A Petrov-Galerkin finite element method for 2D transient and steady state highly advective flows in porous media

W. Cui; K. A. Gawecka; D. M. Potts; D. M.G. Taborda; L. Zdravković

doi:10.1016/j.compgeo.2018.04.013

A Petrov-Galerkin finite element method for 2D transient and steady state highly advective flows in porous media

W. Cui^*
, K. A. Gawecka
, D. M. Potts
, D. M.G. Taborda
, L. Zdravković

^*Corresponding author for this work

Imperial College London

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

A new Petrov-Galerkin finite element method for two-dimensional (2D) highly advective flows in porous media, which removes numerical oscillations and retains its precision compared to the conventional Galerkin finite element method, is presented. A new continuous weighting function for quadratic elements is proposed. Moreover, a numerical scheme is developed to ensure the weighting factors are accurately determined for 2D non-uniform flows and 2D distorted elements. Finally, a series of numerical examples are performed to demonstrate the capability of the approach. Comparison against existing methods in the simulation of a benchmark problem further verifies the robustness of the proposed method.

Original language	English
Pages (from-to)	158-173
Number of pages	16
Journal	Computers and Geotechnics
Volume	100
DOIs	https://doi.org/10.1016/j.compgeo.2018.04.013
State	Published - Aug 2018
Externally published	Yes

Keywords

2D highly advectiveflows
Finite element methods
Porous media

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10.1016/j.compgeo.2018.04.013

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title = "A Petrov-Galerkin finite element method for 2D transient and steady state highly advective flows in porous media",

abstract = "A new Petrov-Galerkin finite element method for two-dimensional (2D) highly advective flows in porous media, which removes numerical oscillations and retains its precision compared to the conventional Galerkin finite element method, is presented. A new continuous weighting function for quadratic elements is proposed. Moreover, a numerical scheme is developed to ensure the weighting factors are accurately determined for 2D non-uniform flows and 2D distorted elements. Finally, a series of numerical examples are performed to demonstrate the capability of the approach. Comparison against existing methods in the simulation of a benchmark problem further verifies the robustness of the proposed method.",

keywords = "2D highly advectiveflows, Finite element methods, Porous media",

author = "W. Cui and Gawecka, \{K. A.\} and Potts, \{D. M.\} and Taborda, \{D. M.G.\} and L. Zdravkovi{\'c}",

note = "Publisher Copyright: {\textcopyright} 2018 The Authors",

year = "2018",

month = aug,

doi = "10.1016/j.compgeo.2018.04.013",

language = "英语",

volume = "100",

pages = "158--173",

journal = "Computers and Geotechnics",

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T1 - A Petrov-Galerkin finite element method for 2D transient and steady state highly advective flows in porous media

AU - Cui, W.

AU - Gawecka, K. A.

AU - Potts, D. M.

AU - Taborda, D. M.G.

AU - Zdravković, L.

PY - 2018/8

Y1 - 2018/8

N2 - A new Petrov-Galerkin finite element method for two-dimensional (2D) highly advective flows in porous media, which removes numerical oscillations and retains its precision compared to the conventional Galerkin finite element method, is presented. A new continuous weighting function for quadratic elements is proposed. Moreover, a numerical scheme is developed to ensure the weighting factors are accurately determined for 2D non-uniform flows and 2D distorted elements. Finally, a series of numerical examples are performed to demonstrate the capability of the approach. Comparison against existing methods in the simulation of a benchmark problem further verifies the robustness of the proposed method.

AB - A new Petrov-Galerkin finite element method for two-dimensional (2D) highly advective flows in porous media, which removes numerical oscillations and retains its precision compared to the conventional Galerkin finite element method, is presented. A new continuous weighting function for quadratic elements is proposed. Moreover, a numerical scheme is developed to ensure the weighting factors are accurately determined for 2D non-uniform flows and 2D distorted elements. Finally, a series of numerical examples are performed to demonstrate the capability of the approach. Comparison against existing methods in the simulation of a benchmark problem further verifies the robustness of the proposed method.

KW - 2D highly advectiveflows

KW - Finite element methods

KW - Porous media

UR - https://www.scopus.com/pages/publications/85046010981

U2 - 10.1016/j.compgeo.2018.04.013

DO - 10.1016/j.compgeo.2018.04.013

M3 - 文章

AN - SCOPUS:85046010981

SN - 0266-352X

VL - 100

SP - 158

EP - 173

JO - Computers and Geotechnics

JF - Computers and Geotechnics

ER -

A Petrov-Galerkin finite element method for 2D transient and steady state highly advective flows in porous media

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Keywords

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