An explicit stabilised finite element method for Navier-Stokes-Brinkman equations

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dc.contributor.authorNillama, Loic Balazi Atchy
dc.contributor.authorYang, Jianhui
dc.contributor.authorYang, Liang
dc.date.accessioned2022-03-03T15:20:21Z
dc.date.available2022-03-03T15:20:21Z
dc.date.issued2022-02-10
dc.description.abstractWe present an explicit stabilised finite element method for solving Navier-Stokes-Brinkman equations. The proposed algorithm has several advantages. First, the lower equal-order finite element space for velocity and pressure is ideal for presenting the pixel images. Stabilised finite element allows the continuity of both tangential and normal velocities at the interface between regions of different micro-permeability or at the interface free/porous domain. Second, the algorithm is fully explicit and versatile for describing complex boundary conditions. Third, the fully explicit matrix–free finite element implementation is ideal for parallelism on high-performance computers. In the last, the implicit treatment of Darcy term allowed larger time stepping and a stable computation, even if the velocity varies for several orders of magnitude in the micro-porous regions (Darcy regime). The stabilisation parameter, that may affect the velocity field, has been discussed and an optimal parameter was chosen based on the numerical examples. Velocity stability at interface between different micro-permeability has been also studied with mesh refinement. We analysed the influence of the micro-permeability field on the regime of the flow (Stokes flow, Darcy flow or a transitional regime). These benchmark tests provide guidelines for choosing the resolution of the grayscale image and its segmentation. We applied the method on real Berea Sandstone micro-CT images, and proceeded the three-phases segmentation. We studied the influence of the micro-porosity field, using the well-known Kozeny-Carman relation to derive the micro-permeability field from the micro-porosity field, on the effective permeability computed. Our analysis shows that a small fraction of micro-porosity in the rock has a significant influence on the effective permeability computed.en_UK
dc.identifier.citationNillama LBA, Yang J, Yang L. (2022) An explicit stabilised finite element method for Navier-Stokes-Brinkman equations, Journal of Computational Physics, Volume 457, May 2022, Article number 111033en_UK
dc.identifier.eissn1090-2716
dc.identifier.issn0021-9991
dc.identifier.urihttps://doi.org/10.1016/j.jcp.2022.111033
dc.identifier.urihttp://dspace.lib.cranfield.ac.uk/handle/1826/17624
dc.language.isoenen_UK
dc.publisherElsevieren_UK
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectStabilised finite element methoden_UK
dc.subjectUnified Navier-Stokes-Brinkman formulationen_UK
dc.subjectGrayscale micro-CT imageen_UK
dc.subjectMicro-porosityen_UK
dc.titleAn explicit stabilised finite element method for Navier-Stokes-Brinkman equationsen_UK
dc.typeArticleen_UK

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