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 comparison of one-, two- and three-dimensional model representations of stratospheric gases

1979 ◽  
Vol 290 (1376) ◽  
pp. 477-494 ◽  
Keyword(s):  
Stratospheric Ozone ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Jet Streams ◽  
Model Calculations ◽  
One Dimensional ◽  
Dimensional Models ◽  
Molecular Number

Three- and two-dimensional model results have been averaged to investigate conceptual errors in two- and one-dimensional models. Average dynamical quantities show inter-hemispheric asymmetries in both mean and eddy vertical motions, with anomalous behaviour of tracers near effective source and sink regions. Zonal, hemispheric and global means of the rates of gas reactions show large deviations between terms like k : [A] [B] and k : [A] [B], causing significant errors in two- and one-dimensional model calculations. These errors are often associated with dynamical features such as jet streams or the tropopause, and affect the entire model atmospheres except in the summer mid-stratosphere. It is concluded that correlated measurements of atmospheric molecular number densities are urgently required to understand the deficiencies in models, which have been widely used to make perturbation calculations of the effects of aircraft and chloro-fluoromethanes on stratospheric ozone. The sources of error described in this work arise from inadequacies in the formulation of one- and two-dimensional models, rather than from uncertainties in the input data, and have not been included in published error analyses.

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

On the modeling of thermohydrodynamic and biogeochemical processes in the inland water objects

2020 ◽  
Author(s):  
Daria Gladskikh ◽  
Evgeny Mortikov ◽  
Victor Stepanenko
Keyword(s):  
Carbon Dioxide ◽  
Numerical Study ◽  
Three Dimensional ◽  
Measurement Data ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Inland Water ◽  
One Dimensional ◽  
Biochemical Processes ◽  
Dimensional Models

<p>Currently, one-dimensional and three-dimensional models are widely used to model thermohydrodynamic and biochemical processes in lakes and water rеreservoirs. One-dimensional models are highly computationally efficient and are used to parameterize land water bodies in climate models, however, when calculating large lakes and reservoirs with complex geometry, such models may incorrectly reproduce processes associated with horizontal heterogeneity. This becomes especially important for the prediction of water quality and euthrophication.</p><p>A three-dimensional model of thermohydrodynamics and biochemistry of an inland water obect is presented, which is based on the hydrostatic RANS model [1-3], and the parameterization of biochemical processes is implemented by analogy with the scheme for calculating biochemistry in the one-dimensional LAKE model [4]. Thus, the three-dimensional model is supplemented by a description of the transport of substances such as oxygen (O<sub>2</sub>), carbon dioxide (CO<sub>2</sub>), methane (CH<sub>4</sub>), as well as phyto- and zooplankton. The effect of turbulent diffusion and large-scale water movements on the distribution of a methane concentration field is studied.</p><p>To verify the calculation results, idealized numerical experiments and comparison with the measurement data on Lake Kuivajärvi (Finland) were used.</p><p>The work was supported by grants of the RF President’s Grant for Young Scientists (MK-1867.2020.5, MD-1850.2020.5) and by the RFBR (18-05-00292, 18-35-00602, 20-05-00776). <br><br>References:<br>[1] Mortikov E.V. Numerical simulation of the motion of an ice keel in stratified flow // Izv. Atmos. Ocean. Phys. 2016. 52. P. 108-115.<br>[2] Mortikov E.V., Glazunov A.V., Lykosov V.N. Numerical study of plane Couette flow: turbulence statistics and the structure of pressure-strain correlations // Russian Journal of Numerical Analysis and Mathematical Modelling. 2019. V. 34, N 2. P. 119-132.<br>[3] D.S. Gladskikh, V.M. Stepanenko, E.V. Mortikov, On the influence of the horizontal dimensions of inland waters on the thickness of the upper mixed layer. // Water Resourses. 2019. 18 pages. (submitted)<br>[4] Victor Stepanenko, Ivan Mammarella, Anne Ojala, Heli Miettinen, Vasily Lykosov, and Vesala Timo. LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes. Geoscientific Model Development, 9(5): 1977–2006, 2016.</p>

scholarly journals Design of Regular One-Dimensional, Two-Dimensional, and Three-Dimensional Linkage-Based Tessellations

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Alden D. Yellowhorse ◽  
Nathan Brown ◽  
Larry L. Howell
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Three Dimensions ◽  
Two Dimensional ◽  
One Dimensional

Abstract Linkage origami is one effective approach for addressing stiffness and accommodating panels of finite size in origami models and tessellations. However, successfully implementing linkage origami in tessellations can be challenging. In this work, multiple theorems are presented that provide criteria for designing origami units or cells that can be assembled into arbitrarily large tessellations. The application of these theorems is demonstrated through examples of tessellations in two and three dimensions.

Multilayer Extension of Two-Dimensional Solvable Statistical Models to Three Dimensions

1997 ◽  
Vol 11 (01n02) ◽  
pp. 175-181
Author(s):  
V. Popkov
Keyword(s):  
Statistical Models ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Solvable Models ◽  
The Third ◽  
Dimensional Models ◽  
Three Dimensional Models

We review the method of constructing solvable models in three dimensions, by starting from two-dimensional solvable models. The solvable three-dimensional models thus constructed do possess positive Boltzmann weights. These are multilayer two-dimensional systems with interactions in the third direction which can be interpreted as nearest-neighbour interactions. The set of conditions corresponding to the general 3D multilayer extension of solvable 2D models is derived.

In Search of Dominance: The Case of the Missing Dimension

2005 ◽  
Vol 100 (2) ◽  
pp. 559-566 ◽  
Author(s):  
Arthur E. Stamps
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Dimensional Theory

Some previous researchers have found that affect can be described in terms of two dimensions (pleasure and arousal), while others have noted three dimensions are needed (pleasure, arousal, and dominance). The competing claims were tested by creating stimuli with factors previously demonstrated to elicit responses of arousal or dominance, asking respondents to rate the stimuli, and contrasting correlations between ratings and the stimulus factors. Under the two-dimensional theory, the planned contrasts should be zero, while under the three-dimensional theory, the planned contrasts should be nonzero. Results supported the three-dimensional model.

scholarly journals Determination of load distribution in a given medium according to the values of the loads at certain points

2021 ◽  
pp. 167-175
Author(s):  
Oleksandr Mostovenko ◽  
Serhii Kovalov ◽  
Svitlana Botvinovska
Keyword(s):  
Boundary Conditions ◽  
Load Distribution ◽  
Numerical Solutions ◽  
Dimensional Space ◽  
Geometric Model ◽  
Three Dimensional ◽  
The Body ◽  
Three Dimensions ◽  
Two Dimensional ◽  
One Dimensional

Taking into account force, temperature and other loads, the stress and strain state calculations methods of spatial structures involve determining the distribution of the loads in the three-dimensional body of the structure [1, 2]. In many cases the output data for this distribution can be the values of loadings in separate points of the structure. The problem of load distribution in the body of the structure can be solved by three-dimensional discrete interpolation in four-dimensional space based on the method of finite differences, which has been widely used in solving various engineering problems in different fields. A discrete conception of the load distribution at points in the body or in the environment is also required for solving problems by the finite elements method [3-7]. From a geometrical point of view, the result of three-dimensional interpolation is a multivariate of the four-dimensional space [8], where the three dimensions are the coordinates of a three-dimensional body point, and the fourth is the loading at this point. Such interpolation provides for setting of the three coordinates of the point and determining the load at that point. The simplest three-dimensional grid in the three-dimensional space is the grid based on a single sided hypercube. The coordinates of the nodes of such a grid correspond to the numbering of nodes along the coordinate axes. Discrete interpolation of points by the finite difference method is directly related to the numerical solutions of differential equations with given boundary conditions and also requires the setting of boundary conditions. If we consider a three-dimensional grid included into a parallelepiped, the boundary conditions are divided into three types: 1) zero-dimensional (loads at points), where the three edges of the grid converge; 2) one-dimensional (loads at points of lines), where the four edges of the grid converge; 3) two-dimensional (loads at the points of faces), where the five edges of the grid converge. The zero-dimensional conditions are boundary conditions for one-dimensional interpolation of the one-dimensional conditions, which, in turn, are boundary conditions for two-dimensional conditions, and the two-dimensional conditions are boundary conditions for determining the load on the inner points of the grid. If a load is specified only at certain points of boundary conditions, then the interpolation problem is divided into three stages: one-dimensional load interpolation onto the line nodes, two-dimensional load interpolation onto the surface nodes and three-dimensional load interpolation onto internal grid nodes. The proposed method of discrete three-dimensional interpolation allows, according to the specified values of force, temperature or other loads at individual points of the three-dimensional body, to interpolate such loads on all nodes of a given regular three-dimensional grid with cubic cells. As a result of interpolation, a discrete point framework of the multivariate is obtained, which is a geometric model of the distribution of physical characteristics in a given medium according to the values of these characteristics at individual points.

Modeling of Combustion in Gasoline Direct Injection Engines for the Optimization of Engine Management System Through Reduction of Three-Dimensional Models to (n × One-Dimensional) Models

2003 ◽  
Vol 125 (3) ◽  
pp. 520-532 ◽  
Author(s):  
P. Emery ◽  
F. Maroteaux ◽  
M. Sorine
Keyword(s):  
Direct Injection ◽  
Three Dimensional ◽  
Gasoline Direct Injection ◽  
Computational Time ◽  
Combustion Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
The One

Gasoline direct injection (GDI) spark ignition engines may be able to run over a wide range of operating conditions. The GDI process allows combustion with lean mixtures which may lead to improved fuel economy and emissions relative to homogeneous spark ignition (SI) engines. To satisfy the different modes of operation, the tuning of GDI engines requires a large number of engine tests which are time-consuming and very expensive. To reduce the number of tests, a model with a very short computational time to simulate the engines in the whole operating range is needed; therefore the objective of this paper is to present a reduced model to analyze the combustion process in GDI engines, applied to a homogeneous stoichiometric mode. The objective of the model is to reproduce the same tendencies as those obtained by three-dimensional models, but with a reduced computational time. The one-dimensional model is obtained thanks to a reduction methodology based on the geometry of the combustion front computed with three-dimensional models of the KIVA-GSM code, a modified version of KIVA-II code including a CFM combustion model. The model is a set of n one-dimensional equations (i.e., for n rays), taking into account a thin flame front, described with the flamelet assumption. It includes a CFM combustion model and a (k,ε)-model including the mean air motions (swirl and tumble). The results of the one-dimensional model are compared to those obtained by the KIVA IIGSM under different engine conditions. The comparison shows that the one-dimensional model overestimates the maximum cylinder pressure, which has an insignificant effect on the net indicated work per cycle. The results obtained by the numerical simulations are close to those given by the three-dimensional model, with a much reduced computation time.

Pattern formation on time-dependent domains

2019 ◽  
Vol 880 ◽  
pp. 136-179 ◽  
Author(s):  
M. Ghadiri ◽  
R. Krechetnikov
Keyword(s):  
Liquid Layer ◽  
Three Dimensional ◽  
Time History ◽  
Domain Size ◽  
Vertical Vibration ◽  
Time Dependent ◽  
Two Dimensional ◽  
Layer Depth ◽  
One Dimensional ◽  
Aspect Ratios

In the quest to understand the dynamics of distributed systems on time-dependent spatial domains, we study experimentally the response to domain deformations by Faraday wave patterns – standing waves formed on the free surface of a liquid layer due to its vertical vibration – chosen as a paradigm owing to their historical use in testing new theories and ideas. In our experimental set-up of a vibrating water container with controlled positions of lateral walls and liquid layer depth, the characteristics of the patterns are measured using the Fourier transform profilometry technique, which allows us to reconstruct an accurate time history of the pattern three-dimensional landscape and reveal how it reacts to the domain dynamics on various length and time scales. Analysis of Faraday waves on growing, shrinking and oscillating domains leads to a number of intriguing results. First, the observation of a transverse instability – namely, when a two-dimensional pattern experiences an instability in the direction orthogonal to the direction of the domain deformation – provides a new facet to the stability picture compared to the one-dimensional systems in which the longitudinal (Eckhaus) instability accounts for pattern transformation on time-varying domains. Second, the domain evolution rate is found to be a key factor dictating the patterns observed on the path between the initial and final domain aspect ratios. Its effects range from allowing the formation of complex sequences of patterns to impeding the appearance of any new pattern on the path. Third, the shrinkage–growth process turns out to be generally irreversible on a horizontally evolving domain, but becomes reversible in the case of a time-dependent liquid layer depth, i.e. when the dilution and convective effects of the domain flow are absent. These experimentally observed enigmatic effects of the domain size variations in time are complemented here with appropriate theoretical insights elucidating the dynamics of two-dimensional pattern evolution, which proves to be more intricate compared to one-dimensional systems.

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