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arXiv 2020年

作者： Hassan, Ahmed Sayadi, Taraneh LeChenadec, Vincent Pitsch, Heinz Attili, Antonio Institute for Combustion Technology Aachen University Germany Jean Le Rond d’Alembert Institute Sorbonne University France Multiscale Modelling and Simulation Laboratory Paris – Est University France

simulations of pulverised coal combustion rely on various models, required in order to correctly approximate the flow, chemical reactions, and behavior of solid particles. These models, in turn, rely on multiple model parameters, which are determined through experiments or small-scale simulations and contain a certain level of uncertainty. The competing effects of transport, particle physics, and chemistry give rise to various scales and disparate dynamics, making it a very challenging problem to analyse. Therefore, the steady combustion process of a single solid particle is considered as a starting point for this study. As an added complication, the large number of parameters present in such simulations makes a purely forward approach to sensitivity analysis very expensive and almost infeasible. Therefore, the use of adjoint-based algorithms, to identify and quantify the underlying sensitivities and uncertainties, is proposed. This adjoint framework bears a great advantage in this case, where a large input space is analysed, since a single forward and backward sweep provides sensitivity information with respect to all parameters of interest. In order to investigate the applicability of such methods, both discrete and continuous adjoints are considered, and compared to the conventional approaches, such as finite differences, and forward sensitivity analysis. Various quantities of interest are considered, and sensitivities with respect to the relevant combustion parameters are reported for two different freestream compositions, describing air and oxy-atmospheres. This study serves as a benchmark for future research, where unsteady and finally turbulent cases will be considered. © 2020, CC0.

关键词： Sensitivity analysis

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An explicit method to determine Casimirs in 2D geophysical flows

arXiv

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arXiv 2023年

作者： Luesink, Erwin Geurts, Bernard Multiscale Modelling and Simulation Department of Applied Mathematics Faculty EEMCS University of Twente PO Box 217 Enschede7500 AE Netherlands Multiscale Physics Center for Computational Energy Research Department of Applied Physics Eindhoven University of Technology PO Box 513 Eindhoven5600 MB Netherlands

Conserved quantities in geophysical flows play an important role in the characterisation of geophysical dynamics and aid the development of structure-preserving numerical methods. A significant family of conserved quantities is formed by the Casimirs i.e., integral conservation laws that are in the kernel of the underlying Poisson bracket. The Casimirs hence determine the geometric structure of the geophysical fluid equations among which the enstrophy is well known. Often Casimirs are proposed on heuristic grounds and later verified to be part of the kernel of the Poisson bracket. In this work, we will explicitly construct Casimirs by rewriting the Poisson bracket in vorticity-divergence coordinates thereby providing explicit construction of Casimirs for 2D geophysical flow dynamics. Copyright © 2023, The Authors. All rights reserved.

关键词： Numerical methods

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Casimir preserving stochastic Lie-Poisson integrators

arXiv

引用

arXiv 2021年

作者： Luesink, Erwin Ephrati, Sagy Cifani, Paolo Geurts, Bernard Multiscale Modelling and Simulation Department of Applied Mathematics Faculty EEMCS University of Twente PO Box 217 Enschede7500 AE Netherlands Gran Sasso Science Institute Viale F. Crispi 7 L’Aquila67100 Italy Multiscale Physics Center for Computational Energy Research Department of Applied Physics Eindhoven University of Technology PO Box 513 Eindhoven5600 MB Netherlands

Casimir preserving integrators for stochastic Lie-Poisson equations with Stratonovich noise are developed extending Runge-Kutta Munthe-Kaas methods. The underlying Lie-Poisson structure is preserved along stochastic trajectories. A related stochastic differential equation on the Lie algebra is derived. The solution of this differential equation updates the evolution of the Lie-Poisson dynamics by means of the exponential map. The constructed numerical method conserves Casimir-invariants exactly, which is important for long time integration. This is illustrated numerically for the case of the stochastic heavy top and the stochastic sine-Euler equations. Copyright © 2021, The Authors. All rights reserved.

关键词： Integration

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Zeitlin truncation of a Shallow Water Quasi-Geostrophic model for planetary flow

arXiv

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arXiv 2023年

作者： Franken, Arnout Caliaro, Martino Cifani, Paolo Geurts, Bernard Multiscale Modelling and Simulation Department of Applied Mathematics Faculty EEMCS University of Twente PO Box 217 Enschede7500 AE Netherlands Gran Sasso Science Institute Viale F. Crispi 7 L’Aquila67100 Italy Multiscale Physics Center for Computational Energy Research Department of Applied Physics Eindhoven University of Technology PO Box 513 Eindhoven5600 MB Netherlands

In this work, we consider a Shallow-Water Quasi Geostrophic equation on the sphere, as a model for global large-scale atmospheric dynamics. This equation, previously studied by Verkley [2009] and Schubert et al. [2009], possesses a rich geometric structure, called Lie-Poisson, and admits an infinite number of conserved quantities, called Casimirs. In this paper, we develop a Casimir preserving numerical method for long-time simulations of this equation. The method develops in two steps: firstly, we construct an N-dimensional Lie-Poisson system that converges to the continuous one in the limit N → ∞;secondly, we integrate in time the finite-dimensional system using an isospectral time integrator, developed by Modin and Viviani [2020]. We demonstrate the efficacy of this computational method by simulating a flow on the entire sphere for different values of the Lamb parameter. We particularly focus on rotation-induced effects, such as the formation of jets. In agreement with shallow water models of the atmosphere, we observe the formation of robust latitudinal jets and a decrease in the zonal wind amplitude with latitude. Furthermore, spectra of the kinetic energy are computed as a point of reference for future studies. Copyright © 2023, The Authors. All rights reserved.

关键词： Kinetic energy

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Critical latitude in global quasi-geostrophic flow on a rotating sphere

arXiv

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arXiv 2024年

作者： Franken, Arnout D. Luesink, Erwin Ephrati, Sagy R. Geurts, Bernard J. Mathematics of Multiscale Modelling and Simulation Department of Applied Mathematics Faculty EEMCS University of Twente PO Box 217 Enschede7500 AE Netherlands Korteweg-de-Vries Institute University of Amsterdam PO Box 94248 Science Park 107 Amsterdam1090 GE Netherlands Department of Mathematical Sciences Chalmers University of Technology Gothenburg412 96 Sweden Multiscale Physics Center for Computational Energy Research Department of Applied Physics Eindhoven University of Technology Eindhoven Netherlands

In this paper, we study geostrophic turbulence without external forcing or dissipation, using a Casimir-preserving numerical method. The research examines the formation of large zonal jets, common in geophysical flows, especially in giant gas planets. These jets form due to the east-west stretching of vortices, influenced by the gradient of the Coriolis parameter, leading to a critical latitude beyond which jets do not form. Using a global quasi-geostrophic model with a fully latitude-dependent Coriolis parameter, we investigate this critical latitude, which is theorized to depend only on the product of the Rossby number and the Lamb parameter. By simulating random flow fields, the critical latitude was identified through zonally averaged zonal velocity profiles. Results align with geostrophic theory, especially near typical Rossby and Lamb parameter values for Earth’s atmosphere. However, in the regime of weak rotation (high Rossby numbers) and strong stratification (high Lamb values), no clear critical latitude emerges;instead, zonal jet amplitude and width decrease gradually towards the poles. This research paves the way for further study of jet dynamics under a fully latitude-dependent Coriolis parameter. Copyright © 2024, The Authors. All rights reserved.

关键词： Miocene

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Casimir preserving numerical method for global multilayer geostrophic turbulence

arXiv

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arXiv 2024年

Accurate long-term predictions of large-scale flow features on planets are crucial for understanding global atmospheric and oceanic systems, necessitating the development of numerical methods that can preserve essential physical structures over extended simulation periods without excessive computational costs. Recent advancements in the study of global single-layer barotropic models have led to novel numerical methods based on Lie-Poisson discretization that preserve energy, enstrophy and higher-order moments of potential vorticity. This work extends this approach to more complex stratified quasi-geostrophic (QG) systems on the sphere. In this work, we present a formulation of the multi-layer QG equations on the full globe. This allows for extending the Lie-Poisson discretization to multi-layer QG models, ensuring consistency with the underlying structure and enabling long-term simulations without additional regularization. The numerical method is benchmarked through simulations of forced geostrophic turbulence and the long-term behaviour of unforced multi-layered systems. These results demonstrate the structure-preserving properties and robustness of the proposed numerical method, paving the way for a better understanding of the role of high-order conserved quantities in large-scale geophysical flow dynamics. Copyright © 2024, The Authors. All rights reserved.

关键词： Atmospheric movements

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Spin polaronics: Static and dynamic properties of spin polarons in La-doped CaMnO3

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Physical Review B 2019年第13期100卷 134443-134443页

作者： N. Bondarenko J. Chico Y. O. Kvashnin A. Bergman N. V. Skorodumova O. Eriksson Division of Materials Theory Department of Physics and Astronomy Uppsala University Box 516 SE-75121 Uppsala Sweden Peter Grünberg Institut and Institute of Advanced Simulation Forschungszentrum Jülich & JARA D-52428 Jülich Germany Maison de la Simulation USR 3441 CEA-CNRS-INRIA-Université Paris-Sud-Université de Versailles F-91191 Gif-sur-Yvette France L_Sim INAC-MEM CEA F-38000 Grenoble France Multiscale Materials Modelling Department of Materials Science and Engineering Royal Institute of Technology SE-100 44 Stockholm Sweden School of Science and Technology Örebro University SE-701 82 Örebro Sweden

The static and dynamic properties of spin polarons in La-doped CaMnO3 are explored theoretically, by means of an effective low-energy Hamiltonian. All parameters of the effective Hamiltonian are evaluated from first-principles theory. The Hamiltonian is used to investigate the temperature stability as well as the response to an external applied electric field, for spin polarons in bulk, surface, and as single two-dimensional layers. Technically this involves atomistic spin-dynamics simulations in combination with kinetic Monte Carlo simulations. Where a comparison can be made, our simulations exhibit excellent agreement with available experimental data and previous theory. Remarkably, we find that excellent control of the mobility of spin polarons in this material can be achieved, and that the critical parameters deciding this are the temperature and strength of the applied electrical field. We outline different technological implications of spin polarons, and point to spin polaronics as an emerging subfield of nanotechnology. In particular, we demonstrate that it is feasible to write and erase information on an atomic scale, by use of spin polarons in CaMnO3.

关键词： Antiferromagnetism Magnetic interactions Magnetization dynamics Methods in magnetism Polarons Spin dynamics Antiferromagnets Density functional calculations

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Spin-polaronics, an emerging technology

arXiv

引用

arXiv 2018年

作者： Bondarenko, N. Chico, J. Kvashnin, Y.O. Bergman, A. Skorodumova, N.V. Eriksson, O. Division of Materials theory Department of Physics and Astronomy Uppsala University Box 516 Uppsala75121 Sweden Peter Grünberg Institut Institute of Advanced Simulation Forschungszentrum Jülich & JARA JülichD-52428 Germany Maison de la Simulation USR 3441 CEA-CNRS-INRIA Université Paris-Sud Université de Versailles Gif-sur-YvetteF-91191 France L Sim INAC-MEM CEA GrenobleF-38000 France Multiscale Materials Modelling Department of Materials Science and Engineering Royal Institute of Technology StockholmSE-100 44 Sweden School of Science and Technology Örebro University ÖrebroSE-701 82 Sweden

The static and dynamic properties of spin-polarons in La-doped CaMnO3 are explored theoretically, by means of an effective low energy Hamiltonian. All parameters from the Hamiltoniain are evaluated from first principles theory, without adjustable parameters. The Hamiltonian is used to investigate the temperature stability as well as the response to an external applied electric field, for spin-polarons in bulk, surface and as single two-dimensional layers. Technically this involves atomistic spin-dynamics simulations in combination with kinetic Monte Carlo simulations. Where a comparison can be made, our simulations exhibit an excellent agreement with available experimental data and previous theory. Remarkably, we find that excellent control of the mobility of spin-polarons in this material can be achieved, and that the critical parameters deciding this is the temperature and strength of the applied electrical field. We outline different technological implications of spin-polarons, and point to spin-polaronics as an emerging sub-field of nano-technology. In particular, we demonstrate that it is feasible to write and erase information on atomic scale, by use of spin-polarons in CaMnO3. Copyright © 2018, The Authors. All rights reserved.

关键词： Hamiltonians

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