A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales

authored by: Wansheng Gao, Insa Neuweiler, Thomas Wick
Abstract: In this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin, and finite differences, are formulated. The resulting schemes are solved with sparse direct numerical solvers. Moreover, time discontinuous Galerkin methods of order one and two are solved monolithically and in a decoupled fashion, respectively, employing finite elements in space on locally refined meshes. Our algorithmic developments are substantiated with one regular fracture network and several further configurations in fractured media with large parameter contrasts on small length scales. Therein, the evaluation of the numerical schemes and implementations focuses on three key aspects, namely accuracy, monotonicity, and computational costs.
Organisation(s): Institute of Fluid Mechanics and Environmental Physics in Civil Engineering
Institute of Applied Mathematics
Type: Article
Journal: Computational geosciences
Volume: 28
Pages: 883–905
No. of pages: 23
ISSN: 1420-0597
Publication date: 10.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computer Science Applications, Computers in Earth Sciences, Computational Mathematics, Computational Theory and Mathematics
Electronic version(s): https://doi.org/10.1007/s10596-024-10293-y (Access: Open)

BibTeX

@article{a979aa386e674e1fa007397a817d693c,
title = "A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales",
abstract = "In this work, various high-accuracy numerical schemes for transport problems in fractured media are further developed and compared. Specifically, to capture sharp gradients and abrupt changes in time, schemes with low order of accuracy are not always sufficient. To this end, discontinuous Galerkin up to order two, Streamline Upwind Petrov-Galerkin, and finite differences, are formulated. The resulting schemes are solved with sparse direct numerical solvers. Moreover, time discontinuous Galerkin methods of order one and two are solved monolithically and in a decoupled fashion, respectively, employing finite elements in space on locally refined meshes. Our algorithmic developments are substantiated with one regular fracture network and several further configurations in fractured media with large parameter contrasts on small length scales. Therein, the evaluation of the numerical schemes and implementations focuses on three key aspects, namely accuracy, monotonicity, and computational costs.",
keywords = "Continuous Galerkin, Discontinuous Galerkin, Finite differences, Fractured media, Space-time, Transport problems",
author = "Wansheng Gao and Insa Neuweiler and Thomas Wick",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",
year = "2024",
month = oct,
doi = "10.1007/s10596-024-10293-y",
language = "English",
volume = "28",
pages = "883–905",
journal = "Computational geosciences",
issn = "1420-0597",
publisher = "Springer Netherlands",
number = "5",
}