Conventional 2D Models Research Articles

Accurate two-dimensional model of an arrayed-waveguide grating demultiplexer and optimal design based on the reciprocity theory

An accurate two-dimensional (2D) model is introduced for the simulation of an arrayed-waveguide grating (AWG) demultiplexer by integrating the field distribution along the vertical direction. The equivalent 2D model has almost the same accuracy as the original three-dimensional model and is more accurate for the AWG considered here than the conventional 2D model based on the effective-index method. To further improve the computational efficiency, the reciprocity theory is applied to the optimal design of a flat-top AWG demultiplexer with a special input structure.

Prediction of solid–liquid interface shape during CZ Si crystal growth using experimental and global simulation

In the Czochralski process, the prediction of characteristics of point defects in growing crystal strongly depends on the geometry of the solid–liquid interface. As the shape of the solid–liquid interface is not known a priori, melt convection and other forms of global simulation are used to determine the interface geometry. Conventional 2D models cannot realize interface shapes precisely, and unsteady 3D models require high large expenditure of both time and money for computer simulation and calculation. To surmount this problem, we found a new parameter ( G ave) that could be used to determine the interface height by means of a simple procedure. By deriving G ave from the average axial temperature gradients in the crystals, we can characterize the thermal ambiance surrounding the crystal by hot zone geometry or the process condition. Interface heights h and G ave are formularized as h= a( V/ G ave)+ b. Fitting parameters a and b were obtained statistically by a number of sets of actual interface heights and calculated temperature distributions with various hot-zone types and process conditions. Pairs of fitting parameters were classified according to the crystal diameter and magnetic field strength.

Calculation of bulk defects in CZ Si growth: impact of melt turbulent fluctuations

We present 3D unsteady analysis of melt turbulent convection coupled with heat transfer in the crystal and crucible during 300 mm CZ Si crystal growth. The 3D analysis includes the calculation of the crystallization front geometry, validated by comparing to experimental data and results obtained with a conventional 2D model. At the second step, an analysis of defect incorporation and evolution in the crystal has been performed within a 2D model.

Prediction of bulk defects in CZ Si crystals using 3D unsteady calculations of melt convection

We present 3D unsteady analysis of melt turbulent convection coupled with heat transfer in the crystal and crucible during CZ Si crystal growth. The 3D analysis includes the calculation of the crystallization front geometry, validated by comparing experimental data and results obtained with a conventional 2D model. At the second step, an analysis of defect incorporation and evolution in the crystal has been performed within a 2D model.

Ekman decay of a dipolar vortex in a rotating fluid

The evolution of quasi-two-dimensional (2D) dipolar vortices over a flat bottom in a rotating fluid system is studied numerically, and the main results are experimentally verified. Our aim is to examine the dipole decay due to bottom friction effects. The numerical simulations are based on the 2D physical model derived by Zavala Sansón and van Heijst [J. Fluid Mech. 412, 75 (2000)], which contains nonlinear Ekman terms, associated with bottom friction, in the vorticity equation. In contrast, the conventional 2D model with bottom friction only retains a linear stretching term in the same equation. It is shown that the dipole trajectory is deflected towards the right (i.e., in the anticyclonic direction) when nonlinear Ekman terms are included. This effect is not observed in simulations based on the conventional model, where the dipole trajectory is a straight line. The basic reason for this behavior is the slower decay of the anticyclonic part of the dipole, with respect to the cyclonic one, due to nonlinear Ekman effects. Another important result is the exchange of fluid between the cyclonic part and the ambient, leaving a tail behind the dipole. By means of laboratory experiments in a rotating tank, these results are qualitatively verified.

EXAMINATIONS OF FLUID FORCES ON THE STRUCTURE BY USING 2D/3D HYBRID MODEL

The fluid forces acting on the structures are examined by using 2D/3D hybrid model in which the conventional 2D model is adopted for the calculation in the wide region located far from the structures. The 3D non-hydrostatic pressure numerical model is used in the limited region adjacent to the coastal structures where the three-dimensional motion could not be neglected anymore. The results of the model tests are compared with the numerical results obtained by both the present hybrid model and the conventional 2D model, to examine the validity of the present model. As a result, it is verified that the present hybrid model reduces a calculation load significantly comparing to the calculation load by using 3D model for the whole domain. Though this model reproduces the characteristics of the three-dimensional complicated flow around the opening of breakwater that cannot be reproduced by the conventional 2D model. The usual method cannot give sufficiently accurate results for a flow around structures.