Details
| Original language | English |
|---|---|
| Number of pages | 23 |
| Journal | Computational geosciences |
| Early online date | 13 May 2024 |
| Publication status | E-pub ahead of print - 13 May 2024 |
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
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
- Mathematics(all)
- Computational Mathematics
- Computer Science(all)
- Computational Theory and Mathematics
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In: Computational geosciences, 13.05.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A comparison study of spatial and temporal schemes for flow and transport problems in fractured media with large parameter contrasts on small length scales
AU - Gao, Wansheng
AU - Neuweiler, Insa
AU - Wick, Thomas
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/5/13
Y1 - 2024/5/13
N2 - 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.
AB - 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.
KW - Continuous Galerkin
KW - Discontinuous Galerkin
KW - Finite differences
KW - Fractured media
KW - Space-time
KW - Transport problems
UR - http://www.scopus.com/inward/record.url?scp=85192803334&partnerID=8YFLogxK
U2 - 10.1007/s10596-024-10293-y
DO - 10.1007/s10596-024-10293-y
M3 - Article
AN - SCOPUS:85192803334
JO - Computational geosciences
JF - Computational geosciences
SN - 1420-0597
ER -