Grid propagation

V. Engel and coworkers [312] also investigated the time-resolved charge reversal process in molecules and applied their theory to the organometallic molecule ironcarbonyl (FeCO). A direct grid propagation of nuclear wave packets was used. Compared with [136], Engel states that the main purpose... 

Once the grid (or two grids) are prepared, there are two similar types of approaches to propagate the initial wavefiinction forward with time. One approach is split-operator methods, [59] where the short-time propagator is divided into a kinetic and potential parts so that... 

In trying to find a generalized solution of problem (43) one can come across oscillations of the grid solution and its derivatives ( ripple ), which essentially reduce the accuracy of a scheme. What is more, the lines of discontinuity of derivatives spread over several grid intervals, thus causing the difficulties in determination of proper discontinuity propagation velocity. This is the result of introducing the fictitious friction (dissipation) in the difference approximation. 

The method used to propagate solutions to the Schrodinger equation [61] requires T to be represented on a grid of points distributed in (/ , r, y), which we will denote using the labels klm >. The first term in T is given by... 

The step that has just been outlined in detail is the most difficult step in the propagation of the wave function. The action with the operator exp —iV R,t)6t/2h) is straightforward as this operator is a local operator in the grid representation and we just multiply the grid representation of the wave function at grid point i by the value of the operator at the same grid point. 

Compared with the use of arbitrary grid interfaces in combination with reduced-order flow models, the porous medium approach allows one to deal with an even larger multitude of micro channels. Furthermore, for comparatively simple geometries with only a limited number of channels, it represents a simple way to provide qualitative estimates of the flow distribution. However, as a coarse-grained description it does not reach the level of accuracy as reduced-order models. Compared with the macromodel approach as propagated by Commenge et al, the porous medium approach has a broader scope of applicability and can also be applied when recirculation zones appear in the flow distribution chamber. However, the macromodel approach is computationally less expensive and can ideally be used for optimization studies. 

Figure 2.59 Grid deformation following a wave propagating from right to left on a liquid surface.

Flame arresters are fitted in the vent lines of equipment that contains flammable material to prevent the propagation of flame through the vents. Various types of proprietary flame arresters are used. In general, they work on the principle of providing a heat sink, usually expanded metal grids or plates, to dissipate the heat of the flame. Flame arrestors and their applications are discussed by Rogowski (1980), Howard (1992) and Mendoza et al. (1988). 

The present research has treated important parts of the modeling of combustion and NOx formation in a biomass grate furnace. All parts resulted in useful approaches. For all these approaches successful first steps were taken. Currently, more research is underway to obtain improved results NH3 production is measured in the grid reactor with the tunable diode laser, detailed kinetics will be attached to the front propagation model, including the measured NH3 release functionalities, and for the turbulent combustion model heat losses are taken into account. In addition, the fuel layer model has to be coupled to the turbulent combustion model in the furnace. 

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