Coupling an unstructured grid three‐dimensional model with a laterally averaged two‐dimensional model for shallow water hydrodynamics and transport processes

2020 ◽  
Author(s):  
XinJian Chen
Keyword(s):  
Shallow Water ◽  
Unstructured Grid ◽  
Three Dimensional ◽  
Transport Processes ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Two Dimensional Model

scholarly journals Viscous dissipation by tidally forced inertial modes in a rotating spherical shell

2010 ◽  
Vol 643 ◽  
pp. 363-394 ◽  
Author(s):  
M. RIEUTORD ◽  
L. VALDETTARO
Keyword(s):  
Spherical Shell ◽  
Shear Layer ◽  
Viscous Dissipation ◽  
Inner Core ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Two Dimensional Model ◽  
Critical Latitude

We investigate the properties of forced inertial modes of a rotating fluid inside a spherical shell. Our forcing is tidal like, but its main property is that it is on the large scales. By numerically solving the linear equations of this problem, including viscosity, we first confirm some analytical results obtained on a two-dimensional model by Ogilvie (J. Fluid Mech., vol. 543, 2005, p. 19); some additional properties of this model are uncovered like the existence of narrow resonances associated with periodic orbits of characteristics. We also note that as the frequency of the forcing varies, the dissipation varies drastically if the Ekman number E is low (as is usually the case). We then investigate the three-dimensional case and compare the results to the foregoing model. The three-dimensional solutions show, like their two-dimensional counterpart, a spiky dissipation curve when the frequency of the forcing is varied; they also display small frequency intervals where the viscous dissipation is independent of viscosity. However, we show that the response of the fluid in these frequency intervals is crucially dominated by the shear layer that is emitted at the critical latitude on the inner sphere. The asymptotic regime, where the dissipation is independent of the viscosity, is reached when an attractor has been excited by this shear layer. This property is not shared by the two-dimensional model where shear layers around attractors are independent of those emitted at the critical latitude. Finally, resonances of the three-dimensional model correspond to some selected least damped eigenmodes. Unlike their two-dimensional counter parts these modes are not associated with simple attractors; instead, they show up in frequency intervals with weakly contracting webs of characteristics. Besides, we show that the inner core is negligible when its relative radius is less than the critical value 0.4E1/5. For these spherical shells, the full sphere solutions give a good approximation of the flows.

Modelling the global sources and sinks of radiatively active gases

1995 ◽  
Vol 351 (1696) ◽  
pp. 397-411 ◽  
Keyword(s):  
Numerical Models ◽  
Stratospheric Ozone ◽  
Trace Gases ◽  
Three Dimensional ◽  
Relative Importance ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Sources And Sinks ◽  
Two Dimensional Model

The use of numerical models in understanding the budgets of atmospheric trace gases is discussed. The budget of methane is calculated in a two-dimensional model. The contrasting behaviour of the Northern and Southern Hemisphere reflects changes in the relative importance of emissions, transport and chemistry. Models can also be used to test hypotheses. An example of such a study is presented in which it is shown that changes in stratospheric ozone could have played a significant role in the dramatic change in methane trend observed in the early 1990s. Finally, use of a three-dimensional model to study tropospheric trace gases is introduced.

Comparative two- and three-dimensional finite element modelling techniques for tibial fractures

2001 ◽  
Vol 215 (2) ◽  
pp. 255-258 ◽  
Author(s):  
S Mishra ◽  
T N Gardner
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Principal Stresses ◽  
Two Dimensional Model ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Often the choice of a two-dimensional modelling approach over a three-dimensional approach is made on the basis of available resources, and not on task appropriateness. In the case of simulating the mechanical behaviour of irregular anatomical structures in biomedical engineering, the authenticity of two-dimensional model behaviour and the interpretation of model solutions is of particular concern since little comparable two-dimensional and three-dimensional data have been published. As part of a research programme, a comparison was made between two-dimensional and three-dimensional finite element models (FEMs) that examine the stress-strain environment of a clinical bone fracture and callus. In comparison with the three-dimensional model, the two-dimensional model substantially underestimated peak compressive principal stresses in the callus tissue and peak equivalent strains. This was a consequence of geometrical and structural asymmetry in a plane perpendicular to the two-dimensional model. However, the two-dimensional model predicted similar patterns of stress and strain distribution to the corresponding mid-longitudinal plane of the three-dimensional model, and underestimates of peak stress and strain were much reduced. This confirmed that despite the irregular geometry and structure of the subject, the two-dimensional model provided a valid mechanical simulation in the plane of the fracture that it represented.

scholarly journals Concentration Data and Dimensionality in Groundwater Models: Evaluation Using Inverse Modelling

1998 ◽  
Vol 29 (3) ◽  
pp. 149-178 ◽  
Author(s):  
Heidi Christiansen Barlebo ◽  
Mary C. Hill ◽  
Dan Rosbjerg ◽  
Karsten Høgh Jensen
Keyword(s):  
Groundwater Flow ◽  
Cross Section ◽  
Nonlinear Regression ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Concentration Data ◽  
Flow And Transport ◽  
Two Dimensional Model

A three-dimensional inverse groundwater flow and transport model that fits hydraulic-head and concentration data simultaneously using nonlinear regression is presented and applied to a layered sand and silt groundwater system beneath the Grindsted Landfill in Denmark. The aquifer is composed of rather homogeneous hydrogeologic layers. Two issues common to groundwater flow and transport modelling are investigated: 1) The accuracy of simulated concentrations in the case of calibration with head data alone; and 2) The advantages and disadvantages of using a two-dimensional cross-sectional model instead of a three-dimensional model to simulate contaminant transport when the source is at the land surface Results show that using only hydraulic heads in the nonlinear regression produces a simulated plume that is profoundly different from what is obtained in a calibration using both hydraulic-head and concentration data. The present study provides a well-documented example of the differences that can occur. Representing the system as a two-dimensional cross-section obviously omits some of the system dynamics. It was, however, possible to obtain a simulated plume cross-section that matched the actual plume cross-section well. The two-dimensional model execution times were about a seventh of those for the three-dimensional model, but some difficulties were encountered in representing the spatially variable source concentrations and less precise simulated concentrations were calculated by the two-dimensional model compared to the three-dimensional model. Summed up, the present study indicates that three-dimensional modelling using both hydraulic heads and concentrations in the calibration should be preferred in the considered type of transport studies.

An alternative algorithm of tunnel piston effect by replacing three-dimensional model with two-dimensional model

2018 ◽  
Vol 128 ◽  
pp. 55-67 ◽  
Author(s):  
Minzhang Liu ◽  
Chunguang Zhu ◽  
Tong Cui ◽  
Huan Zhang ◽  
Wandong Zheng ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Piston Effect ◽  
Two Dimensional Model ◽  
Alternative Algorithm

Rotation Feature of Three-Dimensional Tile Self-Assembly Molecular Structure for Efficient Microprocessor Material

2014 ◽  
Vol 886 ◽  
pp. 132-135
Author(s):  
Zhuo Qian Liang ◽  
Jing Li
Keyword(s):  
Molecular Structure ◽  
Self Assembly ◽  
Molecular Motors ◽  
Three Dimensional ◽  
Future Application ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
New Model ◽  
Two Dimensional Model

Future application of nanoscale tile self-assembly is the production of smaller, more efficient microprocessors.In this paper, a new three-dimensional tile self-assembly molecular structure is presented.The model adds rotation movement where large assemblies of nanoscale tile molecules can be moved around, analogous to molecular motors. We have showed the universalityof the new model and demonstrated that three-dimensional model is capable of simulating two-dimensional model. This paper also covers the details about path encoding. The encoding process makes use of edgecharactersof tilesto simplify the design.

The assembly of ionic currents in a thalamic neuron I. The three-dimensional model

1989 ◽  
Vol 237 (1288) ◽  
pp. 267-288 ◽  
Keyword(s):  
Three Dimensional ◽  
State Diagram ◽  
Ionic Currents ◽  
Stability Diagram ◽  
Repetitive Firing ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Two Dimensional Model ◽  
The Stability

We have previously discussed qualitative models for bursting and thalamic neurons that were obtained by modifying a simple two-dimensional model for repetitive firing. In this paper we report the results of making a similar sequence of modifications to a more elaborate six-dimensional model of repetitive firing which is based on the Hodgkin–Huxley equations. To do this we first reduce the six-dimensional model to a two-dimensional model that resembles our original two-dimensional qualitative model. This is achieved by defining a new variable, which we call q . We then add a subthreshold inward current and a subthreshold outward current having a variable, z , that changes slowly. This gives a three-dimensional ( v, q, z ) model of the Hodgkin–Huxley type, which we refer to as the z -model. Depending on the choice of parameter values this model resembles our previous models of bursting and thalamic neurons. At each stage in the development of these models we return to the corresponding seven-dimensional model to confirm that we can obtain similar solutions by using the complete system of equations. The analysis of the three-dimensional model involves a state diagram and a stability diagram. The state diagram shows the projection of the phase path from v, q, z space into the v, z plane, together with the projections of the curves ż = 0 and v̇ = q̇ = 0. The stability of the points on the curve v̇ = q̇ = 0, which we call the v, q nullcurve, is determined by the stability diagram. Taken together the state and stability diagrams show how to assemble the ionic currents to produce a given firing pattern.

Numerical Analysis of Multi-Pass H-Beam Hot Rolling Processing

2012 ◽  
Vol 190-191 ◽  
pp. 385-389 ◽  
Author(s):  
Qing Qiang He ◽  
Jia Sun ◽  
Jun You Zhao ◽  
Bao Min Yuan ◽  
Li Jian Xu
Keyword(s):  
Steady State ◽  
Plastic Strain ◽  
Hot Rolling ◽  
Three Dimensional ◽  
Simulation Technique ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Two Dimensional Model ◽  
H Beam

Hot rolling is a basic metal forming technique that is used to transform preformed shape into final products of forms more suitable for further processing. As the hot stock progresses through the forming surfaces, the shape eventually reaches a constant state. With the assumption of forming process has reached steady-state condition, a simulation technique based on elements re-meshes has been constructed to analyze the H-beam metal hot roll process. The technique includes the following approaches: the solution was halted as soon as the steady-state criteria were met, and the plane of elements, which first satisfied the steady-state criteria were written to database, SSES for short; a two-dimensional model was created to model the hot stock cooling between the two roll passes and a geometric part was generated and meshed with quadrilateral elements to transfer the nodes temperatures; a new three-dimensional model extruded from the two-dimensional model was constructed to model the next roll pass with the transfer of nodes temperatures and element integration points equivalent plastic strain(PEEQ), identifying the plastic deformation extent for the classical metal plasticity models, from the new two-dimensional model and the first three-dimensional model respectively. Gleeble-1500 tester is used to get the true stress and true plastic strain data for modeling the yield behavior of material Q235. The effectiveness of the simulation technique has been proved by a simulation of 11-pass H-beam rolling process.

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