scholarly journals The Lagrangian coordinate system and what it means for two-dimensional crowd flow models

2016 ◽  
Vol 443 ◽  
pp. 272-285 ◽  
Author(s):  
Femke van Wageningen-Kessels ◽  
Ludovic Leclercq ◽  
Winnie Daamen ◽  
Serge P. Hoogendoorn
Keyword(s):  
Coordinate System ◽  
Two Dimensional ◽  
Flow Models ◽  
Lagrangian Coordinate ◽  
Lagrangian Coordinate System

scholarly journals A quasi-Lagrangian coordinate system based on high resolution tracer observations: implementation for the Antarctic polar vortex

2008 ◽  
Vol 8 (4) ◽  
pp. 16123-16173 ◽  
Author(s):  
E. V. Ivanova ◽  
C. M. Volk ◽  
O. Riediger ◽  
H. Klein ◽  
N. M. Sitnikov ◽  
...  
Keyword(s):  
High Resolution ◽  
Coordinate System ◽  
Vortex Core ◽  
Polar Vortex ◽  
Mixing Ratio ◽  
Lagrangian Coordinate ◽  
Antarctic Polar Vortex ◽  
The Antarctic ◽  
Lagrangian Coordinate System

Abstract. In order to quantitatively analyse the chemical and dynamical evolution of the polar vortex it has proven extremely useful to work with coordinate systems that follow the vortex flow. We propose here a two-dimensional quasi-Lagrangian coordinate system {χi, Δχi}, based on the mixing ratio of a long-lived stratospheric trace gas i, and its systematic use with i = N2O, in order to describe the structure of a well-developed Antarctic polar vortex. In the coordinate system {χi, Δχi} the mixing ratio χi is the vertical coordinate and Δχi = χi(Θ)−χivort(Θ) is the meridional coordinate (χivort(Θ) being a vertical reference profile in the vortex core). The quasi-Lagrangian coordinates {χi, Δχi} persist for much longer time than standard isentropic coordinates, potential temperature Θ and equivalent latitude φe, do not require explicit reference to geographic space, and can be derived directly from high-resolution in situ measurements. They are therefore well-suited for studying the evolution of the Antarctic polar vortex throughout the polar winter with respect to the relevant chemical and microphysical processes. By using the introduced coordinate system {χN2O, ΔχN2O} we analyze the well-developed Antarctic vortex investigated during the APE-GAIA (Airborne Polar Experiment – Geophysica Aircraft in Antarctica – 1999) campaign (Carli et al., 2000). A criterion, which uses the local in-situ measurements of χi=χi(Θ) and attributes the inner vortex edge to a rapid change (δ-step) in the meridional profile of the mixing ratio χi, is developed to determine the (Antarctic) inner vortex edge. In turn, we suggest that the outer vortex edge of a well-developed Antarctic vortex can be attributed to the position of a local minimum of the χH2O gradient in the polar vortex area. For a well-developed Antarctic vortex, the ΔχN2O-parametrization of tracer-tracer relationships allows to distinguish the tracer inter-relationships in the vortex core, vortex boundary region and surf zone and to examine their meridional variation throughout these regions. This is illustrated by analyzing the tracer-tracer relationships χi : χN2O obtained from the in-situ data of the APE-GAIA campaign for i = CFC-11, CFC-12, H-1211 and SF6. A number of solitary anomalous points in the CFC-11 : N2O correlation, observed in the Antarctic vortex core, are interpreted in terms of small-scale cross-isentropic dispersion.

The Stretching of a Viscoplastic Thread of Liquid

2003 ◽  
Vol 125 (6) ◽  
pp. 946-951 ◽  
Author(s):  
M. A. M. Al Khatib
Keyword(s):  
Coordinate System ◽  
Yield Stress ◽  
Special Interest ◽  
Inertial Effects ◽  
Viscoplastic Fluids ◽  
Lagrangian Coordinate ◽  
Lagrangian Coordinate System

The problem of stretching a viscoplastic (yield-stress) thread of a liquid hanging vertically is considered. The length of the thread at later times and the time at which it ruptures is determined. A Lagrangian coordinate system is used to analyze the extension of the thread as it sags under its own weight, with negligible inertial effects. The biviscosity model has been used to characterize viscoplastic fluids; the Newtonian and Bingham models can be recovered as limiting cases. The Bingham limit is of special interest.

Slow Dripping of Yield-Stress Fluids

2005 ◽  
Vol 127 (4) ◽  
pp. 687-690 ◽  
Author(s):  
M. A. M. Al Khatib ◽  
S. D. R. Wilson
Keyword(s):  
Coordinate System ◽  
Yield Stress ◽  
Special Interest ◽  
Vertical Tube ◽  
Viscoplastic Fluids ◽  
Yield Stress Fluids ◽  
Lagrangian Coordinate ◽  
Lagrangian Coordinate System

The dripping problem of a viscoplastic (yield-stress) liquid running slowly out of a narrow vertical tube is considered. The volume of the drops which break away is determined. A Lagrangian coordinate system is used to analyze the extension of the thread as it sags under its own weight, neglecting inertia and capillarity. The biviscosity model has been used to characterize viscoplastic fluids; the Newtonian and Bingham models can be recovered as limiting cases. The Bingham limit is of special interest.

Finite state induced flow models. I - Two-dimensional thin airfoil

1995 ◽  
Vol 32 (2) ◽  
pp. 313-322 ◽  
Author(s):  
David A. Peters ◽  
Swaminathan Karunamoorthy ◽  
Wen-Ming Cao
Keyword(s):  
Two Dimensional ◽  
Flow Models ◽  
Thin Airfoil ◽  
Finite State ◽  
Induced Flow

Flow Over a Cylinder at a Plane Boundary—A Model Based Upon (k–ε) Turbulence

1989 ◽  
Vol 111 (4) ◽  
pp. 414-419 ◽  
Author(s):  
T. Solberg ◽  
K. J. Eidsvik
Keyword(s):  
Pressure Gradient ◽  
Coordinate System ◽  
Adverse Pressure Gradient ◽  
Plane Boundary ◽  
Length Scale ◽  
Two Dimensional ◽  
Curvilinear Coordinate System ◽  
Recirculating Flow ◽  
Model Based ◽  
Curvilinear Coordinate

A model for two-dimensional flows over a cylinder at a plane boundary is developed. The model, based upon a (k-ε) turbulence closure, is formulated in a curvilinear coordinate system based upon frictionless flow. A length scale modification in areas of adverse pressure gradient and recirculating flow appears to be more realistic than the standard (k-ε) model. The main features of the predicted flow do not depend critically upon the details of the grid or model, which means that a well defined solution is obtained. The solution appears to be reasonable and validated to the extent that the data permits.

scholarly journals Analysis of base characteristics of trench gate field termination IGBT

2021 ◽  
Vol 237 ◽  
pp. 02023
Author(s):  
Bo Wang
Keyword(s):  
Coordinate System ◽  
Experimental Verification ◽  
Carrier Transport ◽  
Model Analysis ◽  
Bipolar Transistor ◽  
Two Dimensional ◽  
Base Region ◽  
Dimensional Effect ◽  
Insulated Gate Bipolar Transistor ◽  
Gate Structure

Trench gate structure represents the latest structure of Insulated Gate Bipolar Transistor(IGBT). Because there are great differences in model analysis coordinate system and carrier transport between trench gate structure and planar gate structure, the modeling method using planar gate structure will inevitably have great deviation. Based on the characteristics of trench gate structure and model analysis coordinate system, the base region is divided into PNP and PIN by considering the two-dimensional effect of carriers. According to whether the trench of PIN part can be covered by depletion layer of PNP part, the specific base region current is analyzed. Finally, simulation and experimental verification are carried out.

A numerical approach for simulating two-dimensional dense-snow avalanches in global coordinate systems

2021 ◽  
Author(s):  
Daniel Zugliani ◽  
Giorgio Rosatti ◽  
Stefania Sansone
Keyword(s):  
Coordinate System ◽  
Finite Volume ◽  
Reference System ◽  
Source Term ◽  
Numerical Approach ◽  
The Other ◽  
Snow Avalanche ◽  
Two Dimensional ◽  
Snow Avalanches ◽  
Avalanche Models

<p>Snow avalanche models are commonly based on a continuum fluid scheme, on the assumption of shallow flow in the direction normal to the bed, on a depth-averaged description of the flow quantities and on different assumptions concerning the velocity profile, the friction law, and the pressure in the flow direction (see Bartelt et al, 1999, Barbolini et al., 2000, for an overview). The coordinate reference system is commonly local, i.e., for each point of the domain, one axis is normal to the bed while the other two axes lay in a tangent plane. When the bed is vertical and the flow is not aligned with the steepest direction (e.g., in case of a side wall), the flow depth is no longer defined considering the normal direction and the model based on the local coordinate system is no longer valid. In near-vertical conditions, numerical problems can be expected.</p><p>Another critical point, for numerical models based on finite volume schemes and Godunov fluxes, is the accurate treatment of the source term in case of no-motion conditions (persistence, starting and stopping of the flow) due to the presence of velocity-independent, Coulomb-type terms in the bed shear stress. </p><p>In this work, we provide a numerical approach for a Voellmy-fluid based model, able to overcome the limits depicted above, to accurately simulate analytical solutions and to give reliable solutions in other cases (Zugliani & Rosatti, 2021). Firstly, differently from the other literature models, the chosen coordinate reference system is global (an axis opposite the gravity vector and the other two orthogonal axes lay in the horizontal plane) and therefore, the relevant mass and momentum equations have been derived accordingly. Secondly, these equations have been discretized by using a finite volume method on a Cartesian square grid where the Godunov fluxes has been evaluated by mean of a modified DOT scheme (Zugliani & Rosatti, 2016) while source terms in conditions of motion have been discretized by using an implicit operator-splitting technique. Finally, a specific algorithm has been derived to deal with the source term to determine the no-motion conditions.  Several test cases assess the capabilities of the proposed approach.</p><p> </p><p><strong>References:</strong></p><p>Barbolini, M., Gruber, U., Keylock, C.J., Naaim, M., Savi, F. (2000), <em>Application of statistical and hydraulic-continuum dense-snow avalanche models to five real European sites.</em> Cold Regions Science and Tech. 31, 133–149.</p><p>Bartelt, P., Salm, B., Gruber, U. (1999), <em>Calculating dense-snow avalanche runout using a voellmy-fluid model with active/passive longitudinal straining.</em> Journal of Glaciology 45, 242-254.</p><p>Zugliani D., Rosatti G. (2021), <em>Accurate modeling of two-dimensional dense snow avalanches in global coordinate system: the TRENT2D<sup>❄</sup> approach. </em>Paper under review.</p><p>Zugliani, D., Rosatti, G. (2016), <em>A new Osher Riemann solver for shallow water flow over fixed or mobile bed</em>, Proceedings of the 4th European Congress of the IAHR, pp. 707–713.</p>

Radiographic analysis of hallux valgus. A two-dimensional coordinate system.

1995 ◽  
Vol 77 (2) ◽  
pp. 205-213 ◽  
Author(s):  
Y Tanaka ◽  
Y Takakura ◽  
T Kumai ◽  
N Samoto ◽  
S Tamai
Keyword(s):  
Coordinate System ◽  
Hallux Valgus ◽  
Radiographic Analysis ◽  
Two Dimensional

The Application of a Two-Dimensional Zone Model to the Design and Control of a Continuously Operated, Gas-Fired Furnace

2002 ◽  
Author(s):  
Sara A. C. Correia ◽  
John Ward
Keyword(s):  
Dynamics Simulation ◽  
Relative Mass ◽  
Zone Model ◽  
Two Dimensional ◽  
Furnace Design ◽  
Simplified Approach ◽  
Flow Models ◽  
Discharge Temperature ◽  
Wide Range ◽  
And Control

This paper describes the development of a two-dimensional zone model to predict the throughput and thermal performance of a continuously operated gas-fired furnace heating steel bars to a nominal discharge temperature of 1250°C. Ultimately the model is intended to be a tool which can be used for the design and control of industrial furnaces. Consequently relatively short computing times are necessary and this was achieved by employing an isothermal computational fluid dynamics simulation to estimate the relative mass flows, and hence enthalpy flows to or from adjacent volume zones in the overall model. This simplified approach, which utilises a single “once off” isothermal computation of the flows, was considered to be adequate since isothermal flow models have been used successfully in the past to study the flow related behaviour of combustion systems. The coupling of a multi-zone model with a single “once off” isothermal computation of the flows enables a wide range of furnace design modifications to be studied quickly and easily. To illustrate the potential use of the model in a furnace design application, it was then used to investigate the effects of inclining the burners downwards towards the load as well as those associated with increasing the length of the furnace.

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