Upwinding selective

In the earlier versions of the streamline upwinding scheme the modified weight function was only applied to the convection tenns (i.e. first-order derivatives in the hyperbolic equations) while all other terms were weighted in the usual manner. This is called selective or inconsistent upwinding. Selective upwinding can be interpreted as the introduction of an artificial diffusion in addition to the physical diffusion to the weighted residual statement of the differential equation. This improves the stability of the scheme but the accuracy of the solution declines. 

The finite volume methods have been used to discretised the partial differential equations of the model using the Simple method for pressure-velocity coupling and the second order upwind scheme to interpolate the variables on the surface of the control volume. The segregated solution algorithm was selected. The Reynolds stress turbulence model was used in this model due to the anisotropic nature of the turbulence in cyclones. Standard fluent wall functions were applied and high order discretisation schemes were also used. 

An element for the stress components composed of 16 sub-elements (4x4) on which bilinear (continuous) polynomials are used, was introduced by Marchal and Crochet in [28]. This leads to a continuous C° approximation of the three variables. The velocity is approximated by biquadratic polynomials while the pressure is linear. Fortin and Pierre ([17]) made a mathematical analysis of the Stokes problem for this three-field formulation. They conclude that the polynomial approximations of the different variables should satisfy the generalized inf-sup (Brezzi-Babuska) condition introduced by Marchal and Crochet and they proved it was the case for the Marchal and Crochet element. In order to take into account the hyperbolic character of the constitutive equation, Marchal and Crochet have implemented and compared two different methods. The first is the Streamline-Upwind/Petrov-Galerkin (SUPG). Thus a so-called non-consistent Streamline-Upwind (SU) is also considered (already used in [13]). As a test problem, they selected the "stick-slip" flow. With SUPG method applied to this problem, wiggles in the stress and the velocity field were obtained. In the SU method, the modified weighting function only applies to the convective terms in the constitutive equations. 

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. 

Terms such as anemotaxis and klinotaxis, while seemingly defining a reaction precisely, tend to promote the notion of single-solution orientation systems. Yet insects may well process the available information necessary for several mechanisms, selecting the anemotactic reaction, for example, only when there are sufficient anemo and visual cues and flight directly upwind provides continued contact with the chemical stimulus. Such terms also tend to camouflage the importance of non-chemical and idothetic inputs. 

A female must search at random within a habitat until one of the stimuli important in host selection is encountered. As with insects responding to sex pheromones, some parasitoids respond to air movements and fly upwind (anemotaxis) (Edwards, 1954). Odors stimulate a klinokinetic response in Mormoniella (Edwards, 1954) whereas odors may stimulate chemotaxis in other species (Read et al., 1970). However, there has been relatively little data on the long range orientation of parasitoids. The cues that allow a parasitoid to orient to a potential host community presumably act from a distance. The types of stimuli that meet this criterion include electromagnatic radiation, sound, or odors. 

The method of statistical analysis in many bioassays focuses on analyzing the number and pattern of choices made by subjects. In general, these assays will not involve truly continuous variables, but will involve counts, e.g., the number of times that each branch of an olfactometer was chosen, the number of times that upwind flight was observed, the number of eggs deposited on test or control substrates, or the number of times that test or control feeding substrates were selected. Such data often are distributed following a Poisson distribution and can... 

The influence that upwinding has on the numerical predictions therefore depends not only on the selected numerical mesh, but also on the phase... 

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