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We present a physics-informed deep learning model for the transient heat transfer analysis of three-dimensional functionally graded materials (FGMs) employing a Runge–Kutta discrete time scheme. Firstly, the governing equation, associated boundary conditions and the initial condition for transient heat transfer analysis of FGMs with exponential material variations are presented. Then, the deep collocation method with the Runge–Kutta integration scheme for transient analysis is introduced. The prior physics that helps to generalize the physics-informed deep learning model is introduced by constraining the temperature variable with discrete time schemes and initial/boundary conditions. Further the fitted activation functions suitable for dynamic analysis are presented. Finally, we validate our approach through several numerical examples on FGMs with irregular shapes and a variety of boundary conditions. From numerical experiments, the predicted results with PIDL demonstrate well agreement with analytical solutions and other numerical methods in predicting of both temperature and flux distributions and can be adaptive to transient analysis of FGMs with different shapes, which can be the promising surrogate model in transient dynamic analysis.
Kleine Kommunen im ländlichen Raum sind aufgrund ihrer oft eingeschränkten personellen und finanziellen Kapazitäten bisher eher sporadisch in den Themenfeldern Energieeffizienz und Erneuerbare Energien aktiv. Immer wieder stellt sich daher Frage, wie die Klimaschutzstrategien des Bundes und der Länder dort mit dem verfügbaren Personal kostengünstig realisierbar sind. Vor diesem Hintergrund wird ein Werkzeug entwickelt, mit dessen Hilfe der aktive Einstieg in diese Thematik mit geringen Aufwand und überwiegend barrierefrei möglich ist.
Der Aufbau eines prozessorientierten Entwicklungs- und Moderationsmodells zur Erprobung und Umsetzung bezahlbarer Handlungsoptionen für Energieeinsparungen und effizienten Energieeinsatz im überwiegend ländlichen geprägten Raum ist der Schwerpunkt der Softwarelösung.
Kommunen werden mit deren Hilfe in die Lage versetzt, in die notwendigen Prozesse der Energie- und Wärmewende einzusteigen. Dabei soll der modulare Aufbau die regulären Schritte notwendiger (integrierter) Planungsprozesse nicht vollständig ersetzen. Vielmehr können innerhalb der Online-Anwendung - überwiegend automatisiert - konkrete Maßnahmenvorschläge erstellt werden, die ein solides Fundament der künftigen energetischen Entwicklung der Kommunen darstellen.
Für eine gezielte Validierung der Ergebnisse und der Ableitung potentieller Maßnahmen werden für die Erprobung Modellkommunen in Thüringen, Bayern und Hessen als Reallabore einbezogen.
Das Tool steht bisher zunächst nur den beteiligten Modellkommunen zur Verfügung. Die entwickelte Softwarelösung soll künftig Schritt für Schritt allen interessierten Kommunen mit diversen Hilfsmitteln und einer Vielzahl anderer praktischer Bestandteile zur Verfügung gestellt werden.
Flow velocity is generally presumed to influence flood damage. However, this influence is hardly quantified and virtually no damage models take it into account. Therefore, the influences of flow velocity, water depth and combinations of these two impact parameters on various types of flood damage were investigated in five communities affected by the Elbe catchment flood in Germany in 2002. 2-D hydraulic models with high to medium spatial resolutions were used to calculate the impact parameters at the sites in which damage occurred. A significant influence of flow velocity on structural damage, particularly on roads, could be shown in contrast to a minor influence on monetary losses and business interruption. Forecasts of structural damage to road infrastructure should be based on flow velocity alone. The energy head is suggested as a suitable flood impact parameter for reliable forecasting of structural damage to residential buildings above a critical impact level of 2m of energy head or water depth. However, general consideration of flow velocity in flood damage modelling, particularly for estimating monetary loss, cannot be recommended.
In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.
A coupled thermo-hydro-mechanical model of jointed hard rock for compressed air energy storage
(2014)
Renewable energy resources such as wind and solar are intermittent, which causes instability when being connected to utility grid of electricity. Compressed air energy storage (CAES) provides an economic and technical viable solution to this problem by utilizing subsurface rock cavern to store the electricity generated by renewable energy in the form of compressed air. Though CAES has been used for over three decades, it is only restricted to salt rock or aquifers for air tightness reason. In this paper, the technical feasibility of utilizing hard rock for CAES is investigated by using a coupled thermo-hydro-mechanical (THM) modelling of nonisothermal gas flow. Governing equations are derived from the rules of energy balance, mass balance, and static equilibrium. Cyclic volumetric mass source and heat source models are applied to simulate the gas injection and production. Evaluation is carried out for intact rock and rock with discrete crack, respectively. In both cases, the heat and pressure losses using air mass control and supplementary air injection are compared.