A robust Upwind Mixed Hybrid Finite Element method for transport in variably saturated porous media
Type
PreprintKAUST Department
Physical Science and Engineering (PSE) DivisionEnergy Resources and Petroleum Engineering Program
Ali I. Al-Naimi Petroleum Engineering Research Center (ANPERC)
Date
2022-04-27Permanent link to this record
http://hdl.handle.net/10754/676729
Metadata
Show full item recordAbstract
The Mixed Finite Element (MFE) method is well adapted for the simulation of fluid flow in heterogeneous porous media. However, when employed for the transport equation, it can generate solutions with strong unphysical oscillations because of the hyperbolic nature of advection. In this work, a robust upwind MFE scheme is proposed to avoid such unphysical oscillations. The new scheme is a combination of the upwind edge/face centred Finite Volume (FV) method with the hybrid formulation of the MFE method. The scheme ensures continuity of both advective and dispersive fluxes between adjacent elements and allows to maintain the time derivative continuous, which permits employment of high order time integration methods via the Method of Lines (MOL). Numerical simulations are performed in both saturated and unsaturated porous media to investigate the robustness of the new upwind-MFE scheme. Results show that, contrarily to the standard scheme, the upwind-MFE method generates stable solutions without under and overshoots. The simulation of contaminant transport into a variably saturated porous medium highlights the robustness of the proposed upwind scheme when combined with the MOL for solving nonlinear problems.Citation
Younes, A., Hoteit, H., Helmig, R., & Fahs, M. (2022). A robust Upwind Mixed Hybrid Finite Element method for transport in variably saturated porous media. https://doi.org/10.5194/hess-2022-153Publisher
Copernicus GmbHAdditional Links
https://hess.copernicus.org/preprints/hess-2022-153/ae974a485f413a2113503eed53cd6c53
10.5194/hess-2022-153
Scopus Count
Except where otherwise noted, this item's license is described as Archived with thanks to Copernicus GmbH under a Creative Commons license, details at: https://creativecommons.org/licenses/by/4.0/