Upwinding technique

Development of weighted residual finite element schemes that can yield stable solutions for hyperbolic partial differential equations has been the subject of a considerable amount of research. The most successful outcome of these attempts is the development of the streamline upwinding technique by Brooks and Hughes (1982). The basic concept in the streamline upwinding is to modify the weighting function in the Galerkin scheme as... 

The Peclet number is a measure of convective heat transfer with regard to conductive heat transfer. High Pe values indicate a flow dominated by convection. From a numerical point of view, these flows are notorious because of instabilities that manifest themselves in the form of spurious oscillations in the temperature field. Special upwinding techniques must then be used to remedy the oscillations [37]. Another group related to Pe is the Graetz number defined by... 

After the pressme field is obtained at each vertex node, the finite difference formulation for the energy equation is represented in the gapwise direction at the centroid of each element. Due to the low thermal conductivity of melts and high Pelect numbers, an upwind technique is employed... 

Extension of the streamline Petrov -Galerkin method to transient heat transport problems by a space-time least-squares procedure is reported by Nguen and Reynen (1984). The close relationship between SUPG and the least-squares finite element discretizations is discussed in Chapter 4. An analogous transient upwinding scheme, based on the previously described 0 time-stepping technique, can also be developed (Zienkiewicz and Taylor, 1994). 

The flux terms are discretized at the cell interface. Because transport occurs in the direction of flow, we will use upwind differences. In addition, we will use an exphcit solution technique by discretizing our flux terms at the n (previous) time step ... 

As in most Lepidoptera, spruce budworm males locate conspecific females by flying upwind along a pheromone plume. The blends and release rates of these pheromone components form an important part of a specific communication system for the species. Once the communication system of an insect is understood, especially the pheromone chemistry as it relates to male behavior, it can be used in a variety of ways. For example, pheromones can be used to detect the presence of an insect in an area, to remove males from a population by trapping or poisoning and in air-permeation techniques in which the controlled and continuous release of pheromone components in the forest can disrupt mating. The latter use of pheromones appears to alter the normal male behavioral responses to the natural pheromone (16). 

Like many other insects, moths attract mates by long-distance pheromones. Females produce these pheromones in specialized abdominal glands. Chemically, they are acetates, often active in precise mixtures of geometric isomers. Males fly upwind, following the females pheromone plume to the somce, and mating ensues. In a typical experiment, a female moth, or just the pheromone, serves as odor source. An air current from that source helps to attract males who fly upwind to the pheromone source and attempt to mate. With this technique, we can compare the effects of known pheromones from different, related species on one species (species specificity). We can also test the attractiveness of different compounds that are stracturally similar to a known pheromone. In the laboratory, a wind tunnel, where available, is ideal, for this experience. 

The equations (15a-c) are discretized with upwind finite differences and the resulting linear systems of equations are solved using the Succesive Over Relaxation (SOR) technique. 

Collection of samples of the sea surface microlayer can be performed from a rowed dinghy, at least one mile upwind of the ship. The method usually used is the metallic steel screen technique described by Garrett (1965). 

This technique is called upwind and takes its name from fluid-dynamic applications. Actually, in these problems the direction of the stable integration corresponds to moving against the wind (Ascher and Petzold, 1998). The selection can also be seen as the application of an Euler backward method for the well-conditioned components for increasing and Euler forward for the stable components with decreasing x. 

In addition to the topics reviewed above, which form the vast majority of the articles published to date in the field of electrochemical simulation, there are a number of other alternative methods that have been exploited by workers. These include, statistical techniques such as the Monte Carlo method [174-179], which has been exploited to examine the fractal nature of electrode surfaces and electrodeposited polymer film growth. The finite volume method, which has found significant application in the engineering literature [180, 181], remains poorly exploited in the electrochemical field [182, 183] as does the multidimensional upwinding method, which has been applied by Van Den Boss-che and coworkers [184, 185] to multi-ion systems at the rotating disc electrode. For recent advances, readers are referred to the review of Speiser [19]. 

During Tests 3, 4, 5, and 6, additional atmospheric water vapor was provided to study the effects of increased relative humidity on the resulting eloud. This was attempted using two different methods. First, a steam boiler and water injeetion system was loeated upwind of the spill point. The injection system consisted of an array of spray nozzles, half for steam and half for warm water located approximately 25 m upwind of the release point. The spray system was 22 m long and was located approximately 3 m above the ground. The nozzles were oriented horizontally and pointed upwind from the spill point. The second technique involved a shallow pond, 250 m X 600 m, which was constructed upwind of the spill point. 

To reduce the number of URA elements required in the upwind feteh to develop atmospheric boundary layer depth in the simulated refinery grid, a wind tunnel technique was used. Trip spires were incorporated into the test grid upwind of the release point to decrease the distance required for boundary layer development. 

The terms fi, fg, j are, respectively, the friction terms for the liquid-wall, gas-wall, and gas-hquid interface, while p is the inclination angle of the pipe with respect to an horizontal line. Once the liquid velocity V has been calculated, the new value of the liquid mass in each calculation node can be determined resorting to an upwind finite difference calculation technique. 

A 3D solution for the film and pad temperature using the control cell technique, with upwinding of the film flows. 

The system of equation (1) for steady-state condition contains three unknowns Um, V and p, and it can be solved by one of the following methods. One method is to introduce stream function, which is solved together with pressure (3). The second method is to solve for Ufff, F/h and p in their primitive form (4). Both these methods made use of upwind finite difference technique. 

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