboratoire FAST, Batiment 502, Campus University, 91405 Orsay (France)
 Publication Date:
 OSTI Identifier:
 22622277
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 335; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; APPROXIMATIONS; BOLTZMANN EQUATION; BOUNDARY CONDITIONS; BOUNDARY LAYERS; COMPUTERIZED SIMULATION; CORRECTIONS; DEFECTS; DIRICHLET PROBLEM; EXACT SOLUTIONS; FINITE ELEMENT METHOD; FLOW MODELS; INTERFERENCE; LAPLACIAN; OSCILLATIONS; PERIODICITY; PERMEABILITY; POROUS MATERIALS; RELAXATION TIME; RESOLUTION; VISCOSITY
Citation Formats
Silva, Goncalo, Email: goncalo.nuno.silva@gmail.com, Talon, Laurent, Email: talon@fast.upsud.fr, and Ginzburg, Irina, Email: irina.ginzburg@irstea.fr. Low and highorder accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2017.01.023.
Silva, Goncalo, Email: goncalo.nuno.silva@gmail.com, Talon, Laurent, Email: talon@fast.upsud.fr, & Ginzburg, Irina, Email: irina.ginzburg@irstea.fr. Low and highorder accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes. United States. doi:10.1016/J.JCP.2017.01.023.
Silva, Goncalo, Email: goncalo.nuno.silva@gmail.com, Talon, Laurent, Email: talon@fast.upsud.fr, and Ginzburg, Irina, Email: irina.ginzburg@irstea.fr. Sat .
"Low and highorder accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes". United States.
doi:10.1016/J.JCP.2017.01.023.
@article{osti_22622277,
title = {Low and highorder accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes},
author = {Silva, Goncalo, Email: goncalo.nuno.silva@gmail.com and Talon, Laurent, Email: talon@fast.upsud.fr and Ginzburg, Irina, Email: irina.ginzburg@irstea.fr},
abstractNote = {The present contribution focuses on the accuracy of reflectiontype boundary conditions in the Stokes–Brinkman–Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the tworelaxationtime (TRT) collision and the Brinkmanforce based scheme (BF), called BFTRT scheme. In parallel, we compare it with the Stokes–Brinkman–Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BFTRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocityproportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in latticealigned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the noslip wall condition supported by traditional LBM boundary schemes, such as the bounceback rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundarynode distance and that supports a higher order accuracy in the accommodation of the TRTBrinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one and twopoint families of linear and parabolic linkwise boundary schemes, respectively called BLI and BMLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the lowaccurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the highorder accurate boundary schemes, the simple, uniformmeshbased TRTLBM formulation can even surpass the accuracy of FEM employing hardworking bodyfitted meshes.},
doi = {10.1016/J.JCP.2017.01.023},
journal = {Journal of Computational Physics},
number = ,
volume = 335,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2017},
month = {Sat Apr 15 00:00:00 EDT 2017}
}

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