Eulerian System Research Articles

High resolution modeling of Quercus pollen with an Eulerian modeling system: A case study in Greece

In this study a high resolution modeling system is developed to simulate Quercus pollen concentrations in the greater area of Thessaloniki, Greece, under an a priori oak phenological season. The modeling system consists of three models in series, the Weather Research and Forecasting (WRF) meteorological model, the natural emissions model NEMO for Quercus pollen emissions and the chemistry-transport model CAMx. The modeling system is evaluated with daily meteorological and pollen measurements during the phenological season of 2016 of Quercus taxa. The modeling system's performance is satisfactory on both meteorology and Quercus pollen concentrations, although for the latter the relative uncertainty is slightly above the 50% criterion usually applied in air quality modeling. Additional analysis was performed on three parameters related to pollen emissions, namely the assigned pollen production, the spread of the phenology and the assigned diameter. The analysis shows that the greatest impact on Quercus pollen concentrations, on both near the sources as well at remote areas, is the assigned pollen production, followed by the spread and the assigned diameter.

Investor Impatience and Financial Markets: the Case of the Short Squeeze of Meme Stocks

In this paper, we provide a system of equations to measure investor impatience in financial markets. As in physics, we propose that there exists a measurable force created by external market factors, including investor impatience, which we equate with gravitational force. Using a physics-based Eulerian fluid flow system of equations, we model this force and associated energy conservation equation. We test this hypothesis using minute-by-minute data from meme stocks during a unique market event, the GameStop short squeeze of January 2021. Aside from the effect created by intrinsic market forces, the resulting parameters provide evidence of external force acting on stock prices. We further extend our research to the 2010 flash crash, showing that the system captures external influence on market behavior.

QuanTaichi

High-resolution simulations can deliver great visual quality, but they are often limited by available memory, especially on GPUs. We present a compiler for physical simulation that can achieve both high performance and significantly reduced memory costs, by enabling flexible and aggressive quantization. Low-precision ("quantized") numerical data types are used and packed to represent simulation states, leading to reduced memory space and bandwidth consumption. Quantized simulation allows higher resolution simulation with less memory, which is especially attractive on GPUs. Implementing a quantized simulator that has high performance and packs the data tightly for aggressive storage reduction would be extremely labor-intensive and error-prone using a traditional programming language. To make the creation of quantized simulation practical, we have developed a new set of language abstractions and a compilation system. A suite of tailored domain-specific optimizations ensure quantized simulators often run as fast as the full-precision simulators, despite the overhead of encoding-decoding the packed quantized data types. Our programming language and compiler, based on Taichi , allow developers to effortlessly switch between different full-precision and quantized simulators, to explore the full design space of quantization schemes, and ultimately to achieve a good balance between space and precision. The creation of quantized simulation with our system has large benefits in terms of memory consumption and performance, on a variety of hardware, from mobile devices to workstations with high-end GPUs. We can simulate with levels of resolution that were previously only achievable on systems with much more memory, such as multiple GPUs. For example, on a single GPU, we can simulate a Game of Life with 20 billion cells (8× compression per pixel), an Eulerian fluid system with 421 million active voxels (1.6× compression per voxel), and a hybrid Eulerian-Lagrangian elastic object simulation with 235 million particles (1.7× compression per particle). At the same time, quantized simulations create physically plausible results. Our quantization techniques are complementary to existing acceleration approaches of physical simulation: they can be used in combination with these existing approaches, such as sparse data structures, for even higher scalability and performance.

Partially reflected waves in water of finite depth

This paper presents a second-order asymptotic solution in the Lagrangian description for nonlinear partial standing wave in the finite water depth. The asymptotic solution that is uniformly valid satisfies the irrotationality condition and zero pressure at the free surface. In the Lagrangian approximation, the explicit nonlinear parametric equations for the particle trajectories are obtained. In particular, the Lagrangian mean level of a particle motion for the partial standing wave is found as a part of the solution which is different from that in an Eulerian system. This solution enables the description of wave profile and particle trajectory, which can be progressive, standing or partial standing waves. The dynamic properties of nonlinear partial standing waves, including mass transport velocity, radiation stress, wave setup and pressure due to reflection are also investigated.

A comparative study of atomistic-based stress evaluation

<p style='text-indent:20px;'>This paper presents a comparative study on several issues of the microscopic stress definitions. Firstly, we derived an Irving-Kirkwood formulation for Cauchy stress evaluation in Eulerian coordinates. We showed that quantities, such as density and momentum, should to be defined properly on microscopic level in order to guarantee the conservation relations on macroscopic level. Secondly, the relation between Cauchy and first Piola-Kirchhoff stress was investigated both theoretically and numerically. At zero temperature, classical pointwise relation between these two stress is satisfied both in Virial and Hardy formulation. While at finite temperature, temporal averaging is required to guarantee this relation for Virial formulation. For Hardy formulation, an additional term need to be included in the classical relation between the Cauchy stress and the first Piola-Kirchhoff stress. Meanwhle, the linear relation between the Cauchy stress and the first Piola-Kirchhoff stress with respect to the temperature are obtained in both Virial and Hardy formulations. The thermal expansion coefficients are also studied by using quasi-harmonic approximation. Thirdly, different from that in the Lagrangian coordinates case, where the time averaging procedure can be performed in a post-processing manner when the kernel function is separable, the stress evaluation in Eulerian system must be evaluated spatially and temporally at the same time, even in separable kernel case. This can be seen from the comparison of the two procedures. Numerical examples were provided to illustrate our investigations.

On the Lagrangian version of the Korteweg capillarity system: integrability aspects

A Lagrangian version of the classical 1+1-dimensional Korteweg capillarity system is shown to encapsulate as a particular reduction an integrable Boussinesq equation. The associated integrability of the corresponding Eulerian capillarity system is set down. In turn, hidden integrability cases of the generalised Boussinesq equation are recorded associated with reduction of the Eulerian system to the integrable cubic and resonant nonlinear Schrodinger equations together with extensions obtained by application of invariance under a reciprocal transformation.

Effects of newly developed entrainment model for a thermal hydraulic system code (SPACE) based on breakup of large droplets in reflood

The accurate prediction of the fuel rod temperature from a peak cladding temperature to quenching is required for a thermal–hydraulic system code in the reflood phase within a pressurized water reactor. Although conventional codes have well predicted the wall temperature trends, inaccuracies with the hydraulic parameter such as the steam flow rate still remains. To predict reasonable results that reflect an actual phenomenon, we implemented the breakup of a large droplet generated in an inverted slug flow. We suggested a new method to estimate the entrainment for an Eulerian system code (SPACE). The new method was successfully verified and compared to the analytic results. After the modification, we obtained improvements on the steam flow rate, the wall temperature, PCT times, and quenching times for FLECHT-SEASET. For RBHT, it showed mixed results with a faster decrease of the wall temperature, which implies the possibility of a transition for the reflood phenomena.

Efficient numerical methods for multiscale crowd dynamics with emotional contagion

In this paper, we develop two efficient numerical methods for a multiscale kinetic equation in the context of crowd dynamics with emotional contagion [A. Bertozzi, J. Rosado, M. Short and L. Wang, Contagion shocks in one dimension, J. Stat. Phys. 158 (2014) 647–664]. In the continuum limit, the mesoscopic kinetic equation produces a natural Eulerian limit with nonlocal interactions. However, such limit ceases to be valid when the underlying microscopic particle characteristics cross, corresponding to the blow up of the solution in the Eulerian system. One method is to couple these two situations — using Eulerian dynamics for regions without characteristic crossing and kinetic evolution for regions with characteristic crossing. For such a hybrid setting, we provide a regime indicator based on the macroscopic density and fear level, and propose an interface condition via continuity to connect these two regimes. The other method is based on a level set formulation for the continuum system. The level set equation shares similar forms as the kinetic equation, and it successfully captures the multi-valued solution in velocity, which implies that the multi-valued solution other than the viscosity solution should be the physically relevant ones for the continuum system. Numerical examples are presented to show the efficiency of these new methods.

Contactless Cardiac Activity Detection Based on Head Motion Magnification

The aim of this study is to remotely measure cardiac activity (heart pulse, total cycle length and pulse width) from videos based on a head motion at different positions of the head (front, back and side). As the head motion resulting from the cardiac cycle of blood from the heart to the head via the carotid arteries is not visible to the naked eye and to preserve the signal strength in the video, we used wavelet decomposition and a Chebychev filter to develop a standard Eulerian video magnification in terms of noise removal and execution time. We used both magnification systems to measure cardiac activity and statistically compare the results using Bland–Altman method. Also, we proposed a new video quality system based on fuzzy interface system to select which magnification system has better magnification quality and gives better results for the heart pulse rate. The experimental results on several videos captured from 10 healthy subjects show that the proposed contactless system of heart pulse has an accuracy of 98.3% when magnified video based on the developing magnification system was used and an accuracy of 97.4% when magnified video based on Eulerian magnification system was used instead. The proposed system has low computational complexity, making it suitable for advancing health care applications, mobile health applications and telemedicine.

Aramis un modelo regional para la gestión de la calidad del aire. Evaluación y validación

The aim of this research was to better understand the dynamics of air pollutants and to forecast the air quality over regional areas in order to develop emission abatement strategies for air pollution and adverse health effects. To accomplish this objective, we developed and applied a high resolution Eulerian system named ARAMIS (A Regional Air Quality Modelling Integrated System) over the north-east of Spain (Catalonia), where several pollutants exceed threshold values for the protection of human health. The results indicate that the model reproduced reasonably well observed concentrations, as statistical values fell within Environmental Protection Agency (EPA) recommendations and European (EU) regulations. Nevertheless, some hourly O3 exceedances in summer and hourly peaks of NO2 in winter were underestimated. Concerning PM10 concentrations less accurate model levels were obtained with a moderate trend towards underestimation during the day.

NONLINEAR BREAKER CHARACTERISTICS AND IMPULSE ON A SLOPING BOTTOM

This paper presents an experimental and theoretical investigation of nonlinear surface-wave propagation over a sloping bed. First, a second-order analytical solution for nonlinear surface-wave propagation over a sloping bed is derived using a perturbation method for the bottom slope α and the wave steepness e in an Eulerian system. Then, by transforming the flow field solution from an Eulerian system into a Lagrangian system, more accurate wave profiles are determined. New theoretical breaker characteristics and breaker impulses are derived using the kinematic stability parameter. Subsequently, a series of experiments to measure breaker characteristics and the breaker impulse are conducted in a wave tank. The theoretical solutions are compared with both the present experimental data and previously published experimental results. The results reveal that the analytical solution can reasonably describe the wave breaking phenomenon. In this paper, a new theoretical solution for the breaker characteristics and impulses is provided, which is proven to be a useful approach for follow-up studies to predict breaker characteristics and impulses.

Toward better surface tracking for fluid simulation.

Representing moving surfaces as polygonal meshes offers a unique set of advantages as well as challenges. In his dissertation, the author attempted to address several of the difficulties traditionally associated with explicit surface tracking. In later research, he and his colleagues sought to address one of the main challenges in incorporating an explicit surface tracker into an existing Eulerian fluid simulation system: the potential for resolution mismatch between the surface and the simulation. This article discusses issues of numerical robustness in geometric queries when dealing with moving explicit surfaces and summarizes the work by other researchers that has been undertaken concurrently and subsequently to the author's dissertation work.

A Projection Preconditioner for Solving the Implicit Immersed Boundary Equations

This paper presents a method for solving the linear semi-implicit immersed boundary equations which avoids the severe time step restriction presented by explicit-time methods. The Lagrangian variables are eliminated via a Schur complement to form a purely Eulerian saddle point system, which is preconditioned by a projection operator and then solved by a Krylov subspace method. From the viewpoint of projection methods, we derive an ideal preconditioner for the saddle point problem and compare the efficiency of a number of simpler preconditioners that approximate this perfect one. For low Reynolds number and high stiffness, one particular projection preconditioner yields an efficiency improvement of the explicit IB method by a factor around thirty. Substantial speed-ups over explicit-time method are achieved for Reynolds number below 100. This speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.

A Projection Preconditioner for Solving the Implicit Immersed Boundary Equations

This paper presents a method for solving the linear semi-implicit immersed boundary equations which avoids the severe time step restriction presented by explicit-time methods. The Lagrangian variables are eliminated via a Schur complement to form a purely Eulerian saddle point system, which is preconditioned by a projection operator and then solved by a Krylov subspace method. From the viewpoint of projection methods, we derive an ideal preconditioner for the saddle point problem and compare the efficiency of a number of simpler preconditioners that approximate this perfect one. For low Reynolds number and high stiffness, one particular projection preconditioner yields an efficiency improvement of the explicit IB method by a factor around thirty. Substantial speed-ups over explicit-time method are achieved for Reynolds number below 100. This speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.

TU‐G‐BRA‐03: Reconstructing Motion Manifold from Real‐Time MRI: A Level Set Approach

Purpose: To reconstruct the motion manifold defined on anatomical interfaces from real‐time MR imaging. Methods∷We have developed a novel method to construct the evolving motion manifold in real‐time by preserving the point correspondence when a level set function is updated to track moving anatomical interfaces. The key to our development is to define a correspondence function in a Eulerian system and advecting it along the level set function under the same velocity. The motion manifold is ‘grown’ by concatenating the point correspondence maps. The proposed method was tested with renal MR image sequences under both synthetic and physiological motion. The synthetic sequence was generated by shifting a static MR image continuously in one dimension to a maximum of 29mm. Performance of the estimation was analyzed by comparing the reconstructed motion manifold and the known truth. Physiological motion manifold was reconstructed from real‐time EPI data acquired from human subjects under heavy breathing condition. Results: In the synthetic motion test, the reconstructed motion manifold translates each particle to closely follow the underlying motion. The mean error along and perpendicular to the motion direction is −2.58mm and 0.03mm respectively. These are reasonable results considering the low signal‐to‐noise ratio of the real‐time MR images with pixel size equals 1.52mm. The motion manifold reconstructed from physiological real‐time renal MR exhibits a semiperiodic pattern that agrees with respiratory behavior. Spatially varying motion pattern from different parts of the kidney interface can be observed. Conclusions: We have proposed a novel level set method to track and estimate anatomical moving interface while preserving the point correspondence during the dynamic evolution. The generated motion manifold provides important knowledge about the characteristics of a particular organ movement and facilitates further model development for retrospective analyzing dose impact of motion or predicting motion for real‐time delivery adaptation. NIH grant 1R01CA159471. PI: Michael Gach.

A dynamic, embedded Lagrangian model for ocean climate models. Part I: Theory and implementation

A framework for embedding a Lagrangian model within ocean climate models that employ horizontal Eulerian grids is presented. The embedded Lagrangian model can be used to explicitly represent processes that are at the subgrid scale to the Eulerian model. The framework is applied to open ocean deep convection and gravity driven downslope flows, both of which are subgridscale in the present generation of level coordinate ocean climate models. In order to apply the embedded Lagrangian framework to these processes, it is necessary to partition the mass and momentum of the model into an Eulerian system and a Lagrangian system. This partitioning allows the Lagrangian model to transport seawater using a more appropriate set of dynamics.A number of schemes suitable for implementation in the embedded Lagrangian model are derived. Two dynamically passive schemes are derived that emulate existing parameterisations and two dynamically active schemes are also derived that evolve Lagrangian parcels of water (termed “blobs”) according to a set of physical equations. Some details of the implementation into the Geophysical Fluid Dynamics Modular Ocean Model are also given. Finally, results are presented that show that the dynamically passive schemes are able to emulate their Eulerian counterparts to within roundoff error in idealised test cases.

The asymmetric fragmentation operator applied to meteo-limnological time series in a tropical reservoir

Ecological data are sometimes difficult to analyze due to the intrinsic complexity of natural systems containing nonlinear equations. Efficient methods are required to better understand the information extracted from complex processes and to support the development of ecological prediction models. In this context, two techniques were used in this work to analyze meteo-limnological time series from a tropical reservoir: the Wavelet Transform (WT) and the Asymmetric Fragmentation Operator (AFO). The in situ data is based on a dataset acquired from an Eulerian system deployed in Manso Reservoir, Brazil, in 2007. The results indicated that the AFO method outperformed the WT method in the analysis of ecological parameters. The pioneering use of AFO in this sort of study proved to be a useful tool to study the variability of water quality parameters.

Green’s functions for a loaded rolling tyre

A new formulation to determine the unit impulse response (Green’s) functions of a loaded rotating tyre in the vehicle-fixed (Eulerian) reference frame for tyre/road noise predictions is presented. The proposed formulation makes use of the set of eigenfrequencies and eigenmodes for the statically loaded tyre obtained from a finite element (FE) model of the tyre. A closed-form expression for the Green’s functions of a rotating tyre in the Eulerian reference system as a function of the eigenfrequencies and eigenmodes of the statically loaded tyre is found. Non-linear effects during loading are accounted for in the FE model, while the frequency shift due to the rotational velocity is included in the calculation of the Green’s functions. In the literature on tyre/road noise these functions are generally used to determine the tyre response during tyre/road contact calculations. The presented formulation opens the possibility to solve the contact problem directly in the Eulerian reference frame and to include local tyre softening due to non-linear effects while keeping the computational advantage of describing the tyre dynamics as a set of impulse response functions. The advantage of obtaining the Green’s functions in the Eulerian reference system is that only the Green’s functions corresponding to the potential contact zone need to be determined, which significantly reduces the computational cost of solving the tyre/road contact and since the mesh is fixed in space, a finer mesh can be used for the potential contact zone, improving the accuracy of the contact force calculations. Although these effects might be less pronounced if a more accurate tyre model is used, it is found that using the Green’s functions of the loaded tyre in a contact force calculation leads to smaller forces than in the unloaded case, lower frequencies are present in the response and they decrease faster as the rotational velocity increases.

Modelling the formation and atmospheric transport of secondary inorganic aerosols with special attention to regions with high ammonia emissions

Regional simulations of sulfate, nitrate and ammonium aerosols were performed by a nested application of the online-coupled three-dimensional Eulerian model system COSMO-MUSCAT. This was done in a domain covering the northern part of Germany and surrounding regions for the full month of May and a 6-week period in August/September 2006 with the primary focus on secondary inorganic aerosol levels caused by ammonia emissions from domesticated animals and agricultural operations. The results show that in situations with westerly winds ammonium nitrate dominates with concentrations of about 5–10 μg m −3 whereas the ammonium sulfate concentrations are about 5 μg m −3. In situations with winds mainly from the East characterized by warmer and dryer air the ammonium sulfate concentrations have their maximum at about 10 μg m −3 whereas at the same time no ammonium nitrate is present. A reduction of agricultural NH 3 emissions by 50% in a regional scale reduces the ammonium nitrate concentrations to a maximum of 30%, while the ammonium sulfate concentrations are unchanged. The reduction of NH 3 emissions in a more limited area (here in the Federal state of Germany Niedersachsen) does have no noticeable effect neither on ammonium sulfate nor on ammonium nitrate.

Development of a moving artificial compressibility solver on unified coordinates

AbstractBased on the unified Eulerian and Lagrangian coordinate transformations, the unsteady incompressible Navier–Stokes equations with artificial compressibility effects are developed. As we know, the Eulerian coordinates cause excessive numerical diffusion across flow discontinuities, slip lines in particular. The Lagrangian coordinates, on the other hand, can resolve slip lines sharply but cause severe grid deformation, resulting in large errors and even breakdown of the computation. Recently, Hui et al. (J. Comput. Phys. 1999; 153:596–637) have introduced a unified coordinate system that moves with velocity hq, q being the velocity of the fluid particle. It includes the Eulerian system as a special case when h=0, and the Lagrangian when h=1, and was shown for the two‐dimensional unsteady Euler equations of compressible flow to be superior than both Eulerian and Lagrangian systems. In the framework of unified coordinates, our work will derive the unsteady incompressible flow equations and moving geometry equations, when hq equals grid velocity in conservation form and is updated simultaneously during each time step. Thus, the accurate estimation of geometry conservation and controlling the grid velocity or the h value based on the unified approach can keep numerical stability and avoid computation breakdown caused by moving body or boundary layers (considered as slip lines in Lagrangian coordinates). Also, the existing high‐resolution Riemann solver can be extended to discretize the current unified incompressible flow equations. Our benchmark tests including the lid‐driven cavity flow and backward step flow, oscillating flat plat and pulsating stenotic tube are used to validate the computations. The results verify the accuracy and robustness of the unified artificial compressibility solver on the moving body simulation. Copyright © 2009 John Wiley &amp; Sons, Ltd.