IA Scholar Query: Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 23 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Data Science Symposium No. 7 - Book of Abstracts
https://scholar.archive.org/work/fgmn4zu6onfhxkggd74nc5gt5y
The 7th Data Science Symposium took place at Helmholtz-Zentrum Hereon, Geesthacht (Germany), on 27 and 28 June 2022. The Data Science Symposium is part of a series of symposia organized by AWI, GEOMAR and Hereon that was established in 2017. The focus of the symposium was on the following topics: • Artificial Intelligence/ Machine Learning in Earth System Sciences • Data Strategies and Exchange in POF IV • Collaborations and Initiatives • Towards Digital Twins and other Lighthouse Projects • Early Career – Science and Perspectives This book of abstracts contains all abstracts of all presentations, posters and live demos presented at the symposium.Linda Baldewein, Viktoria Wichert, Jan Bumberger, Marcel Rothenbeck, P. Leibold, N. Diller, S. Reißmann, Daniel Damaske, Jakob Eckstein, Felix Mittermayer, Kirsten Elger, Birgit Heim, Alexander Brauser, Simone Frenzel, Ulrike Kleeberg, Ben Norden, Christian Werner, Christof Lorenz, Hildegard Gödde, J. Kuppler, K. Ntageretzis, E.-L. Drews, Gauvain Wiemer, Christina Bienhold, L. Harms, S. Neuhaus, T. Bayer, Roland Koppe, Marcus Lange, Ralf Ebinghaus, Philipp Sebastian Sommer, Daniel Eggert, Tilman Dinter, Marie Ryan, Holger Brix, N. Abraham, D. Rabe, Marc Bocquet, Siddhant Agarwal, N. Tosi, Annika Nolte, Naveen Kumar Parameswaran, K. Wallmann, M. Braack, Everardo Gonzalez, E. Burwicz-Galerne, Willi Rath, C. Trahms, P. Handmann, Y. Wölker, Stephan Paul, Celia Baumhoer, A. J. Dietz, K. Heidler, X. X. Zhu, M. Scheinert, E. Loebel, I. Nitze, Stephan Frickenhaus, Frauke Albrecht, C. Arnold, D. Caus, H. Grover, A. Vlasenko, Tobias Weigel, Timm Schoening, Salva Rühling Cachay, V. Ramesh, J. Cole, H. Barker, D. Rolnick, Laurens Menno Bouwer, Sweety Mohanty, D. D. Kazempour, D. L. Patara, P. D. P. Kröger, Marco Landt-Hayen, Yunfei Huang, David S. Greenberg, Tobias Schanz, Klas Ove Möller, Saskia Rühl, Michelle Lin, Elnaz Azmi, J. Meyer, M. Strobl, A. Streit, Mohamed Chouai, F. Reimers, M. Vredenborg, S. Pinkernell, Sebastian Mieruch-Schnülle, Shivani Sharma, Elena Shchekinova, A. Biastoch, N. Amann, F. Hennemann, P. Kraus, A. Myagotin, M. Renz, S. van der Wulp, Hugo Georgenthum, R. Fablet, C. Bukas, Mohit Anand, G. Camps-Valls, J. Zscheischler, Lily-Belle Sweet, Martin Visbeck, Andreas Plüß, Martin Claus, S. Gundlach, W. Hasselbring, R. Jung, Flemming Stäbler, Valentin Buck, Julia Freier, R. Schlitzer, Max Böcke, Joost Hemmen, Christian Jacobsen, Tim Leefmann, Oliver Listing, Jörn Plewkawork_fgmn4zu6onfhxkggd74nc5gt5yWed, 23 Nov 2022 00:00:00 GMTDiscretisations and Preconditioners for Magnetohydrodynamics Models
https://scholar.archive.org/work/e3ywh5aywrhypdoh5slgo3t3lm
The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the electromagnetic and hydrodynamic variables, especially for high Reynolds and coupling numbers. In the first part of this work, we present a scalable augmented Lagrangian preconditioner for a finite element discretisation of the 𝐁-𝐄 formulation of the incompressible viscoresistive MHD equations. For stationary problems, our solver achieves robust performance with respect to the Reynolds and coupling numbers in two dimensions and good results in three dimensions. Our approach relies on specialised parameter-robust multigrid methods for the hydrodynamic and electromagnetic blocks. The scheme ensures exactly divergence-free approximations of both the velocity and the magnetic field up to solver tolerances. In the second part, we focus on incompressible, resistive Hall MHD models and derive structure-preserving finite element methods for these equations. We present a variational formulation of Hall MHD that enforces the magnetic Gauss's law precisely (up to solver tolerances) and prove the well-posedness of a Picard linearisation. For the transient problem, we present time discretisations that preserve the energy and magnetic and hybrid helicity precisely in the ideal limit for two types of boundary conditions. In the third part, we investigate anisothermal MHD models. We start by performing a bifurcation analysis for a magnetic Rayleigh–Bénard problem at a high coupling number S=1,000 by choosing the Rayleigh number in the range between 0 and 100,000 as the bifurcation parameter. We study the effect of the coupling number on the bifurcation diagram and outline how we create initial guesses to obtain complex solution patterns and disconnected branches for high coupling numbers.Fabian Laakmannwork_e3ywh5aywrhypdoh5slgo3t3lmSun, 20 Nov 2022 00:00:00 GMTPhysics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing
https://scholar.archive.org/work/tcqvo63gy5cfnc22icud3flnzi
Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, such as fluid mechanics, solid mechanics, materials science, etc. Neural networks, in particular, play a central role in this hybridization. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse; a scenario that is true in many scientific fields. Nonetheless, neural networks offer a strong foundation to digest physical-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce underlying physics: (i) physics-guided neural networks (PgNN), (ii) physics-informed neural networks (PiNN) and (iii) physics-encoded neural networks (PeNN). These approaches offer unique advantages to accelerate the modeling of complex multiscale multi-physics phenomena. They also come with unique drawbacks and suffer from unresolved limitations (e.g., stability, convergence, and generalization) that call for further research. This study aims to present an in-depth review of the three neural network frameworks (i.e., PgNN, PiNN, and PeNN) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed; limitations are discussed; and future research opportunities in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers are presented. This critical review provides a solid starting point for researchers and engineers to comprehend how to integrate different layers of physics into neural networks.Salah A Faroughi, Nikhil Pawar, Celio Fernandes, Subasish Das, Nima K. Kalantari, Seyed Kourosh Mahjourwork_tcqvo63gy5cfnc22icud3flnziMon, 14 Nov 2022 00:00:00 GMTEvaporation of binary liquids from a capillary tube
https://scholar.archive.org/work/dqb2sfyvpbcelghusohqchdora
Evaporation of multi-component liquid mixtures in confined geometries, such as capillaries, is crucial in applications such as microfluidics, two-phase cooling devices, and inkjet printing. Predicting the behaviour of such systems becomes challenging because evaporation triggers complex spatio-temporal changes in the composition of the mixture. These changes in composition, in turn, affect evaporation. In the present work, we study the evaporation of aqueous glycerol solutions contained as a liquid column in a capillary tube. Experiments and one-dimensional simulations show three evaporation regimes characterised by different time evolutions of the normalised mass transfer rate (or Sherwood number, Sh), namely Sh (t̃) = 1, Sh ∼ 1/√(t̃), and Sh ∼exp(-t̃). Here t̃ is a normalised time. We present a simplistic analytical model which shows that the evaporation dynamics can be expressed by the classical relation Sh = exp( t̃) erfc( √(t̃)). For small and medium t̃, this expression results in the first and second of the three observed scaling regimes, respectively. This analytical model is formulated in the limit of pure diffusion and when the penetration depth δ(t) of the diffusion front is much smaller than the length L(t) of the liquid column. When δ≈ L, finite length effects lead to Sh ∼exp(-t̃), i.e. the third regime. Finally, we extend our analytical model to incorporate the effect of advection and determine the conditions under which this effect is important. Our results provide fundamental insight into the physics of selective evaporation from a multi-component liquid column.Lijun Thayyil Raju, Christian Diddens, Javier Rodríguez-Rodríguez, Marjolein N. van der Linden, Xuehua Zhang, Detlef Lohse, Uddalok Senwork_dqb2sfyvpbcelghusohqchdoraSat, 12 Nov 2022 00:00:00 GMTAccelerating Eulerian Fluid Simulation With Convolutional Networks
https://scholar.archive.org/work/udhlm52xufdaxljfsdtnqrgyim
Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that leverages the approximation power of deep-learning with the precision of standard solvers to obtain fast and highly realistic simulations. Our method solves the incompressible Euler equations using the standard operator splitting method, in which a large sparse linear system with many free parameters must be solved. We use a Convolutional Network with a highly tailored architecture, trained using a novel unsupervised learning framework to solve the linear system. We present real-time 2D and 3D simulations that outperform recently proposed data-driven methods; the obtained results are realistic and show good generalization properties.Jonathan Tompson, Kristofer Schlachter, Pablo Sprechmann, Ken Perlinwork_udhlm52xufdaxljfsdtnqrgyimTue, 08 Nov 2022 00:00:00 GMTCosmic inhomogeneities in the early Universe: A numerical relativity approach
https://scholar.archive.org/work/n67mfqbzofhtdc7kkrk6ssfuhm
Cosmic inflation is arguably the most favoured paradigm of the very early Universe. It postulates an early phase of fast, nearly exponential, and accelerated expansion. Inflationary models are capable of explaining the overall flatness and homogeneity of today's Universe at large scales. Despite being widely accepted by the physics community, these models are not absent from criticism. In scalar field inflation, a necessary condition to begin inflation is the requirement of a Universe dominated by the field's potential, which implies a subdominant contribution from the scalar field dynamics. This has originated to large amounts of scientific debate and literature on the naturalness, and possible fine-tuning of the initial conditions for inflation. Another controversial issue concerns the end of inflation, and the fact that a preheating mechanism is necessary to originate the hot big bang plasma after inflation. In this thesis, we present full general relativistic simulations to study these two problems, with a particular focus on the Starobinsky and Higgs models of inflation. First, we consider the fine-tuning problem of beginning inflation from a highly dynamical and inhomogeneous "preinflation" epoch in the single-field case. In our second study, we approach the multifield paradigm of preinflation, together and consistently, with the preheating phase. These investigations confirm the robustness of these inflationary models to generic initial conditions, while putting in evidence the non-negligible gravitational effects during preheating. At the end of the manuscript, we discuss potential applications of numerical simulations in cosmology, including our preliminary investigations on primordial black hole formation.Cristian Joanawork_n67mfqbzofhtdc7kkrk6ssfuhmMon, 07 Nov 2022 00:00:00 GMTDetermining the Reaction Zone Length in Shock Initiated PETN
https://scholar.archive.org/work/ud2l24zn6bbtzdjbrwhlvnrkse
Pentaerythritol tetranitrate (PETN) is a secondary explosive used in electrical detonators in the form of a pressed powder. The reaction zone length of PETN is smaller than that of most other explosives, therefore there is a lack of data due to insufficient resolution of existing methods. Furthermore, most prior work has been on steady state behaviour, so the transition regime before steady state is particularly poorly understood. The research described in this thesis was undertaken in order to characterise the reaction zone length and wave curvature during the evolution from initiation to steady state. The investigation was focused on a detonator setting, so confined cylindrical pellets of a similar scale were used here. To separate the effect of the chemical reaction from the mechanical response to shock, plate impact experiments were performed on an inert simulant: a fine icing sugar with comparable particle size. The shock velocity and rise time were found to exhibit dependence on the thickness of the bed, suggesting that these effects may also play a role in PETN prior to development of detonation. A fibre launched laser flyer detonator system was constructed to allow repeatable shock initiation of the target samples with a high throughput. This apparatus could produce a highly tuneable shock without much of the electrical noise present with electrical detonators. High-rate capacitive sensing was applied as a technique for measuring detonation properties in small columns of PETN. Development of the diagnostic incorporated design of the sensor itself, event synchronisation handling and noise reduction. A custom-made data processing algorithm was used to extract useful information from the sensor signal. This technology was found to have the temporal and spatial resolution required, as well as being cheaper and easier to implement than competing methods. Experiments using this diagnostic were performed to measure the reaction zone length and curvature for a range of densities and sample sizes. The data could a [...]James Edgeley, Apollo-University Of Cambridge Repository, Chris Braithwaitework_ud2l24zn6bbtzdjbrwhlvnrkseThu, 03 Nov 2022 00:00:00 GMTSpline Model: a Hydrostatic / non-hydrostatic Dynamic Core with Space-time Second-order Precision and its Exact Tests
https://scholar.archive.org/work/qqogjjmim5e4rpwcawntjm3wpu
We present a new explicit quasi-Lagrangian integration scheme with the three-dimensional cubic spline function transform (transform = fitting + interpolation, referred to as "spline format") on a spherical quasi-uniform longitude-latitude grid. It is a consistent longitude-latitude grid, and to verify its feasibility, accuracy, convergence, and stability of the spline format interpolation scheme for the upstream point on the longitude-latitude grid, which may map a quasi-uniform longitude-latitude grid, a set of ideal, exact test schemes, which are recognized and effective internationally, are adopted. The equilibrium flow test, cross-polar flow test, and Rossby–Haurwitz wave test are used to illustrate the spline scheme uniformity to the linear scheme and to overcome the over-dense grid in the polar region and the non-singularity of the poles. The cross-polar flow test demonstrates that the geostrophic wind crosses the correctly polar area, including the South Pole and North Pole. A non-hydrostatic fully compressible dynamical core is used to complete the density flow test, demonstrating the existence of a time-varying reference atmosphere, and that the spline format can simulate highly nonlinear fine-scale transient flows. It can be compared for the two results of the density flow test between the solution of with spline format and the benchmark reference solution of with linear format. The non-hydrostatic dynamical core in the spline format is adopted: it can be successfully simulated for the flow over an ideal mountain, called "topographic gravity wave test", which demonstrating the bicubic surface terrain and terrain-following height coordinates, time-split integration, and vector discrete decomposition method. These can serve as the foundation for the global, unified spline format, numerical model in future.xuzan Gu, zhibin Wang, yinglian Guowork_qqogjjmim5e4rpwcawntjm3wpuTue, 01 Nov 2022 00:00:00 GMTCircumbinary Accretion: From Binary Stars to Massive Binary Black Holes
https://scholar.archive.org/work/z3mh6gwq6vcttgz44oekzklg3u
We review recent works on the dynamics of circumbinary accretion, including time variability, angular momentum transfer between the disk and the binary, and the secular evolution of accreting binaries. These dynamics can impact stellar binary formation/evolution, circumbinary planet formation/migration, and the evolution of (super)massive black-hole binaries. We discuss the dynamics and evolution of inclined/warped circumbinary disks and connect with recent observations of protoplanetary disks. A special kind of circumbinary accretion involves binaries embedded in "big" disks, which may contribute to the mergers of stellar-mass black holes in AGN disks. Highlights include: ∙ Circumbinary accretion is highly variable, being modulated at P_ b (the binary period) or ∼ 5P_ p, depending on the binary eccentricity e_ b and mass ratio q_ b. ∙ The inner region of the circumbinary disk can develop coherent eccentric structure, which may modulate the accretion and affect the physical processes (e.g. planet migration) taking place in the disk. ∙ Over long timescales, circumbinary accretion steers binaries toward equal masses, and it does not always lead to binary orbital decay, as is commonly assumed. The secular orbital evolution depends on the binary parameters (e_ b and q_ b), and on the thermodynamic properties of the accreting gas. ∙ A misaligned disk around a low-eccentricity binary tends to evolve toward coplanarity due to viscous dissipation. But when e_ b is significant, the disk can evolve toward "polar alignment", with the disk plane perpendicular to the binary plane.Dong Lai, Diego J. Muñozwork_z3mh6gwq6vcttgz44oekzklg3uMon, 31 Oct 2022 00:00:00 GMTCosmological simulations from the cosmic web to supermassive black holes
https://scholar.archive.org/work/2ix4lo3rlzcgxbe2dhpzindcf4
This thesis presents an investigation of the evolution of supermassive black holes (SMBHs) and galaxies through cosmological hydrodynamic simulations on petascale supercomputers. With the large volume, high-resolution cosmological simulation BlueTides and ASTRID, we study the local and large scale environment of the first quasars, mass assembly and dynamics of the SMBHs over cosmic history, as well as the interplay between SMBHs and galaxy formation. We also diagnose the high redshift galaxy population predicted by cosmological simulations, and use current and future observations of high redshift galaxy abundance to test the alternative dark matter models such as the fuzzy dark matter. Finally, we also explore the possibility of using deep learning methods to model the small scale physical process for larger volume simulations, as a potential way to further extend the dynamic range that can be covered by next generation cosmological simulations.Yueying Niwork_2ix4lo3rlzcgxbe2dhpzindcf4Mon, 31 Oct 2022 00:00:00 GMTData-driven discovery of Green's functions
https://scholar.archive.org/work/vm7xv3zz65e2hgzyq3bnwmzoce
Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis. This doctoral thesis introduces theoretical results and deep learning algorithms to learn Green's functions associated with linear partial differential equations and rigorously justify PDE learning techniques. A theoretically rigorous algorithm is derived to obtain a learning rate, which characterizes the amount of training data needed to approximately learn Green's functions associated with elliptic PDEs. The construction connects the fields of PDE learning and numerical linear algebra by extending the randomized singular value decomposition to non-standard Gaussian vectors and Hilbert--Schmidt operators, and exploiting the low-rank hierarchical structure of Green's functions using hierarchical matrices. Rational neural networks (NNs) are introduced and consist of neural networks with trainable rational activation functions. The highly compositional structure of these networks, combined with rational approximation theory, implies that rational functions have higher approximation power than standard activation functions. In addition, rational NNs may have poles and take arbitrarily large values, which is ideal for approximating functions with singularities such as Green's functions. Finally, theoretical results on Green's functions and rational NNs are combined to design a human-understandable deep learning method for discovering Green's functions from data. This approach complements state-of-the-art PDE learning techniques, as a wide range of physics can be captured from the learned Green's functions such as dominant modes, symmetries, and singularity locations.Nicolas Boulléwork_vm7xv3zz65e2hgzyq3bnwmzoceFri, 28 Oct 2022 00:00:00 GMTDust dynamics in RAMSES – I. Methods and turbulent acceleration
https://scholar.archive.org/work/k5slhrspx5hphhg4f7x2ipza3q
Supernova ejecta and stellar winds are believed to produce interstellar dust grains with relatively large sizes. Smaller grains can be produced via the shattering of large grains that have been stochastically accelerated. To understand this stochastic acceleration, we have implemented novel magnetohydrodynamic(MHD)-particle-in-cell(PIC) methods into the astrophysical fluid code RAMSES. We treat dust grains as a set of massive "superparticles" that experience aerodynamic drag and Lorentz force. We subject our code to a range of numerical tests designed to validate our method in different physical conditions, as well as to illustrate possible mechanisms by which grains can be accelerated. As a final test as well as a foundation for future work, we present the results of decaying dusty MHD turbulence simulations with grain parameters chosen to resemble 1-2 μm grains in typical cold neutral medium conditions. We find that in these conditions, these grains can be effectively accelerated to well beyond their shattering velocities. This is true for both electrically charged and neutral grains. While the peak of the gas-grain relative drift velocity distribution is higher for neutral grains, the drift velocity distribution of charged grains exhibits an extended exponential tail out to much greater velocities. Even so, the shapes of the distributions are such that the extra gas-grain coupling provided by the Lorentz force offers grains relative protection from shattering. We also discuss the connection between our simulations and the relatively pristine μm sized presolar grains that do not appear to have undergone significant wear in their lifetimes.Eric R. Moseley, Romain Teyssier, B. T. Drainework_k5slhrspx5hphhg4f7x2ipza3qFri, 28 Oct 2022 00:00:00 GMTObserver-based power forecast of individual and aggregated offshore wind turbines
https://scholar.archive.org/work/j436n4raafhk5gkrywzepra4na
Abstract. Due to the increasing share of wind energy in the power system, minute-scale wind power forecasts have gained importance. Remote-sensing-based approaches have proven to be a promising alternative to statistical methods and thus need to be further developed towards an operational use, aiming to increase their forecast availability and skill. Therefore, the contribution of this paper is to extend lidar-based forecasts to a methodology for observer-based probabilistic power forecasts of individual wind turbines and aggregated wind farm power. To do so, lidar-based forecasts are combined with supervisory control and data acquisition (SCADA)-based forecasts that advect wind vectors derived from wind turbine operational data. After a calibration, forecasts of individual turbines are aggregated to a probabilistic power forecast of turbine subsets by means of a copula approach. We found that combining the lidar- and SCADA-based forecasts significantly improved both forecast skill and forecast availability of a 5 min ahead probabilistic power forecast at an offshore wind farm. Calibration further increased the forecast skill. Calibrated observer-based forecasts outperformed the benchmark persistence for unstable atmospheric conditions. The aggregation of probabilistic forecasts of turbine subsets revealed the potential of the copula approach. We discuss the skill, robustness and dependency on atmospheric conditions of the individual forecasts, the value of the observer-based forecast, its calibration and aggregation, and more generally the value of minute-scale power forecasts of offshore wind. In conclusion, combining different data sources to an observer-based forecast is beneficial in all regarded cases. For an operational use one should distinguish between and adapt to atmospheric stability.Frauke Theuer, Andreas Rott, Jörge Schneemann, Lueder von Bremen, Martin Kühnwork_j436n4raafhk5gkrywzepra4naMon, 24 Oct 2022 00:00:00 GMTPlanetary-Scale Impacts and their Geophysical Consequences
https://scholar.archive.org/work/xbq7db4j3vde7jf3ewfvhwen2y
Planetary-scale impacts are thought to have been common during the final stages of planet formation. Such events may be responsible for many of the most distinguishing features of the Solar System's celestial inhabitants, such as the stark contrast between the two hemisphere's of Mars, known as the Martian Dichotomy, or the relatively small iron core and high angular momentum of the Moon. With such long-term consequences, the study of planetary-scale impacts requires the careful consideration of both the highly energetic, shock-inducing conditions directly after the impact and the geophysical implications that follow. In this thesis, such an approach is adopted throughout, as smoothed-particle hydrodynamics (SPH) simulations are coupled with geophysical models to study both the immediate and long-term effects of planetaryscale impacts. In Chapter 1, a general introduction to the topic is given, placing planetary-scale impacts in the broader context of star and planet formation. In Chapter 2, the SPH code used to simulate planetary-scale impacts, SPHLATCH, is described in detail, including derivations of the background continuum mechanics theory along with descriptions of any practical developments applied to the code. In Chapter 3, the application of these SPH impact simulations to geophysical investigations is described. A particular focus of this chapter is the crust distribution inferred by an impact simulation; a novel scheme that estimates postimpact crust across a body directly from SPH simulations is described, as well as a more sophisticated approach involving a long-term mantle convection code. In the remaining chapters, these methods are applied in two scientific studies: Chapter 4 investigates the feasibility of an impactinduced Martian Dichotomy through a large suite of SPH simulations coupled with the crust-production scheme of Chapter 3, and finally, Chapter 5 presents a previously undiscovered impact regime that may explain the Sputnik Planitia region of Pluto.Harry Ballantynework_xbq7db4j3vde7jf3ewfvhwen2yMon, 24 Oct 2022 00:00:00 GMTBond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics
https://scholar.archive.org/work/7ml6wf3fzzcrbikkwsvf5qdkli
AbstractPeridynamic (PD) theories have become widespread in various research areas due to the ability of modeling discontinuity formation and evolution in materials. Bond-based peridynamics (BB-PD), notwithstanding some modeling limitations, is widely employed in numerical simulations due to its easy implementation combined with physical intuitiveness and stability. In this paper, we review and investigate several aspects of bond-based peridynamic models. We present a detailed description of peridynamics theory, applications, and numerical models. We display the employed BB-PD integral kernels together with their differences and commonalities; then we discuss some consequences of their mathematical structure. We critically analyze and comment on the kinematic role of nonlocality, the relation between kernel structure and material impenetrability, and the role of PD kernel nonlinearity in crack formation prediction. Finally, we propose and present the idea of extending BB-PD to fluids in the framework of fading memory material, drawing some perspectives for a deeper and more comprehensive understanding of the peridynamics in fluids.Nunzio Dimola, Alessandro Coclite, Giuseppe Fanizza, Tiziano Politiwork_7ml6wf3fzzcrbikkwsvf5qdkliSun, 23 Oct 2022 00:00:00 GMTTidally excited gravity waves in the cores of solar-type stars: resonances and critical-layer formation
https://scholar.archive.org/work/ihlzrjokincuthkr35xmb3c7ku
We simulate the propagation and dissipation of tidally induced nonlinear gravity waves in the cores of solar-type stars. We perform hydrodynamical simulations of a previously developed Boussinesq model using a spectral-element code to study the stellar core as a wave cavity that is periodically forced at the outer boundary with a given azimuthal wavenumber and an adjustable frequency. For low-amplitude forcing, the system exhibits resonances with standing g-modes at particular frequencies, corresponding to a situation in which the tidal torque is highly frequency-dependent. For high-amplitude forcing, the excited waves break promptly near the centre and spin up the core so that subsequent waves are absorbed in an expanding critical layer, as found in previous work, leading to a tidal torque with a smooth frequency-dependence. For intermediate-amplitude forcing, we find that linear damping of the waves gradually spins up the core such that the resonance condition can be altered drastically. The system can evolve towards or away from g-mode resonances, depending on the difference between the forcing frequency and the closest eigenfrequency. Eventually, a critical layer forms and absorbs the incoming waves, leading to a situation similar to the high-amplitude case in which the waves break promptly. We study the dependence of this process on the forcing amplitude and frequency, as well as on the diffusion coefficients. We emphasize that the small Prandtl number in the centre of solar-like stars facilitates the development of a differentially rotating core owing to the nonlinear feedback of waves. Our simulations and analysis reveal that this important mechanism may drastically change the phase of gravity waves and thus the classical picture of resonance locking in solar-type stars needs to be revised.Zhao Guo, Gordon I. Ogilvie, Adrian J. Barkerwork_ihlzrjokincuthkr35xmb3c7kuSun, 23 Oct 2022 00:00:00 GMTGeometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains
https://scholar.archive.org/work/iadjayq5dzezdagtduj45njeaa
In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion problem on a moving domain is studied. For geometrically higher order accuracy, we apply a parametric mapping on a background space-time tensor-product mesh. Concerning discretisation in time, we consider discontinuous Galerkin, as well as related continuous (Petrov-)Galerkin and Galerkin collocation methods. For stabilisation with respect to bad cut configurations and as an extension mechanism that is required for the latter two schemes, a ghost penalty stabilisation is employed. The article puts an emphasis on the techniques that allow to achieve a robust but higher order geometry handling for smooth domains. We investigate the computational properties of the respective methods in a series of numerical experiments. These include studies in different dimensions for different polynomial degrees in space and time, validating the higher order accuracy in both variables.Fabian Heimann, Christoph Lehrenfeld, Janosch Preußwork_iadjayq5dzezdagtduj45njeaaFri, 21 Oct 2022 00:00:00 GMTStable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data
https://scholar.archive.org/work/dxnj7ulyc5azxaratkwjbopadm
Inspired by the numerical evidence of a potential 3D Euler singularity [Luo-Hou-14a, Luo-Hou-14b], we prove finite time blowup of the 2D Boussinesq and 3D axisymmetric Euler equations with smooth initial data of finite energy and boundary. There are several essential difficulties in proving finite time blowup of 3D Euler with smooth initial data. One of the essential difficulties is to control a number of nonlocal terms that do not seem to offer any damping effect. Another essential difficulty is that the strong advection normal to the boundary introduces a large growth factor for the perturbation if we use weighted L^2 estimates. We overcome this difficulty by using a combination of a weighted L^∞ norm and a weighted C^1/2 norm, and develop sharp functional inequalities using the symmetry properties of the kernels and some techniques from optimal transport. Moreover we decompose the linearized operator into a leading order operator plus a finite rank operator. The leading order operator is designed in such a way that we can obtain sharp stability estimates. The contribution from the finite rank operator can be captured by an auxiliary variable and its contribution to linear stability can be estimated by constructing approximate solution in space-time. This enables us to establish nonlinear stability of the approximate self-similar profile and prove stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth initial data and boundary.Jiajie Chen, Thomas Y. Houwork_dxnj7ulyc5azxaratkwjbopadmWed, 19 Oct 2022 00:00:00 GMTNanoscale modelling of ionic transport in the porous C-S-H network
https://scholar.archive.org/work/rvl3etyfqjh2rpdta2ubhfq3qe
Khalil Ferjaouiwork_rvl3etyfqjh2rpdta2ubhfq3qeMon, 17 Oct 2022 00:00:00 GMTMachine learning algorithms for three-dimensional mean-curvature computation in the level-set method
https://scholar.archive.org/work/gxhzvgxi7javve6ley6axv2fuy
We propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to ℝ^3 of our two-dimensional strategy in [arXiv:2201.12342][1] and the hybrid inference system of [DOI: 10.1016/j.jcp.2022.111291][2]. However, in contrast to [1,2], which built resolution-dependent neural-network dictionaries, here we develop a pair of models in ℝ^3, regardless of the mesh size. Our feedforward networks ingest transformed level-set, gradient, and curvature data to fix numerical mean-curvature approximations selectively for interface nodes. To reduce the problem's complexity, we have used the Gaussian curvature to classify stencils and fit our models separately to non-saddle and saddle patterns. Non-saddle stencils are easier to handle because they exhibit a curvature error distribution characterized by monotonicity and symmetry. While the latter has allowed us to train only on half the mean-curvature spectrum, the former has helped us blend the data-driven and the baseline estimations seamlessly near flat regions. On the other hand, the saddle-pattern error structure is less clear; thus, we have exploited no latent information beyond what is known. In this regard, we have trained our models on not only spherical but also sinusoidal and hyperbolic paraboloidal patches. Our approach to building their data sets is systematic but gleans samples randomly while ensuring well-balancedness. We have also resorted to standardization and dimensionality reduction as a preprocessing step and integrated regularization to minimize outliers. In addition, we leverage curvature rotation/reflection invariance to improve precision at inference time. Several experiments confirm that our proposed system can yield more accurate mean-curvature estimations than modern particle-based interface reconstruction and level-set schemes around under-resolved regions.Luis Ángel Larios-Cárdenas, Frédéric Gibouwork_gxhzvgxi7javve6ley6axv2fuySun, 16 Oct 2022 00:00:00 GMT