Steep Front Research Articles

A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.

Fractional spectral vanishing viscosity method: Application to the quasi-geostrophic equation

We introduce the concept of fractional spectral vanishing viscosity (fSVV) to solve conservations laws that govern the evolution of steep fronts. We apply this method to the two-dimensional surface quasi-geostrophic (SQG) equation. The classical solutions of the inviscid SQG equation can develop finite-time singularities. By applying the fSVV method, we are able to simulate these solutions with high accuracy and long-time integration with relatively low resolution. Numerical diffusion in fSVV can be tuned by the fractional order as needed. Hence, fSVV can also be applied to integer-order conservation laws that exhibit steep solutions and evolving fronts.

Effect of piecewise linear current waveforms on surge arrester residual voltage

The object of research is the magnitude and shape of the residual voltage that arises between the terminals of the surge arrester models when they are subjected to current and voltage pulses of a piecewise linear waveform. One of the most problematic places in this problem is the approximation of current switching pulses with a short duration and also steep front current pulses. With the help of the well-known double-exponential pulse, it is impossible to describe a pulse whose time-to-half duration is twice bigger the time-to-crest duration . At the same time, current pulses in the manufacturer catalogs of the surge arresters have exactly this ratio (1/2, 30/60 or 45/90 ). With the help of piecewise linear approximation, it is possible, bypassing complex calculations, to describe pulses of almost any shape, including switching current pulses and steep front current pulses. By means of evaluation version of Micro-Cap 11 circuit simulator the residual voltage on the surge arrester terminals is computed during a passage of the current pulses with different amplitude and wave shape. Current sources used in this research represent sources of simplified triangular (piecewise linear) current pulses. It is considered that the current wave rises linearly to its maximum value, and then also decays linearly to half its amplitude value. Comparison of the results suggests that proposed simplification of discharge current waveform has no significant effect on relative calculation error of residual voltage on surge arrester. If it is necessary to estimate only maximum value of residual voltage on surge arrester, it is possible to use piecewise linear approximation of switching and lightning currents with any amplitude and shape without loss of accuracy.

Fracturing Effect of Electrohydraulic Shock Waves Generated by Plasma-Ignited Energetic Materials Explosion

Electrohydraulic shock waves (ESWs) are widely applied to many fields such as sterilization, lithotripsy, food processing, and so on. Based on high-pulsed power technology, electrical explosion is increasingly utilized to generate shock waves with steep fronts and short duration. In order to further magnify the shock waves, we have proposed a new technique by using energetic materials (EMs) loads. This paper investigated the fracturing effect of the ESWs generated by plasma-ignited EMs explosion. During the ESWs fracturing process, a large-scale triaxial stress pressurizing equipment and a dynamic strain measurement system were applied to the shale samples. The most evident experimental results showed that a large number of cell-shaped multiple cracks developed after the ESWs fracturing process. In addition, interior crack morphology and fluorescent tracing proved the evidence of penetration cracks. These cracks contributed to a great reduction of fracture pressure in fracturing test, which laid a scientific foundation for ESWs technique to be a promising method of well stimulation in those low permeability reservoir and further optimized into a new plugging relief and injection gain technology.

Gradient‐based nodal limiters for artificial diffusion operators in finite element schemes for transport equations

SummaryThis paper presents new linearity‐preserving nodal limiters for enforcing discrete maximum principles in continuous (linear or bilinear) finite element approximations to transport problems with steep fronts. In the process of algebraic flux correction, the oscillatory antidiffusive part of a high‐order base discretization is decomposed into a set of internodal fluxes and constrained to be local extremum dim inishing. The proposed nodal limiter functions are designed to be continuous and satisfy the principle of linearity preservation that implies the preservation of second‐order accuracy in smooth regions. The use of limited nodal gradients makes it possible to circumvent angle conditions and guarantee that the discrete maximum principle holds on arbitrary meshes. A numerical study is performed for linear convection and anisotropic diffusion problems on uniform and distorted meshes in two space dimensions. Copyright © 2017 John Wiley & Sons, Ltd.

Effects of horizontal pressure gradients on bed destabilization under waves

We report on new experiments designed to investigate bed destabilization processes in a two-dimensional wave flume physical model of a beach. The mobile bed consists of non-cohesive granular material of low density. The wave conditions are provided by repeating a cycle of waves made of two bichromatic groups of different period. The horizontal and vertical velocities are acoustically profiled vertically from free-stream elevation down to the still bed level in the surf zone. Additional measurements of the fluid pressure at positions closely aligned horizontally and vertically in and slightly above the sediment bed are undertaken. Mobile bed interfaces, still bed and top interface, are detected via acoustic and optical methods. Both methods are cross-compared and give similar results. Flow turbulence over the bed is analysed, the Reynolds turbulent shear stress is found negligible compared to the orbital flow induced momentum diffusion. The shear stress and the horizontal pressure gradient are computed at near-bed elevation and used in the bed incipient plug flow model of Sleath (Cont. Shelf Res., vol. 19 (13), 1999, pp. 1643–1664). Both the model and the measurements confirm that destabilization occurs when the non-dimensional pressure gradient (or Sleath number) exceeds the threshold value of 0.3 which is simultaneous with strong flow acceleration. The near-bottom fluid shear stress detected during these flow accelerations at steep wave fronts is found experimentally to be negative, which is retrieved with an unsteady plug flow model. This is suggesting that the fluid above the bed resists the sediment layer motion at these particular phases.

Identification of impurities in high-purity sulfur using gas chromatography-mass spectrometry method

For the first time the molecular impurity composition of high-purity sulfur was investigated using gas chromatography-mass spectrometry method. The sample preparation consisted of extracting the impurities from the sulfur samples during their vacuum distillation. The sample mass of sulfur, which was used for the extraction, was up to 1 kg. Impurities were condensed in glass ampoules which then carried them to the inlet in the dosing system of gas chromatography-mass spectrometer. For their separation, GS-GasPro capillary adsorption columns with a modified silica gel sorbent and with polytrimethylsilylpropyne were used. The joint application of these columns made it possible to determine a wide range of impurity substances in sulfur. Identification of impurities was carried out by comparing their experimental mass spectra with the data from the NIST database. In the case of overlapping chromatographic peaks of impurities their identification was carried out according to the characteristic ions and subtracting the peaks of ions that belong to the adjacent component. It was found that, when using the column with polytrimethylsilylpropyne, oxygen and nitrogen containing organic substances elute in asymmetric peaks with a steep front and a diffused rear. In high purity sulfur the impurities of permanent gases, carbon dioxide, hydrogen sulfide, sulfur dioxide, сarbonyl sulphide, saturated and unsaturated hydrocarbons C 2 -C 8 , aromatic hydrocarbons, oxygen-, nitrogen-, sulfur-containing hydrocarbons were identified. The total number of identified impurities equaled to 51. Keywords : high-purity sulfur, impurities, identification, gas chromatography-mass spectrometry, capillary column DOI: http://dx.doi.org/10.15826/analitika.2017.21.3.005 А .Iu. Sozin, M.F. Churbanov, О .Iu. Chernova, T.G. Sorochkina, I.V. Skripachev, G.E. Snopatin G.G. Devyatykh Institute of Chemistry of High-Purity Substances of the Russian Academy of Science, Tropinina Str., 49, Nizhny Novgood, 603950, Russian Federation

A Self-Adaptive Numerical Method to Solve Convection-Dominated Diffusion Problems

Convection-dominated diffusion problems usually develop multiscaled solutions and adaptive mesh is popular to approach high resolution numerical solutions. Most adaptive mesh methods involve complex adaptive operations that not only increase algorithmic complexity but also may introduce numerical dissipation. Hence, it is motivated in this paper to develop an adaptive mesh method which is free from complex adaptive operations. The method is developed based on a range-discrete mesh, which is uniformly distributed in the value domain and has a desirable property of self-adaptivity in the spatial domain. To solve the time-dependent problem, movement of mesh points is tracked according to the governing equation, while their values are fixed. Adaptivity of the mesh points is automatically achieved during the course of solving the discretized equation. Moreover, a singular point resulting from a nonlinear diffusive term can be maintained by treating it as a special boundary condition. Serval numerical tests are performed. Residual errors are found to be independent of the magnitude of diffusive term. The proposed method can serve as a fast and accuracy tool for assessment of propagation of steep fronts in various flow problems.

Kame deltas provide evidence for a new glacial lake and suggest early glacial retreat from central Lower Michigan, USA

In association with an undergraduate Honors Seminar at Michigan State University, we studied two small kame deltas in north-central Lower Michigan. These recently identified deltas provide clear evidence for a previously unknown proglacial lake (Glacial Lake Roscommon) in this large basin located in an interlobate upland. Our first goal was to document and characterize the geomorphology of these deltas. Because both deltas are tied to ice-contact ridges that mark the former position of the retreating ice margin within the lake, our second goal was to establish the age of one of the deltas, thereby constraining the timing of ice retreat in this part of Michigan, for which little information currently exists. Both deltas are composed of well-sorted fine and medium sands with little gravel, and have broad, nearly flat surfaces and comparatively steep fronts. Samples taken from the upper 1.5m of the deltas show little spatial variation in texture, aside from a general fining toward their outer margins. Gullies on the outer margins of both deltas probably postdate the formation of the deltas proper; we suggest that they formed by runoff during a permafrost period, subsequent to lake drawdown. We named the ice lobe that once covered this area the Mackinac Lobe, because it had likely advanced into the region across the Mackinac Straits area. Five of six optically stimulated luminescence (OSL) ages from one of the deltas had minimal scatter and were within ±1000years of one another, with a mean age of 23.1±0.4ka. These ages suggest that the Mackinac Lobe had started to retreat from the region considerably earlier than previously thought, even while ice was near its maximum extent in Illinois and Indiana, and the remainder of Michigan was ice-covered. This early retreat, which appears to coincide with a short-lived warm period indicated from the Greenland ice core, formed an “opening” that was at least occasionally flooded. Thick and deep, fine-textured deposits, which underlie much of the region, probably date to this time. Our work provides the first evidence of this extremely early ice retreat from central Lower Michigan, occurring almost 4000years before the southern margin of the ice (Saginaw Lobe) had started its retreat from the state.

Modeling and Mitigation for High Frequency Switching Transients Due to Energization in Offshore Wind Farms

This paper presents a comprehensive investigation on high frequency (HF) switching transients due to energization of vacuum circuit breakers (VCBs) in offshore wind farms (OWFs). This research not only concerns the modeling of main components in collector grids of an OWF for transient analysis (including VCBs, wind turbine transformers (WTTs), submarine cables), but also compares the effectiveness between several mainstream switching overvoltage (SOV) protection methods and a new mitigation method called smart choke. In order to accurately reproduce such HF switching transients considering the current chopping, dielectric strength (DS) recovery capability and HF quenching capability of VCBs, three models are developed, i.e., a user–defined VCB model, a HF transformer terminal model and a three-core (TC) frequency dependent model of submarine cables, which are validated through simulations and compared with measurements. Based on the above models and a real OWF configuration, a simulation model is built and several typical switching transient cases are investigated to analyze the switching transient process and phenomena. Subsequently, according to the characteristics of overvoltages, appropriate parameters of SOV mitigation methods are determined to improve their effectiveness. Simulation results indicate that the user–defined VCB model can satisfactorily simulate prestrikes and the proposed component models display HF characteristics, which are consistent with onsite measurement behaviors. Moreover, the employed protection methods can suppress induced SOVs, which have a steep front, a high oscillation frequency and a high amplitude, among which the smart choke presents a preferable HF damping effect.

Subaqueous landslides at the distal basin of Lago Nahuel Huapi (Argentina): Towards a tsunami hazard evaluation in Northern Patagonian lakes

The May 22nd, 1960 Valdivia earthquake, Chile (Mw 9.5) triggered a series of subaqueous mass-wasting processes (debris flows and slides) in Lago Nahuel Huapi (Argentina), generating a tsunami-like wave that hit the coasts of San Carlos de Bariloche. Aiming to provide a first preliminary insight into tsunami hazards for the lakeshore communities, in this paper we identify and characterize the subaqueous landslides at the populated distal basin of the lake. Swath bathymetric and seismic profiling surveys were carried out and high-resolution digital elevation models were derived from these data to perform a landslide inventory map. A series of morphometrical parameters (including the landslide area, the volume of displaced materials and the run-out distance, among others) were estimated upon selected events. The results indicated that landslide activity at the distal basin of Lago Nahuel Huapi has been concentrated in the vicinity of Bariloche (massive landslide triggered by the 1960 earthquake) and within steep delta fronts where the slope failures typically initiate at shallow waters (9–11m depth). The sliding mass frequently travels basinward along a great distance (≥1000m). At the delta fronts, the volume of material removed by landslides can reach ~40×104m3, leaving scar areas of up to 13m thick. The periodic occurrence of rotational–translational mass movements initiating at the upper edge of the delta fronts, with vertical displacements of the mobilized materials reaching ~200m, probably represents a potential tsunami hazard for the nearby populated coasts.

Influence of prestress on shock behavior of polycrystalline iron via atomistic simulations

Plasticity behavior and phase transition of metal Fe subjected to shock loading have attracted considerable attention in shock physics community, in particular for underlying relationship between them. Experimental examinations and atomistic simulations on shocked Fe have displayed a three-wave structure: elastic wave, plastic wave and transformation wave. However, these studies are primarily limited to the one-dimensional planar case. Recently, owing to the rapid development of experimental techniques, investigating dynamic property of shocked metal has extended to the multi-dimensional loading conditions, such as cylindrical or spherical shocks. In this regard, fruitful findings are achieved, for example, twinning ratio in polycrystalline Fe under implosive compression is found to be much higher than that under planar shock, implying that the the complex stress state plays a critical role. In this paper, we explore the effects of prestress on plasticity and phase transition of shocked polycrystalline iron. The imposed presstress normal to the impact direction in one-dimensional planar shocking represents the varying deviatoric stress, and does not nearly affect the principal stress. The utilized empirical potential for iron could describe the plasticity dislocation and phase transition very well. The simulations show that as the prestress increases, the shock speed at elastic stage and Hugoniot elastic limit increase, which is in accordance with the theoretical analyses based on shock wave theory and experimental measurement. Meanwhile the plastic wave speed increases more quickly and catches up with the transformation wave more easily, resulting in a steep shockwave front. Atomistic snapshots show that plasticity dislocation stemming from the grain boundary precedes phase transition, where most of BCC atoms are transformed into the HCP atoms and shear stress significantly decreases. Further observations from these images find that plastic zone becomes narrower with increasing prestress, representing a shorter plastic relaxation time, which accelerates the completion of phase transition. This rapid phase transition process is also indicated by quantitatively evaluating the ratio of transitioned closed packed atoms as a function of evolution time. The origin based on the atomistical prediction model of Fe phase transition is attributed to the fact that higher prestress gives rise to the larger von-Mises stress for easier dislocation emission while lower one cannot. But the final transformed atoms are independent of prestress. Additionally, the measured free surface velocity profiles from planar and cylindrical impact loading validate the simulations conducted here. These findings will help to understand experimentally the microscopically dynamic evolution of Fe, imposed by complex stress state.

Wave Characteristics of Falling Film on Inclination Plate at Moderate Reynolds Number

Falling water film on an inclined plane is studied by shadowgraphy. The ranges of inclination angle and the film Reynolds number are, respectively, up to 21° and 60. Water is used as working fluid. The scenario of wave regime evolution is identified as three distinctive regimes, namely, initial quiescent smooth film flow, two-dimensional regular solitary wave pattern riding on film flow, and three-dimensional irregular wave pattern. Three characteristic parameters of two-dimensional solitary wave pattern, namely, inception length, primary pulse spacing, and propagation velocity, are examined, which are significant in engineering applications for estimation of heat and mass transfer on film flow. The present experimental data are well in agreement with the Koizumi correlations, the deviation from which is limited to 20% and 15%, respectively, for primary pulse spacing and propagation velocity. Through the scrutiny of the present experimental observation, it is concluded that wave evolution on film flow at the moderate Reynolds number is controlled by gravity and drag and the Rayleigh-Taylor instability that occurred on the steep front of primary pulse triggers the disintegration of continuous two-dimensional regular solitary wave pattern into three-dimensional irregular wave pattern.

Wave fronts and packets in 1D models of different meta-materials: Graphene, left-handed media and transmission line

A comparative study is made of the propagation of wave packets and fronts in three different meta-media, i.e. graphene, left-handed media (LHM) and transmission lines, using one-dimensional models. It is shown that a potential step in graphene influences only the frequency of the electronic wave, i.e., the particular spectrum branch (electron or hole) to which the wave belongs to, while the envelop function (the wave front or packet form) remains unchanged. Although the model for a vacuum and LHM interface is similar to that of the potential step in graphene, the solutions are quite different due to differences in the chirality of the waves. Comparing the propagation of wave fronts and packets in a standard transmission line and its meta-analog we demonstrate that the propagating packets in the meta-line are much more deformed as compared to the standard one, including broadening, asymmetry and even the appearance of fast moving precursors. This influence is seen not only in the case of packets with steep fronts but in soft Gaussian packets as well.

Self-organized shocks in the sedimentation of a granular gas.

A granular gas in gravity heated from below develops a certain stationary density profile. When the heating is switched off, the granular gas collapses. We investigate the process of sedimentation using computational hydrodynamics, based on the Jenkins-Richman theory, and find that the process is significantly more complex than generally acknowledged. In particular, during its evolution, the system passes several stages which reveal distinct spatial regions of inertial (supersonic) and diffusive (subsonic) dynamics. During the supersonic stages, characterized by Mach>1, the system develops supersonic shocks which are followed by a steep front of the hydrodynamic fields of temperature and density, traveling upward.

Numerical solution of steady-state groundwater flow and solute transport problems: Discontinuous Galerkin based methods compared to the Streamline Diffusion approach

In this study, we consider the simulation of subsurface flow and solute transport processes in the stationary limit. In the convection-dominant case, the numerical solution of the transport problem may exhibit non-physical diffusion and under- and overshoots. For an interior penalty discontinuous Galerkin (DG) discretization, we present a $h$-adaptive refinement strategy and, alternatively, a new efficient approach for reducing numerical under- and overshoots using a diffusive $L^2$-projection. Furthermore, we illustrate an efficient way of solving the linear system arising from the DG discretization. In $2$-D and $3$-D examples, we compare the DG-based methods to the streamline diffusion approach with respect to computing time and their ability to resolve steep fronts.

Towards a large-scale scalable adaptive heart model using shallow tree meshes

Electrophysiological heart models are sophisticated computational tools that place high demands on the computing hardware due to the high spatial resolution required to capture the steep depolarization front. To address this challenge, we present a novel adaptive scheme for resolving the deporalization front accurately using adaptivity in space. Our adaptive scheme is based on locally structured meshes. These tensor meshes in space are organized in a parallel forest of trees, which allows us to resolve complicated geometries and to realize high variations in the local mesh sizes with a minimal memory footprint in the adaptive scheme. We discuss both a non-conforming mortar element approximation and a conforming finite element space and present an efficient technique for the assembly of the respective stiffness matrices using matrix representations of the inclusion operators into the product space on the so-called shallow tree meshes.We analyzed the parallel performance and scalability for a two-dimensional ventricle slice as well as for a full large-scale heart model. Our results demonstrate that the method has good performance and high accuracy.

Current state and changes of glaciers in the Tavan Bogd Mountains (Mongolia)

This study is the first stage of detailed investigation of large glaciers located in the Tavan-Bogd Mountains. The main task of this work is to estimate a current state and dynamics of glaciers and to update glacier and rock-glacier inventory. Basing on results of 2013 field survey together with remote sensing data the main glaciers located on eastern slopes of the Tavan Bogd mountain massif in the Tsagan-Us and Tsagan-Gol river basins are described (these glaciers are Potanin, Alexandra, Grane, Kozlov, and Krylov ones). In order to monitor regime of glacier systems the geodetic survey of glaciers and rock-glacier edges was carried out using Trimble GNSS system and the ranging mark system. The Landsat satellite images made taken in August-September of 1989, 2006, and 2013, their spatial resolution 15-30 m, were used to map areas of debris-free glaciers and to estimate the glacier changes between 1989 and 2013. Pictures were taken from the USGS site, the ArcGIS software was used for this work. In addition, the high-resolution satellite pictures with resolution of 0.5–2.5 m made at the end of the ablation season if 2008 (CARTOSAT-1) and 2010 (Geoeye-1 and SPOT-5) were also used to analyze current conditions and changes of the above glaciers and to improve visual estimation of the Landsat imagery. In 2013, the study included 26 glaciers with the debris-free glacier area of 67 km 2 in the Tsagan-Gol river basin and 37 glaciers with area of 30 km 2 in the Tsagan-Us river basin. According to our estimates, areas of these glaciers did not significantly changed since 1989 however a certain regression of the glacier tongues had been fixed. The Kozlov glacier retreated with average rate of 21 m/year between 2001 and 2013. Retreat of the Potanin glacier was slower and between 1989 and 2001 the average rate was equal to 5 m/year, but between 2001 and 2013 it became more active and its average rate reached 24 m/year. One of the largest One of the largest rock-glacier of the Tavan Bogd Mountains was found in the Tsagan-Us valley on its south-eastern slope, its area was estimated 1.2 km 2 , length – 3 km, steep front height – 20–25 m. Indirect indicators of its activity such as transverse and longitudinal furrows were noticed. Using data of local weather station data we calculated some climatic characteristics needed to monitor equilibrium line for end of the 2013 ablation season. Mean summer temperature on the weighted mean equilibrium line of five glaciers (3250 m a.s.l.) was defined as 1.0 °С. Ablation–accumulation value was estimated 110 g/cm 2 and the mean annual snowfall on the equilibrium line as 785 mm.

Modeling dam-break flows in channels with 90 degree bend using an alternating-direction implicit based curvilinear hydrodynamic solver

This paper presents a combined numerical and experimental investigation of dam break induced free-surface flows in channels with 90 degree bend. These types of flows are best described by the two-dimensional shallow water equations (SWE) representing the conservations of mass and horizontal momentums. In this study, the governing equations are solved numerically by means of an alternating-direction implicit (ADI) finite-difference scheme in a curvilinear coordinate and contravariant velocity system. This model is tested by simulating for various flow conditions including dam-break flows onto dry beds in a converging–diverging channel and a channel with 45 degree bend. Good fits of the present model predictions with published laboratory measurements are achieved. To further the validation of the model, a series of physical model tests for dam-break flows in a channel with 90 degree bend were conducted. The predicted time-varying water depths downstream of the dam face are shown to have a fairly good agreement with recorded data from model tests. The present ADI solver is found to be capable of capturing the formation and movement of steep wave fronts.

Formation mechanism of steep wave front in magnetized plasmas

Bifurcation from a streamer to a solitary drift wave is obtained in three dimensional simulation of resistive drift waves in cylindrical plasmas. The solitary drift wave is observed in the regime where the collisional transport is important as well as fluctuation induced transport. The solitary drift wave forms a steep wave front in the azimuthal direction. The phase of higher harmonic modes are locked to that of the fundamental mode, so that the steep wave front is sustained for a long time compared to the typical time scale of the drift wave oscillation. The phase entrainment between the fundamental and second harmonic modes is studied, and the azimuthal structure of the stationary solution is found to be characterized by a parameter which is determined by the deviation of the fluctuations from the Boltzmann relation. There are two solutions of the azimuthal structures, which have steep wave front facing forward and backward in the wave propagation direction, respectively. The selection criterion of these solutions is derived theoretically from the stability of the phase entrainment. The simulation result and experimental observations are found to be consistent with the theoretical prediction.