Second-order schemes for axisymmetric Navier-Stokes-Brinkman and transport equations modelling water filters
type: Item
instance of: scholarly article
title: Second-order schemes for axisymmetric Navier-Stokes-Brinkman and transport equations modelling water filters
zbMATH Open document ID: 1459.65178
author: Graham Baird
author: Paul E. Méndez
author: Ricardo Ruiz-Baier
author: Raimund Bürger
published in: Numerische Mathematik
publication date: 2021-03-03T00:00:00Z
review text: The paper concerns with the analysis and numerical approximation of the flow of a viscous fluid through a porous medium, where the fluid carries a number \(m\) of components that are absorbed by the porous medium. This kind of problem arises in designing soil-based water filtering devices. The governing equations are the Navier-Stokes-Brinkman equations for the flow of the fluid through a porous medium coupled with a convection-diffusion equation for the transport of the contaminants plus a system of ordinary differential equations. Most of the filter designs in the three-dimensional domain, display rotational symmetry around their central axis, with the flow also expected to exhibit such symmetry. The axisymmetric formulation allows the reduction from three to two spatial dimensions, which reduces the computational cost associated with the numerical solution. The authors introduce an axisymmetric \(H(\operatorname{div})\)-conforming method based on two-dimensional Brezzi-Douglas-Marini (BDM) spaces combined with an implicit, second-order backward differentiation formula (BDF2) for temporal discretization. The conditional uniqueness of the solution is proved using the discrete stability properties. An optimal a priori error estimate for the numerical scheme is derived. Numerical examples with the accuracy tests, validation against experimental data, and two contaminants in the two-layer filter, illustrate the model and reconfirm the theoretical order of accuracy.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q49
zbMATH DE Number: 7317385
zbMATH Keywords: Navier-Stokes-Brinkman equations
zbMATH Keywords: transport equations
zbMATH Keywords: viscous flow
zbMATH Keywords: porous media
zbMATH Keywords: water filters
reviewed by: Bülent Karasözen
describes a project that uses: FEniCS
MaRDI profile type: Publication
full work available at URL: s00211-020-01169-1
OpenAlex ID: W3122530923
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DOI: 10.1007/S00211-020-01169-1