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Efficient Long-Term Simulation of the Heat Equation with Application in Geothermal Energy Storage

Bähr, Martin and Breuß, Michael (2022) Efficient Long-Term Simulation of the Heat Equation with Application in Geothermal Energy Storage. Mathematics, 10 (13). Multidisciplinary Digital Publishing Institute (MDPI). doi: 10.3390/math10132309. ISSN 2227-7390.

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Official URL: https://www.mdpi.com/2227-7390/10/13/2309

Abstract

Long-term evolutions of parabolic partial differential equations, such as the heat equation, are the subject of interest in many applications. There are several numerical solvers marking the state-of-the-art in diverse scientific fields that may be used with benefit for the numerical simulation of such long-term scenarios. We show how to adapt some of the currently most efficient numerical approaches for solving the fundamental problem of long-term linear heat evolution with internal and external boundary conditions as well as source terms. Such long-term simulations are required for the optimal dimensioning of geothermal energy storages and their profitability assessment, for which we provide a comprehensive analytical and numerical model. Implicit methods are usually considered the best choice for resolving long-term simulations of linear parabolic problems; however, in practice the efficiency of such schemes in terms of the combination of computational load and obtained accuracy may be a delicate issue, as it depends very much on the properties of the underlying model. For example, one of the challenges in long-term simulation may arise by the presence of time-dependent boundary conditions, as in our application. In order to provide both a computationally efficient and accurate enough simulation, we give a thorough discussion of the various numerical solvers along with many technical details and own adaptations. By our investigation, we focus on two largely competitive approaches for our application, namely the fast explicit diffusion method originating in image processing and an adaptation of the Krylov subspace model order reduction method. We validate our numerical findings via several experiments using synthetic and real-world data. We show that we can obtain fast and accurate long-term simulations of typical geothermal energy storage facilities. We conjecture that our techniques can be highly useful for tackling long-term heat evolution in many applications.

Item URL in elib:https://elib.dlr.de/187264/
Document Type:Article
Title:Efficient Long-Term Simulation of the Heat Equation with Application in Geothermal Energy Storage
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Bähr, MartinMartin.Baehr (at) dlr.dehttps://orcid.org/0000-0002-5420-5947
Breuß, MichaelFachgebiet Angewandte Mathematik, BTU Cottbus-Senftenberghttps://orcid.org/0000-0002-5322-2411
Date:1 July 2022
Journal or Publication Title:Mathematics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:10
DOI:10.3390/math10132309
Publisher:Multidisciplinary Digital Publishing Institute (MDPI)
Series Name:Special Issue "Numerical Analysis and Scientific Computing II"
ISSN:2227-7390
Status:Published
Keywords:heat equation, internal boundary conditions, efficient long-term evolution, fast explicit diffusion, Krylov subspace model order reduction, geothermal energy storage
HGF - Research field:Energy
HGF - Program:Materials and Technologies for the Energy Transition
HGF - Program Themes:High-Temperature Thermal Technologies
DLR - Research area:Energy
DLR - Program:E SP - Energy Storage
DLR - Research theme (Project):E - Low-Carbon Industrial Processes
Location: Cottbus
Institutes and Institutions:Institute of Low-Carbon Industrial Processes
Deposited By: Bähr, Martin
Deposited On:24 Nov 2022 09:52
Last Modified:24 Nov 2022 09:52

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