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Solving transport network problems can be complicated by non-linear effects. In the particular case of gas transport networks, the most complex non-linear elements are compressors and their drives. They are described by a system of equations, composed of a piecewise linear ‘free’ model for the control logic and a non-linear ‘advanced’ model for calibrated characteristics of the compressor. For all element equations, certain stability criteria must be fulfilled, providing the absence of folds in associated system mapping. In this paper, we consider a transformation (warping) of a system from the space of calibration parameters to the space of transport variables, satisfying these criteria. The algorithm drastically improves stability of the network solver. Numerous tests on realistic networks show that nearly 100% convergence rate of the solver is achieved with this approach.
In this paper, an analysis of the error ellipsoid in the space of solutions of stationary gas transport problems is carried out. For this purpose, a Principal Component Analysis of the solution set has been performed. The presence of unstable directions is shown associated with the marginal fulfillment of the resistivity conditions for the equations of compressors and other control elements in gas networks. Practically, the instabilities occur when multiple compressors or regulators try to control pressures or flows in the same part of the network. Such problems can occur, in particular, when the compressors or regulators reach their working limits. Possible ways of resolving instabilities are considered.
The lattice Boltzmann method (LBM) is an efficient simulation technique for computational fluid mechanics and beyond. It is based on a simple stream-and-collide algorithm on Cartesian grids, which is easily compatible with modern machine learning architectures. While it is becoming increasingly clear that deep learning can provide a decisive stimulus for classical simulation techniques, recent studies have not addressed possible connections between machine learning and LBM. Here, we introduce Lettuce, a PyTorch-based LBM code with a threefold aim. Lettuce enables GPU accelerated calculations with minimal source code, facilitates rapid prototyping of LBM models, and enables integrating LBM simulations with PyTorch's deep learning and automatic differentiation facility. As a proof of concept for combining machine learning with the LBM, a neural collision model is developed, trained on a doubly periodic shear layer and then transferred to a different flow, a decaying turbulence. We also exemplify the added benefit of PyTorch's automatic differentiation framework in flow control and optimization. To this end, the spectrum of a forced isotropic turbulence is maintained without further constraining the velocity field.
Das Cutting sticks-Problem ist in seiner allgemeinen Formulierung ein NP-vollständiges Problem mit Anwendungspotenzialen im Bereich der Logistik. Unter der Annahme, dass P ungleich NP (P != NP) ist, existieren keine effizienten, d.h. polynomiellen Algorithmen zur Lösung des allgemeinen Problems.
In diesem Papier werden Ansätze aufgezeigt, mit denen bestimmte Instanzen des Problems effizient berechnet werden können. Für die Berechnung wichtige Parameter werden charakterisiert und deren Beziehung untereinander analysiert.
Das Cutting sticks-Problem ist ein NP-vollständiges Problem mit Anwendungspotenzialen im Bereich der Logistik. Es werden grundlegende Definitionen für die Behandlung sowie bisherige Ansätze zur Lösung des Problems aufgearbeitet und durch einige neue Aussagen ergänzt. Insbesondere stehen Ideen für eine algorithmische Lösung des Problems bzw. von Varianten des Problems im Fokus.
Das Cutting sticks-Problem ist in seiner allgemeinen Formulierung ein NP-vollständiges Problem mit Anwendungspotenzialen im Bereich der Logistik. Unter der Annahme, dass P ungleich NP (P != NP) ist, existieren keine effizienten, d.h. polynomiellen Algorithmen zur Lösung des allgemeinen Problems.
In diesem Papier werden für eine Reihe von Instanzen effiziente Lösungen angegeben.
Novel methods for contingency analysis of gas transport networks are presented. They are motivated by the transition of our energy system where hydrogen plays a growing role. The novel methods are based on a specific method for topological reduction and so-called supernodes. Stationary Euler equations with advanced compressor thermodynamics and a gas law allowing for gas compositions with up to 100% hydrogen are used. Several measures and plots support an intuitive comparison and analysis of the results. In particular, it is shown that the newly developed methods can estimate locations and magnitudes of additional capacities (injection, buffering, storage etc.) with a reasonable performance for networks of relevant composition and size.