Numerical treatment of the energy equation in compressible flows simulations

We analyze the conservation properties of various discretizations of the system of compressible Euler equations for shock-free flows, with special focus on the treatment of the energy equation and on the induced discrete equations for other thermodynamic quantities. The analysis is conducted both theoretically and numerically and considers two important factors characterizing the various formulations, namely the choice of the energy equation and the splitting used in the discretization of the convective terms. The energy equations analyzed are total and internal energy, total enthalpy, pressure, speed of sound and entropy. In all the cases examined the discretization of the convective terms is made with locally conservative and kinetic-energy preserving schemes. Some important relations between the various formulations are highlighted and the performances of the various schemes are assessed by considering two widely used test cases. Together with some popular formulations from the literature, also new and potentially useful ones are analyzed

Asymptotically entropy-conservative and kinetic-energy preserving numerical fluxes for compressible Euler equations

This paper proposes a hierarchy of numerical fluxes for the compressible flow equations which are kinetic-energy and pressure equilibrium preserving and asymptotically entropy conservative, i.e., they are able to arbitrarily reduce the numerical error on entropy production due to the spatial discretization. The fluxes are based on the use of the harmonic mean for internal energy and only use algebraic operations, making them less computationally expensive than the entropy-conserving fluxes based on the logarithmic mean. The use of the geometric mean is also explored and identified to be well-suited to reduce errors on entropy evolution. Results of numerical tests confirmed the theoretical predictions and the entropy-conserving capabilities of a selection of schemes have been compared.Comment: 9 pages, 4 figure

Asymptotically entropy conservative discretization of convective terms in compressible Euler equations

A new class of Asymptotically Entropy Conservative schemes is proposed for the numerical simulation of compressible (shock-free) turbulent flows. These schemes consist of a suitable spatial discretization of the convective terms in the Euler equations, which retains at the discrete level many important properties of the continuous formulation, resulting in enhanced reliability and robustness of the overall numerical method. In addition to the Kinetic Energy Preserving property, the formulation guarantees the preservation of pressure equilibrium in the case of uniform pressure and velocity distributions, and arbitrarily reduces the spurious production of entropy. The main feature of the proposed schemes is that, in contrast to existing Entropy Conservative schemes, which are based on the evaluation of costly transcendental functions, they are based on the specification of numerical fluxes involving only algebraic operations, resulting in an efficient and economical procedure. Numerical tests on a highly controlled one-dimensional problem, as well as on more realistic turbulent three-dimensional cases, are shown, together with a cost-efficiency study

Enhancing human cognition with cocoa flavonoids

Enhancing cognitive abilities has become a fascinating scientific challenge, recently driven by the interest in preventing age-related cognitive decline and sustaining normal cogni-tive performance in response to cognitively demanding environments. In recent years, cocoa and cocoa-derived products, as a rich source of flavonoids, mainly the flavanols sub-class, have been clearly shown to exert cardiovascular benefits. More recently, neuromodulation and neuroprotective actions have been also suggested. Here, we dis-cuss human studies specifically aimed at investigating the effects of acute and chronic administration of cocoa flavanols on different cognitive domains, such as executive func-tions, attention and memory. Through a variety of direct and indirect biological actions, in part still speculative, cocoa and cocoa-derived food have been suggested to possess the potential to counteract cognitive decline and sustain cognitive abilities, particularly among patients at risk. Although still at a preliminary stage, research investigating the relations between cocoa and cognition shows dose-dependent improvements in general cognition, attention, processing speed, and working memory. Moreover, cocoa flavanols administration could also enhance normal cognitive functioning and exert a protective role on cognitive performance and cardiovascular function specifically impaired by sleep loss, in healthy subjects. Together, these findings converge at pointing to cocoa as a new interesting nutraceutical tool to protect human cognition and counteract different types of cognitive decline, thus encouraging further investigations. Future research should include complex experimental designs combining neuroimaging techniques with physiological and behavioral measures to better elucidate cocoa neuromodulatory properties and directly compare immediate versus long-lasting cognitive effects

EEG oscillations during sleep and dream recall. State- or trait-like individual differences?

Dreaming represents a peculiar form of cognitive activity during sleep. On the basis of the well-known relationship between sleep and memory, there has been a growing interest in the predictive role of human brain activity during sleep on dream recall. Neuroimaging studies indicate that rapid eye movement (REM) sleep is characterized by limbic activation and prefrontal cortex deactivation. This pattern could explain the presence of emotional contents in dream reports. Furthermore, the morphoanatomical measures of amygdala and hippocampus predict some features of dream contents (bizarreness, vividness, and emotional load). More relevant for a general view of dreaming mechanisms, empirical data from neuropsychological and electroencephalographic (EEG) studies support the hypothesis that there is a sort of continuity between the neurophysiological mechanisms of encoding and retrieval of episodic memories across sleep and wakefulness. A notable overlap between the electrophysiological mechanisms underlying emotional memory formation and some peculiar EEG features of REM sleep has been suggested. In particular, theta (5–8 Hz) EEG oscillations on frontal regions in the pre-awakening sleep are predictive of dream recall, which parallels the predictive relation during wakefulness between theta activity and successful retrieval of episodic memory. Although some observations support an interpretation more in terms of an intraindividual than interindividual mechanism, the existing empirical evidence still precludes from definitely disentangling if this relation is explained by state- or trait-like differences

The spatiotemporal pattern of the human electroencephalogram at sleep onset after a period of prolonged wakefulness

During the sleep onset (SO) process, the human electroencephalogram (EEG) is characterized by an orchestrated pattern of spatiotemporal changes. Sleep deprivation (SD) strongly affects both wake and sleep EEG, but a description of the topographical EEG power spectra and oscillatory activity during the wake-sleep transition after a period of prolonged wakefulness is still missing. The increased homeostatic sleep pressure should induce an earlier onset of sleep-related EEG oscillations. The aim of the present study was to assess the spatiotemporal EEG pattern at SO following SD. A dataset of a previous study was analyzed. We assessed the spatiotemporal EEG changes (19 cortical derivations) during the SO (5 min before vs. 5 min after the first epoch of Stage 2) of a recovery night after 40 h of SD in 39 healthy subjects, analyzing the EEG power spectra (fast Fourier transform) and the oscillatory activity [better oscillation (BOSC) detection method]. The spatiotemporal pattern of the EEG power spectra mostly confirmed the changes previously observed during the wake-sleep transition at baseline. The comparison between baseline and recovery showed a wide increase of the post- vs. pre-SO ratio during the recovery night in the frequency bins 10 Hz. We found a predominant alpha oscillatory rhythm in the pre-SO period, while after SO the theta oscillatory activity was prevalent. The oscillatory peaks showed a generalized increase in all frequency bands from delta to sigma with different predominance, while beta activity increased only in the fronto-central midline derivations. Overall, the analysis of the EEG power replicated the topographical pattern observed during a baseline night of sleep but with a stronger intensity of the SO-induced changes in the frequencies 10 Hz, and the detection of the rhythmic activity showed the rise of several oscillations at SO after SD that was not observed during the wake-sleep transition at baseline (e.g., alpha and frontal theta in correspondence of their frequency peaks). Beyond confirming the local nature of the EEG pattern at SO, our results show that SD has an impact on the spatiotemporal modulation of cortical activity during the falling-asleep process, inducing the earlier emergence of sleep-related EEG oscillations

State- or trait-like individual differences in dream recall. Preliminary findings from a within-subjects study of multiple nap REM sleep awakenings

We examined the question whether the role of EEG oscillations in predicting presence/absence of dream recall (DR) is explained by "state-" or "trait-like" factors. Six healthy subjects were awakened from REM sleep in a within-subjects design with multiple naps, until a recall and a non-recall condition were obtained. Naps were scheduled in the early afternoon and were separated by 1 week. Topographical EEG data of the 5-min of REM sleep preceding each awakening were analyzed by power spectral analysis [Fast Fourier Transform (FFT)] and by a method to detect oscillatory activity [Better OSCillations (BOSC)]. Both analyses show that REC is associated to higher frontal theta activity (5-7 Hz) and theta oscillations (6.06 Hz) compared to NREC condition, but only the second comparison reached significance. Our pilot study provides support to the notion that sleep and wakefulness share similar EEG correlates of encoding in episodic memories, and supports the "state-like hypothesis": DR may depend on the physiological state related to the sleep stage from which the subject is awakened rather than on a stable individual EEG pattern

Customer-driven design of the recharge infrastructure and Vehicle-to-Grid in urban areas: A large-scale application for electric vehicles deployment

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Fast-projection methods for the incompressible navier–stokes equations

An analysis of existing and newly derived fast-projection methods for the numerical integration of incompressible Navier–Stokes equations is proposed. Fast-projection methods are based on the explicit time integration of the semi-discretized Navier–Stokes equations with a Runge–Kutta (RK) method, in which only one Pressure Poisson Equation is solved at each time step. The methods are based on a class of interpolation formulas for the pseudo-pressure computed inside the stages of the RK procedure to enforce the divergence-free constraint on the velocity field. The procedure is independent of the particular multi-stage method, and numerical tests are performed on some of the most commonly employed RK schemes. The proposed methodology includes, as special cases, some fast-projection schemes already presented in the literature. An order-of-accuracy analysis of the family of interpolations here presented reveals that the method generally has second-order accuracy, though it is able to attain third-order accuracy only for specific interpolation schemes. Applications to wall-bounded 2D (driven cavity) and 3D (turbulent channel flow) cases are presented to assess the performances of the schemes in more realistic configurations.Peer ReviewedPostprint (published version

Performance and error analysis of structure-preserving time-integration procedures for incompressible-flow simulations

The effects of kinetic-energy preservation errors due to Runge-Kutta (RK) temporal integrators have been analyzed for the case of large-eddy simulations of incompressible turbulent channel flow. Simulations have been run using the open-source solver Xcompact3D with an implicit spectral vanishing viscosity model and a variety of temporal Runge-Kutta integrators. Explicit pseudo-symplectic schemes, with improved energy preservation properties, have been compared to standard RK methods. The results show a marked decrease in the temporal error for higher-order pseudo-symplectic methods, and suggest that these schemes could be used to attain results comparable to traditional methods at a reduced computational cost.Postprint (published version