SUMMARYThe main features of a numerical model aiming at predicting the drift of ions in electrolytic solutions are presented. The mechanisms of ionic di usion are described by solving the Nernst-Planck system of equations. The electrical coupling between the various ionic uxes is accounted for by the Poisson equation. Two algorithms using the ÿnite element method for spatial discretization are compared for simple test cases. One is based on the Picard iteration method while the other is based on the Newton-Raphson scheme. Test results clearly indicate that the range of application is broader for the algorithm based on the Newton-Raphson method. Selected examples of the application of the algorithm to more complex 1-D and 2-D cases are given.
Scale-dependent influence of environmental complexity has become a central issue in ecology. We quantified the impact of artificial reefs on community characteristics (biomass, density) and on individual mussel growth, and we tested the relative importance of physical processes (i.e. flow velocity, substratum temperature) as intermediate factors mediating the scale-dependent influence of topographic heterogeneity on benthic communities. Twelve concrete reefs (cylinders) of 3 different sizes (52, 76 and 115 cm) were placed on randomly selected sites along a rocky intertidal platform. The area around each reef and 4 control sites were divided into 24 sampling cells (6 orientation and 4 distance categories). Hydrodynamic patterns around reefs and control sites were determined using the dissolution of plaster cylinders. Flow velocity was simulated around reefs using a finite-element hydrodynamic model. Substratum temperature was also measured. The biomass and density of benthic community adjacent to the reefs was sampled using 10 × 10 cm quadrats before and 1 yr after installation. Growth of individual Mytilus edulis attached to experimental panels was measured. A flow index revealed a strong scale-dependent gradient of decreasing water motion intensity with distance from the reefs, and the hydrodynamic model showed a reduction of flow velocity on the downstream side of large reefs. Substratum temperature was lower closer to reefs, and shaded areas increased with reef size. Maximum M. edulis biomass was around large reefs, while the biomasses of other dominant species were not positively influenced by reef size. Biomass and density patterns close to the reefs were significant only around large reefs, with the downstream side having the lowest M. edulis biomass. Growth of M. edulis decreased significantly with distance away from the reefs. Biomass patterns were best explained by the flow velocity around the large reefs (R 2 = 0.27), while mussel growth was best correlated with substratum temperature close to the medium reefs (R 2 = 0.66). Our study shows that the spatial structure of the benthic community studied and its scaling with topographic heterogeneity depends on dominant mediating physical factors (i.e. hydrodynamic processes or substratum temperature).
The Colebrook-White equation is often used for calculation of the friction factor in turbulent regimes; it has succeeded in attracting a great deal of attention from researchers. The Colebrook–White equation is a complex equation where the computation of the friction factor is not direct, and there is a need for trial-error methods or graphical solutions; on the other hand, several researchers have attempted to alter the Colebrook-White equation by explicit formulas with the hope of achieving zero-percent (0%) maximum deviation, among them Dejan Brkić and Pavel Praks. The goal of this paper is to discuss the results proposed by the authors in their paper:” Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” and to propose more accurate formulas.
The two dimensional phase change problem was solved using the extended finite element method with a Lagrange formulation to apply the interface boundary condition. The Lagrange multiplier space is identical to the solution space and does not require stabilization. The solid-liquid interface velocity is determined by the jump in heat flux across the i nterface. Two methods to calculate the jump are used and c ompared. The first is based on an averaged temperature gradient near the interface. The second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust and precise.
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