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

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 ele...

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Bibliographic Details
Published in:Computers and geotechnics 2018-08, Vol.100, p.158-173
Main Authors: Cui, W., Gawecka, K.A., Potts, D.M., Taborda, D.M.G., Zdravković, L.
Format: Article
Language:English
Subjects:
2D highly advectiveflows
Computer simulation
Continuity (mathematics)
Equilibrium flow
Finite element analysis
Finite element method
Finite element methods
Galerkin method
Geotechnology
Mathematical analysis
Mathematical models
Oscillations
Porous materials
Porous media
Robustness (mathematics)
Two dimensional flow
Weighting functions
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Summary: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.
ISSN:0266-352X
1873-7633
DOI:10.1016/j.compgeo.2018.04.013