scholarly journals Collisional growth in a particle-based cloud microphysical model: insights from column model simulations using LCM1D (v1.0)

2020 ◽  
Vol 13 (11) ◽  
pp. 5119-5145
Author(s):  
Simon Unterstrasser ◽  
Fabian Hoffmann ◽  
Marion Lerch
Keyword(s):  
Three Dimensional ◽  
Vertical Position ◽  
Grid Spacing ◽  
Diffusional Growth ◽  
Time Step ◽  
One Dimensional ◽  
Cloud Models ◽  
The Future ◽  
Vertical Grid ◽  
Linear Sampling

Abstract. Lagrangian cloud models (LCMs) are considered the future of cloud microphysical modelling. Compared to bulk models, however, LCMs are computationally expensive due to the typically high number of simulation particles (SIPs) necessary to represent microphysical processes such as collisional growth of hydrometeors successfully. In this study, the representation of collisional growth is explored in one-dimensional column simulations, allowing for the explicit consideration of sedimentation, complementing the authors' previous study on zero-dimensional collection in a single grid box. Two variants of the Lagrangian probabilistic all-or-nothing (AON) collection algorithm are tested that mainly differ in the assumed spatial distribution of the droplet ensemble: the first variant assumes the droplet ensemble to be well-mixed in a predefined three-dimensional grid box (WM3D), while the second variant considers the (sub-grid) vertical position of the SIPs, reducing the well-mixed assumption to a two-dimensional, horizontal plane (WM2D). Since the number of calculations in AON depends quadratically on the number of SIPs, an established approach is tested that reduces the number of calculations to a linear dependence (so-called linear sampling). All variants are compared to established Eulerian bin model solutions. Generally, all methods approach the same solutions and agree well if the methods are applied with sufficiently high resolution (foremost is the number of SIPs, and to a lesser extent time step and vertical grid spacing). Converging results were found for fairly large time steps, larger than those typically used in the numerical solution of diffusional growth. The dependence on the vertical grid spacing can be reduced if AON-WM2D is applied. The study also shows that AON-WM3D simulations with linear sampling, a common speed-up measure, converge only slightly slower compared to simulations with a quadratic SIP sampling. Hence, AON with linear sampling is the preferred choice when computation time is a limiting factor. Most importantly, the study highlights that results generally require a smaller number of SIPs per grid box for convergence than previous one-dimensional box simulations indicated. The reason is the ability of sedimenting SIPs to interact with a larger ensemble of particles when they are not restricted to a single grid box. Since sedimentation is considered in most commonly applied three-dimensional models, the results indicate smaller computational requirements for successful simulations, encouraging a wider use of LCMs in the future.

scholarly journals Collection/Aggregation in a Lagrangian cloud microphysical model: Insights from column model applications using LCM1D (v0.9)

2020 ◽  
Author(s):  
Simon Unterstrasser ◽  
Fabian Hoffmann ◽  
Marion Lerch
Keyword(s):  
Three Dimensional ◽  
Grid Spacing ◽  
Vertical Coordinate ◽  
Applied Model ◽  
Cloud Models ◽  
The Future ◽  
Vertical Grid ◽  
Explicit Consideration ◽  
Three Dimensional Models ◽  
Linear Sampling

Abstract. Lagrangian cloud models (LCMs) are considered the future of cloud microphysical modeling. However, LCMs are computationally expensive due to the typically high number of simulation particles (SIPs) necessary to represent microphysical processes such as collection/aggregation successfully. In this study, the representation of collection/aggregation is explored in one-dimensional column simulations, allowing for the explicit consideration of sedimentation, complementing the authors' previous study on zero-dimensional collection in a single grid box. Two variants of the Lagrangian probabilistic all-or-nothing (AON) collection algorithm are tested that mainly differ in the assumed spaatial distribution of the droplet ensemble: The first variant assumes the droplet ensemble to be well-mixed in a predefined three-dimensional grid box (WM3D), while the second variant considers explicitly the vertical coordinate of the SIPs, reducing the well-mixed assumption to a two-dimensional, horizontal plane (WM2D). Since the number of calculations in AON depends quadratically on the number of SIPs, an approach is tested that reduces the number of calculations to a linear dependence (so-called linear sampling). All variants are compared to established Eulerian bin model solutions. Generally, all methods approach the same solutions, and agree well if the methods are applied with sufficiently high accuracy (foremost the number of SIPs, timestep, vertical grid spacing). However, it is found that the rate of convergence depends on the applied model variant. The dependence on the vertical grid spacing can be reduced if AON WM2D is applied. The study also shows that the AON simulations with linear sampling, a common speed-up measure, converges slower, as smaller timesteps are required to reach convergence compared to simulations with a quadratic dependence on the number of SIPs. Most importantly, the study highlights that results generally require a smaller number of SIPs per grid box for convergence than previous box simulations indicated. The reason is the ability of sedimenting SIPs to interact with an effectively larger ensemble of particles when they are not restricted to a single grid box. Since sedimentation is considered in most commonly applied three-dimensional models, the results indicate smaller computational requirements for successful simulations than previously assumed, encouraging a wider use of LCMs in the future.

scholarly journals Collection/Aggregation in a Lagrangian cloud microphysical model: Insights from column model applications

2020 ◽  
Author(s):  
Simon Unterstrasser ◽  
Fabian Hoffmann ◽  
Marion Lerch
Keyword(s):  
Three Dimensional ◽  
Vertical Coordinate ◽  
Applied Model ◽  
Cloud Models ◽  
Model Variant ◽  
The Future ◽  
Vertical Grid ◽  
Explicit Consideration ◽  
Microphysical Processes ◽  
Three Dimensional Models

<p>Lagrangian cloud models (LCMs) are considered the future of cloud microphysical modeling. However, LCMs are computationally expensive due to the typically high number of simulation particles (SIPs) necessary to represent microphysical processes such as collection/aggregation successfully. In this study, the representation of collection/aggregation is explored in one-dimensional column simulations, allowing for the explicit consideration of sedimentation, complementing the authors' previous study on zero-dimensional collection in a single grid box. Two variants of the Lagrangian probabilistic all-or-nothing (AON) collection algorithm are tested that mainly differ in the assumed spatial distribution of the droplet ensemble: The first variant assumes the droplet ensemble to be well-mixed in a predefined three-dimensional grid box (WM3D), while the second variant considers explicitly the vertical coordinate of the SIPs, reducing the well-mixed assumption to a two-dimensional, horizontal plane (WM2D). Both variants are compared to established Eulerian bin model solutions. Generally, all methods approach the same solutions, and agree well if the methods are applied with sufficiently high accuracy (foremost the number of SIPs, timestep, vertical grid spacing). However, it is found that the rate of convergence depends on the applied model variant.  Most importantly, the study highlights that results generally require a smaller number of SIPs per grid box for convergence than previous box simulations indicated. The reason is the ability of sedimenting SIPs to interact with an effectively larger ensemble of particles when they are not restricted to a single grid box. Since sedimentation is considered in most commonly applied three-dimensional models, the results indicate smaller computational requirements for successful simulations than previously assumed, encouraging a wider use of LCMs in the future.</p>

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

A Simplified Analytical Approach for Calculating the Start-Up Time of Industrial Steam Turbines for Optimal and Fast Start-Up Procedures

2015 ◽  
Author(s):  
Wolfgang Beer ◽  
Lukas Propp ◽  
Lutz Voelker
Keyword(s):  
Steam Turbine ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Steam Turbines ◽  
Time Step ◽  
One Dimensional ◽  
Start Up ◽  
Time Calculation ◽  
Fast Start ◽  
The One

New flexible operational regimes with fast start-ups and fast-changing load cycles for steam turbines require calculation procedures for determining optimal start-up times in order not to exceed the limits of thermal stress for the steam turbine parts. This work presents a start-up time calculation for various kinds of industrial steam turbines. An analytical approach for estimating the optimal thermal load of a turbine from quasi-steady or steady condition is developed. The geometry of the respective turbine components, the changing of the steam parameters and heat transfer effects during the start-up procedure are taken into account while observing the respective material properties and stress limits. The temperature distributions of the respective turbine parts are calculated with a one-dimensional numerical algorithm of Fourier’s heat conduction equation. Three-dimensional influences of the geometry and of the the heat flux are considered analytically by adjusting the numerical solutions of elementary bodies (e.g. one-dimensional plate). The start-up time calculation is performed in small time steps to guarantee the stability of the numerical solution. The unsteady stress analysis for the start-up procedure does not uniquely identify one critical component. The calculation must be repeated for each time step to identify the component which limits the start-up gradient. Other boundary conditions, such as restricted speed ranges of the rotor with minimum transients and time for synchronization with the electrical grid, are considered by the model too and can further limit the start-up gradient and lead to slower start-up procedures. The one-dimensional calculation models were verified with a three-dimensional FEA of the casing and a two axis symmetrical FEA of the rotor. The results for the temperature distribution are presented and compared to the one-dimensional results. The final result of the analytical approach for an optimized start-up time calculation is verified with two typical start-up calculations, one for a generator drive steam turbine and one for a mechanical-drive steam turbine.

Solution of problems in dynamic elasticity via a mixed least squares method

2015 ◽  
Vol 32 (3) ◽  
pp. 687-704 ◽  
Author(s):  
Maria Tchonkova
Keyword(s):  
Least Squares ◽  
Analytical Solutions ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Time Step ◽  
Theoretical Formulation ◽  
Content Type ◽  
One Dimensional ◽  
Dynamic Elasticity ◽  
Backward Euler

Purpose – The purpose of this paper is to present an original mixed least squares method for solving problems in dynamic elasticity. Design/methodology/approach – The proposed approach involves two different types of unknowns: velocities and stresses. The approximate solution to the dynamic elasticity equations is obtained via a minimization of a least squares functional, consisting of two terms: a term, which includes the squared residual of a weak form of the time rate of the constitutive relationships, expressed in terms of velocities and stresses, and a term, which depends on the squared residual of the equations of motion. At each time step the functional is minimized with respect to the velocities and stresses, which for the purpose of this study, are approximated by equal order piece-wise linear polynomial functions. The time discretization is based upon the backward Euler scheme. The displacements are computed from the obtained velocities in terms of a finite difference interpolation. The proposed theoretical formulation is given the general three-dimensional case and is tested numerically on the solution of one-dimensional wave equations. Findings – To test the performance of the method, it has been implemented in an original computer code, using object-oriented logic and written from scratch. Two one-dimensional problems from the mathematical physics, with well-known exact analytical solutions, have been solved. The numerical examples include a forced vibrating spring, fixed at its both ends and a rod, vibrating under its own weight, when one of its ends is fixed and the other is traction-free. The performed convergence study suggests that the method is convergent for both: velocities and stresses. The obtained results show excellent agreement between the exact and analytical solutions for displacement modes, velocities and stresses. It is observed that this method appears to be stable for the different mesh sizes and time step values. Originality/value – The mixed least squares formulation, described in this paper, serves as a basis for interesting future developments and applications to two and three-dimensional problems in dynamic elasticity.

Numerical evaluation of land subsidence induced by groundwater pumping in Shanghai

2011 ◽  
Vol 48 (9) ◽  
pp. 1378-1392 ◽  
Author(s):  
Shui-Long Shen ◽  
Ye-Shuang Xu
Keyword(s):  
Land Subsidence ◽  
Three Dimensional ◽  
Groundwater Withdrawal ◽  
Soil Deformation ◽  
Groundwater Pumping ◽  
Consolidation Process ◽  
One Dimensional ◽  
Future Behavior ◽  
Proposed Model ◽  
The Future

To predict the future behavior of land subsidence in Shanghai due to pumping of groundwater, a numerical model is established. In the proposed model, groundwater flow in three-dimensional conditions and soil deformation in one-dimensional conditions are calculated. The model takes into account the multi-aquifer-aquitard hydrogeological condition of the soft deposit of Shanghai. The variation of the coefficient of compressibility and coefficient of hydraulic conductivity of the soils with the consolidation process are simulated. Relationships among land subsidence, groundwater withdrawal volume, and groundwater level are analyzed. Comparison between the measured value and calculated value shows that the model simulates the measured value fairly well. The future of land subsidence behavior due to groundwater withdrawal is predicted and discussed via consideration of the variation of the following parameters in the future 30 years: net withdrawn volume of groundwater, pumping layer, and pumping region.

scholarly journals Fine-Scale Structures in the Mid-Level Eyewall of Super Typhoon Rammasun (2014) Simulated With the WRF-LES Framework

2022 ◽  
Vol 9 ◽  
Author(s):  
Zhen Gao ◽  
Liguang Wu ◽  
Xingyang Zhou
Keyword(s):  
Tropical Cyclone ◽  
Three Dimensional ◽  
Wrf Model ◽  
Rapid Intensification ◽  
Grid Spacing ◽  
Super Typhoon ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Vertical Grid ◽  
Horizontal Grid

It has been numerically demonstrated that the turbulence above the boundary is important to tropical cyclone intensification and rapid intensification, but the three-dimensional structures of the sub-grid-scale (SGS) eddy have not been revealed due to the lack of observational data. In this study, two numerical simulations of Super Typhoon Rammasun (2014) were conducted with the Advanced Weather Research and Forecast (WRF) model by incorporating the large-eddy simulation (LES) technique, in which the enhanced eyewall convection and the process of rapid intensification are captured. Consistent with previous observational studies, the strong turbulent kinetic energy (TKE) is found throughout the whole eyewall inside of the radius of maximum wind in both experiments. The simulations indicate that the strong TKE is associated with horizontal rolls with the horizontal extent of 2–4 km, which are aligned azimuthally in the intense eyewall convection. It is indicated that the three-dimensional structures of the SGS eddy can be simulated with the vertical grid spacing of ∼100 m when the horizontal grid spacing is 74 m. It is suggested that there is considerable turbulence associated with azimuthally-aligned horizontal rolls in the mid-level eyewall of tropical cyclone.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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