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

Authors: Cui, W., Gawecka, K.A., Potts, D.M., Taborda, D.M.G., Zdravković, L.

Journal: Computers and Geotechnics

Publication Date: 01/08/2018

Volume: 100

Pages: 158-173

eISSN: 1873-7633

ISSN: 0266-352X

DOI: 10.1016/j.compgeo.2018.04.013

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.

Source: Scopus