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This paper is devoted to the numerical analysis of a numerical scheme for the simulation of front advection. The scheme has been recently proposed and it is based on the ideas used for Glimm's scheme. It relies on a two-step approach: a convection step is followed by a projection step, which is based on a random choice. The main advantage of this scheme is that it is applicable to multidimensional problems. In the present paper, a convergence result for this scheme is provided for a particular class of multidimensional problems. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we introduce the so-called symplectic discrete singular convolution differentiator (SDSCD) method for structure-preserving modelling of elastic waves. In the method presented, physical space is discretized by the DSCD, whereas an explicit third-order symplectic scheme is used for the time discretization. This approach uses optimization and truncation to form a localized operator. This preserves the fine structure of the wavefield in complex media and avoids non-causal interaction when parameter discontinuities are present in the medium. Theoretically, the approach presented is a structure-preserving algorithm. Also, some numerical experiments are shown in this paper. Elastic wavefield modelling experiments on a laterally heterogeneous medium with high parameter contrasts demonstrate the superior performance of the SDSCD for suppression of numerical dispersion. Long-term computational experiments exhibit the remarkable capability of the approach presented for long-time simulations. Promising numerical results suggest the SDSCD is suitable for high-precision and long-time numerical simulations, as it has structure-preserving property and it can suppress effectively numerical dispersion when coarse grids are used. [ABSTRACT FROM AUTHOR]

Recent contributions to the financial econometrics literature exploit high-frequency (HF) data to improve models for daily asset returns. This paper proposes a new class of dynamic extreme value models that profit from HF data when estimating the tails of daily asset returns. Our realized peaks-over-threshold approach provides estimates for the tails of the time-varying conditional return distribution. An in-sample fit to the S&P 500 index returns suggests that HF data convey information on daily extreme returns beyond that included in low frequency (LF) data. Finally, out-of-sample forecasts of conditional risk measures obtained with HF measures outperform those obtained with LF measures. [ABSTRACT FROM AUTHOR]

Wind energy has emerged as a promising renewable energy source and wind turbine technology has developed rapidly in recent years. Improved wind turbine performance depends heavily on the design and optimization of wind blades. This work offers a critical evaluation of the state of the art in the field of numerical modelling and simulation analysis, which have become crucial for the design and optimization of wind blades. The evaluation of the literature includes considerable research on the application of numerical methods for the structural and aerodynamic performance of wind blades under various operating situations, as well as for analysis and optimization of wind blades. The article illustrates how numerical techniques can be used to analyse wind blade performance and maximize design efficiency. The study of blade performance under various wind conditions has also been made possible through the use of simulation analysis, thus enhancing the efficiency and dependability of wind turbines. Improvements in wind turbine efficiency and dependability, and ultimately the move towards a more sustainable energy future, will be greatly helpful for the development of numerical modelling and simulation techniques. [ABSTRACT FROM AUTHOR]

This paper introduces a quasi-maximum likelihood estimator for discretely observed diffusions when a closed-form transition density is unavailable. Higher-order Wagner-Platen strong approximation is used to derive the first two conditional moments and a normal density function is used in estimation. Simulation study shows that the proposed estimator has high numerical precision and good numerical robustness. This method is applicable to a large class of diffusions. [ABSTRACT FROM AUTHOR]

Takagi, T., Shimizu, T., and Korte, H. 2007. Evaluating the impact of gillnet ghost fishing using a computational analysis of the geometry of fishing gear. – ICES Journal of Marine Science, 64: 1517–1524.We developed a net shape and load analysis system (NaLA) that can estimate the three-dimensional shape of fishing gear underwater computationally. This paper introduces the latest version of the numerical model of the NaLA. Previously, NaLA was used to estimate the net geometries and internal forces of some fishing gear, demonstrating its general versatility. However, the ultimate goal of our study has been to learn about the impact of fishing and the capture process from a physical perspective, not simply to develop elemental technologies for gear design. Accurate, quantitative evaluation of fishing gear performance from a physical perspective can be used to estimate the potentialities of the ghost fishing to gillnet gears. Although the applications are not limited to geometries and internal forces, the paper describes how computer-aided simulations of fishing gear should be applied to investigations of the impact of ghost fishing caused by lost drift and bottom gillnets. The computational results showed that a driftnet with homogenous net panels was deformed slightly and bent only at the two ends of the net. Accumulation of periphyton on a bottom gillnet after 25 d of immersion caused it to settle to the sea bottom. [ABSTRACT FROM PUBLISHER]

Stimulated by the recent advances in computational tools for the simulation of seismic wave propagation problems in realistic geological configurations, this paper presents a 3D physicsbased numerical analysis of near-source ground motion during the MW 6.0 2012 May 29 earthquake in the Po Plain, Northern Italy. To reproduce with sufficient accuracy some of the most peculiar features of the near-source strong-motion records and of the spatial variability of damage distribution, this study required a sequence of investigations, starting from the analysis of a wide set of near-source records, to the calibration of an improved kinematic seismic source model, up to the development of a 3D numerical model of the portion of the Po Plain interested by the earthquake. The latter includes the basin geometry, characterized by sediment thickness sharply varying from few tens of metres to some kilometres. The spatial resolution of the numerical model is suitable to propagate frequencies up to about 1.5 Hz. Numerical simulations were performed using the open-source high-performance code SPEED, based on the Discontinuous Galerkin Spectral Elements method. The 3D numerical model, coupled with the updated slip distribution along the rupturing fault, proved successful to reproduce with good agreement, measured through quantitative goodness-of-fit criteria, the most relevant features of the observed ground motion. These include: (i) the large fault normal velocity peaks at the near-source stations driven by updip directivity effects; (ii) the small-scale variability at short distance from the source, resulting in the out-of-phase motion at stations separated by only 3 km distance; (iii) the propagation of prominent trains of surface waves, especially in the Northern direction; (iv) the map of earthquake-induced ground uplift with maximum values of about 10 cm, in substantial agreement with geodetic measurements and (v) the two-lobed pattern of the peak ground velocity map, well correlated with the distribution of macroseismic intensity. [ABSTRACT FROM AUTHOR]

D-D source has a promising prospect of application in the field of controllable source density logging. However, the spatial distribution of a D-D 'induced γ-ray source' varies significantly and such a source is more susceptible to the influence of various formation factors, resulting in relatively low accuracy of density measurement. This study researched the spatial distribution of an induced γ-ray source. First, the principle of D-D controllable source density measurement was analyzed. Second, the generation process of a D-D induced γ-ray source and the spatial distribution under different formation conditions were simulated and studied. Finally, the associated influential factors were summarized. The results indicate that the spatial position and intensity of the induced γ-ray source were susceptible to the influence of various formation factors, such as HI, lithology and salinity. Among these factors, HI had greatest impact on the spatial position of induced γ-ray source and, particularly, when formation HI varied within the range of 0–0.1, the spatial positions of capture γ-rays changed significantly. In addition, as HI increased, the intensity of γ-rays also increased gradually. Formation lithology and salinity had a greater impact on the intensity of induced γ-rays than on the spatial distribution of these γ-rays. For formations of different lithologies, as the types and contents of main elements were different, the intensity of capture γ-rays also varied. This research provides the basic data for correcting the effects on a D-D induced γ-ray source and establishing a method of density measurement using a D-D controllable source. [ABSTRACT FROM AUTHOR]

In recent years, the application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint elastic wave propagation problems. An important challenge is to design an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D convolution formulation of the complex-frequency-shifted unsplit-field perfectly matched layer (CFS-UPML) derived in previous work more flexible by providing a new treatment to analytically remove singular parameters in the formulation. We also extend this new formulation to 3-D. Furthermore, we derive the auxiliary differential equation (ADE) form of CFS-UPML, which allows for extension to higher order time schemes and is easier to implement. Secondly, we rigorously derive the CFS-UPML formulation for time-domain adjoint elastic wave problems, which to our knowledge has never been done before. Thirdly, in the case of classical low-order FE methods, we show numerically that we achieve long-time stability for both forward and adjoint problems both for the convolution and the ADE formulations. In the case of higher order Legendre spectral-element methods, we show that weak numerical instabilities can appear in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and the main domain only, thus avoiding the need to solve a backward wave propagation problem inside the CFS-UPML, which is known to be highly ill-posed. Finally, by providing several examples we show numerically that our formulation is efficient at absorbing acoustic waves for normal to near-grazing incident body waves as well as surface waves. [ABSTRACT FROM AUTHOR]

In this article, we investigate the relationship between the range of optimal parameters of active contour models and the shape of the target object. We focus on the weights of the internal and external energy terms of the snakes functional. Our contributions are 3-fold. First, we propose a normalization step that brings the search space for optimal parameters into a bounded range. Secondly, we perform a systematic study of the behaviour of active contour models for all possible settings of their parameters and on a large set of synthetic geometric shapes. We introduce the concept of stability diagrams as a novel approach for assessing the stability of active contour models given a range of parameter values. Finally, we show that over a series of evolving shapes the region of the parameter domain that corresponds to suitable coefficients for segmentation, hereinafter referred to as feasible solution region, follows a predictable trend. Using shape diagrams as a metric for characterizing shapes quantitatively, we are able to correlate the shape of the objects to segment with the location and extent of the feasible solution region in the parameter domain. [ABSTRACT FROM AUTHOR]

This is the second in a series of three papers in which we present an end-to-end simulation from the MICE collaboration, the MICE Grand Challenge (MICE-GC) run. The N-body contains about 70 billion dark-matter particles in a (3 h-1 Gpc)³ comoving volume spanning five orders of magnitude in dynamical range. Here, we introduce the halo and galaxy catalogues built upon it, both in a wide (5000 deg²) and deep (z < 1.4) lightcone and in several comoving snapshots. Haloes were resolved down to few 1011 h-1M⊙. This allowed us to model galaxies down to absolute magnitude Mr < -18.9. We used a new hybrid halo occupation distribution and abundance matching technique for galaxy assignment. The catalogue includes the spectral energy distributions of all galaxies. We describe a variety of halo and galaxy clustering applications. We discuss how mass resolution effects can bias the large-scale two-pt clustering amplitude of poorly resolved haloes at the ≲5 per cent level, and their three-pt correlation function. We find a characteristic scale-dependent bias of ≲6 per cent across the BAO feature for haloes well above M* ~ 1012 h-1M⊙ and for luminous red galaxy like galaxies. For haloes well below M* the scale dependence at 100 h-1 Mpc is ≲2 per cent. Lastly, we discuss the validity of the large-scale Kaiser limit across redshift and departures from it towards non-linear scales. We make the current version of the lightcone halo and galaxy catalogue (MICECATv1.0) publicly available through a dedicated web portal to help develop and exploit the new generation of astronomical surveys. [ABSTRACT FROM AUTHOR]

High-fidelity Monte Carlo simulation of atmospheric turbulence phase screens is important for performance testing of astronomical adaptive optics systems.With a sparse spectrummodel and an optimal sampling method, it is possible to generate an atmospheric turbulence phase screen with high fidelity. However, the phase screen generation speed is limited by the algorithm structure of this technique. A non-uniform fast Fourier transform technique is proposed in this paper to accelerate phase screen generation speed. This method is able to generate huge atmospheric turbulence phase screens with high fidelity and an acceptable time-cost enabling practical adaptive optics simulations of forthcoming Extremely Large Telescopes. [ABSTRACT FROM AUTHOR]

Background: A seasonal transmission environment including seasonal variation of snail population density and human-snail contact patterns can affect the dynamics of Schistosoma infection and the success of control interventions. In projecting control outcomes, conventional modeling approaches have often ignored seasonality by using simplified intermediate-host modeling, or by restricting seasonal effects through use of yearly averaging.Methods: We used mathematical analysis and numerical simulation to estimate the impact of seasonality on disease dynamics and control outcomes, and to evaluate whether seasonal averaging or intermediate-host reduction can provide reliable predictions of control outcomes. We also examined whether seasonality could be used as leverage in creation of effective control strategies.Results: We found models that used seasonal averaging could grossly overestimate infection burden and underestimate control outcomes in highly seasonal environments. We showed that proper intraseasonal timing of control measures could make marked improvement on the long-term burden reduction for Schistosoma transmission control, and we identified the optimal timing for each intervention. Seasonal snail control, implemented alone, was less effective than mass drug administration, but could provide additive impact in reaching control and elimination targets.Conclusions: Seasonal variation makes Schistosoma transmission less sustainable and easier to control than predicted by earlier modeling studies. [ABSTRACT FROM AUTHOR]

The use of generalized Lasso is a common technique for recovery of structured high-dimensional signals. There are three common formulations of generalized Lasso ; each program has a governing parameter whose optimal value depends on properties of the data. At this optimal value, compressed sensing theory explains why Lasso programs recover structured high-dimensional signals with minimax order-optimal error. Unfortunately in practice, the optimal choice is generally unknown and must be estimated. Thus, we investigate stability of each of the three Lasso programs with respect to its governing parameter. Our goal is to aid the practitioner in answering the following question: given real data, which Lasso program should be used? We take a step towards answering this by analysing the case where the measurement matrix is identity (the so-called proximal denoising setup) and we use |$\ell _{1}$| regularization. For each Lasso program, we specify settings in which that program is provably unstable with respect to its governing parameter. We support our analysis with detailed numerical simulations. For example, there are settings where a 0.1% underestimate of a Lasso parameter can increase the error significantly and a 50% underestimate can cause the error to increase by a factor of |$10^{9}$|⁠. [ABSTRACT FROM AUTHOR]

A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which is enabled thanks to second-order operator splitting. The error analysis builds up on previous results for the elastic flow. To obtain an error estimate for the quantity on the curve a better control of the velocity is required. For this purpose, a penalty approach is employed and then combined with a generalized Gronwall lemma. Numerical simulations support the theoretical convergence results. Further numerical experiments indicate stability beyond the parameter regime with respect to the penalty term that is covered by the theory. [ABSTRACT FROM AUTHOR]

Summary: Motivated by a cutting edge problem related to the shape of α‐helices in proteins, we formulate a parametric statistical model, which incorporates the cylindrical nature of the helix. Our focus is to detect a “kink,” which is a drastic change in the axial direction of the helix. We propose a statistical model for the straight α‐helix and derive the maximum likelihood estimation procedure. The cylinder is an accepted geometric model for α‐helices, but our statistical formulation, for the first time, quantifies the uncertainty in atom positions around the cylinder. We propose a change point technique “Kink‐Detector” to detect a kink location along the helix. Unlike classical change point problems, the change in direction of a helix depends on a simultaneous shift of multiple data points rather than a single data point, and is less straightforward. Our biological building block is crowdsourced data on straight and kinked helices; which has set a gold standard. We use this data to identify salient features to construct Kink‐detector, test its performance and gain some insights. We find the performance of Kink‐detector comparable to its computational competitor called “Kink‐Finder.” We highlight that identification of kinks by visual assessment can have limitations and Kink‐detector may help in such cases. Further, an analysis of crowdsourced curved α‐helices finds that Kink‐detector is also effective in detecting moderate changes in axial directions. [ABSTRACT FROM AUTHOR]

We propose a framework for constructing goodness-of-fit tests in both low and high dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or lasso fit to the data, and using some proxy for prediction error as the final test statistic. We call this family residual prediction tests. We show that simulation can be used to obtain the critical values for such tests in the low dimensional setting and demonstrate using both theoretical results and extensive numerical studies that some form of the parametric bootstrap can do the same when the high dimensional linear model is under consideration. We show that residual prediction tests can be used to test for significance of groups or individual variables as special cases, and here they compare favourably with state of the art methods, but we also argue that they can be designed to test for as diverse model misspecifications as heteroscedasticity and non-linearity. [ABSTRACT FROM AUTHOR]

We present WHFAST, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFAST is significantly faster and conserves energy better than all other Wisdom-Holman integrators tested. We achieve this by significantly improving the Kepler solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error that is present in other implementations. For small enough timesteps, we achieve Brouwer's law, i.e. the energy error is dominated by an unbiased random walk due to floating-point round-off errors. We implement symplectic correctors up to order 11 that significantly reduce the energy error. We also implement a symplectic tangent map for the variational equations. This allows us to efficiently calculate two widely used chaos indicators the Lyapunov characteristic number and the Mean Exponential Growth factor of Nearby Orbits. WHFAST is freely available as a flexible C package, as a shared library, and as an easy-to-use PYTHON module. [ABSTRACT FROM AUTHOR]

We present analytical derivations and 2-D numerical simulations that quantify magnitudes of deviatoric stress and tectonic overpressure (i.e. difference between the pressure, or mean stress, and the lithostatic pressure) by relating them to lateral variations in the gravitational potential energy (GPE). These predictions of tectonic overpressure and deviatoric stress associated with GPE differences are independent of rock rheology (e.g. viscous or elastic) and rock strength. We consider a simple situation with lowlands and mountains (plateau). We use a numerical two-layer model consisting of a crust with higher Newtonian viscosity than that in the mantle, and also a three-layer model in which the two-layer lithosphere overlies a much less viscous asthenosphere. Our results (1) explain why estimates for the magnitude of stresses in Tibet, previously published by different authors, vary by a factor of two, (2) are applied to test the validity of the thin sheet approximation, (3) show that the magnitude of the depth-integrated tectonic overpressure is equal to the magnitude of the depth-integrated deviatoric stress if depth-integrated shear stresses on vertical and horizontal planes within the lithosphere are negligible (the thin sheet approximation) and (4) show that under thin sheet approximation tectonic overpressure is required to build and support continental plateaus, such as in Tibet or in the Andes, even if the topography and the crustal root are in isostatic equilibrium. Under thin sheet approximation, the magnitude of the depth-integrated tectonic overpressure is equal to the depth-integrated horizontal deviatoric stress, and both are approximately 3.5 × 1012 N m−1 for Tibet. The horizontal driving force per unit length related to lateral GPE variations around Tibet is composed of the sum of both tectonic overpressure and deviatoric stress, and is approximately 7 × 1012 N m−1. This magnitude exceeds previously published estimates for the force per unit length required to fold the Indo-Australian Plate south of India, and hence the uplift of the Tibetan plateau could have folded the Indian Plate. We also discuss the mechanical conditions that are necessary to achieve isostasy, for which the lithostatic pressure is constant at a certain depth. The results show that tectonic overpressure can exist at a certain depth even if all deviatoric stresses are zero at this depth, because this tectonic overpressure is related to horizontal gradients of vertical shear stresses integrated across the entire depth of the lithosphere. The magnitude of the depth-integrated tectonic overpressure of 3.5 × 1012 N m−1 implies that the pressure estimated from observed mineral assemblages in crustal rocks is likely significantly different from the lithostatic pressure, and pressure recorded by crustal rocks is not directly related to depth. In case of significant weakening of the entire lithosphere by any mechanism our analytical and numerical studies provide a simple estimation of tectonic overpressure via variations in GPE. [ABSTRACT FROM AUTHOR]

A sequence of large earthquakes happened along the Longitudinal Valley in eastern Taiwan in 1951. The first three (and largest) earthquakes took place near the harbour city of Hualien at the northern tip of the valley during the first day, the second of which (‘Event II’) severely damaged the city. The epicentre of Event II had previously been allocated at some 15 km offshore, which would result in a vertical subsidence of the Hualien city according to model calculations for the supposed seismic source mechanism. However, the Hualien tide gauge record speaks the opposite—the site experienced a co-seismic uplift by 255 mm due to Event II. We conduct a series of numerical grid-search simulations and determine a most likely scenario for the earthquake sequence. We assert that Event II's hypocentre was actually on land (rather than offshore), right along the recognized active Milun Fault below the city of Hualien at a very shallow depth. This result advances our understanding of the spatio-temporal seismotectonic behaviour associated with these historical events, and is important towards the assessment of the potential seismic and tsunami hazards of the region. [ABSTRACT FROM AUTHOR]

We consider two quasistatic problems that describe the contact between a viscoplastic body and an obstacle, the so-called foundation. The contact is frictionless and is modelled with normal compliance of such a type that the penetration is not restricted in the first problem, but is restricted with unilateral constraint, in the second one. For each problem we derive a variational formulation, then we prove its unique solvability. The proofs are based on a recent result on history-dependent quasivariational inequalities obtained in (Sofonea and Matei, Eur. J. Appl. Math. 22 (2011)). Next, we prove the convergence of the weak solution of the first problem to the weak solution of the second problem, as the stiffness coefficient of the foundation converges to infinity. Finally, we provide a numerical validation of this convergence result. To this end we introduce fully discrete schemes for the numerical approximation of the contact problems, implement them on a computer code and present numerical simulation results in the study of a two-dimensional example. [ABSTRACT FROM AUTHOR]

ABSTRACT We present collapse simulations of 100 M⊙ turbulent cloud cores threaded by a strong magnetic field. During the initial collapse phase, filaments are generated which fragment quickly and form several protostars. Around these protostars Keplerian discs with typical sizes of up to 100 au build up in contrast to previous simulations neglecting turbulence. We examine three mechanisms potentially responsible for lowering the magnetic braking efficiency and therefore allowing for the formation of Keplerian discs. Analysing the condensations in which the discs form, we show that the build-up of Keplerian discs is neither caused by magnetic flux loss due to turbulent reconnection nor by the misalignment of the magnetic field and the angular momentum. It is rather a consequence of the turbulent surroundings of the disc which exhibit no coherent rotation structure while strong local shear flows carry large amounts of angular momentum. We suggest that the 'magnetic braking catastrophe', i.e. the formation of sub-Keplerian discs only, is an artefact of the idealized non-turbulent initial conditions and that turbulence provides a natural mechanism to circumvent this problem. [ABSTRACT FROM AUTHOR]

ABSTRACT The outflow efficiency (η) from black hole (BH) accretion disc systems is known to depend upon both the BH spin ( a) and the amount of large-scale magnetic flux threading the BH and disc. Semi-analytical flux-trapping models suggest retrograde BHs should trap much more large-scale magnetic flux near the BH leading to much higher η than for prograde BHs. We self-consistently determine the amount of large-scale magnetic flux trapped by rapidly spinning ( a=−0.9 and 0.9) BHs using global 3D time-dependent non-radiative general relativistic magnetohydrodynamic simulations of thick ( h/ r≈ 0.3-0.6) discs. We find that BH-trapped flux builds up until it is strong enough to disrupt the inner accretion disc. Contrary to prior flux-trapping models, which do not include the back-reaction of magnetic flux on the disc, our simulations show prograde BHs trap more magnetic flux, leading to about three times higher η than retrograde BHs for | a|= 0.9. Both spin orientations can produce highly efficient jets, η∼ 100 per cent, with increasing η for increasing disc thickness. The similarity of η for prograde and retrograde BHs makes it challenging to infer the sign of a based on jet energetics alone. [ABSTRACT FROM AUTHOR]

An ionization front expanding into a neutral medium can be slowed down significantly by recombinations. In cosmological numerical simulations the recombination rate is often computed using a 'clumping factor' that takes into account that not all scales in the simulated density field are resolved. Here we demonstrate that using a single value of the clumping factor significantly overestimates the recombination rate, and how a local estimate of the clumping factor is both easy to compute, and gives significantly better numerical convergence. We argue that this lower value of the recombination rate is more relevant during the reionization process and hence that the importance of recombinations during reionization has been overestimated. [ABSTRACT FROM AUTHOR]

The equations of planar motion of a mass attached to two anchored massless springs form a symmetric Hamiltonian system. The system has a single dimensionless parameter L, corresponding to the spacing between the anchors. For L > 1, there is a stable equilibrium at which the springs are in tension and lie on a line, but for L < 1, this equilibrium has both springs in compression and is unstable. However, there are then two stable equilibria at which both springs carry no force. Oscillations are studied in both regimes, but more systematically in the tension case, where techniques of bifurcation theory, numerical approximation and numerical simulation are used to explore the rich variety of periodic solutions. [ABSTRACT FROM PUBLISHER]

We derive a second-order, semi-discrete central-upwind scheme for the incompressible 2D Euler equations in the vorticity formulation. The reconstructed velocity field preserves an exact discrete incompressibility relation. We state a local maximum principle for a fully discrete version of the scheme and prove it using a convexity argument. We then show how similar convexity arguments can be used to prove that the scheme maps certain Orlicz spaces into themselves. The consequences of this result on the convergence of the scheme are discussed. Numerical simulations support the expected properties of the scheme. [ABSTRACT FROM PUBLISHER]