A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Analysis of the accumulated energy by thermal stratification of liquid inside storage tanks with porous layers

A mathematical model was developed in order to study the behavior of thermal stratification of liquid in a typical storage tank with porous medium. The model employs a transient stream function-vorticity formulation to predict the development of stream function and temperature fields in a charging process. Parameters analyzed include Biot, Darcy, Reynolds and Richardson numbers, position, and the thickness of the porous medium. The results show the influence of these physical parameters that should be considered for a good design of storage tanks with thermal stratification.

A generalized alternating-direction implicit scheme for incompressible magnetohydrodynamic viscous flows at low magnetic Reynolds number

This paper presents numerical simulations of incompressible fluid flows in the presence of a magnetic field at low magnetic Reynolds number. The equations governing the flow are the Navier-Stokes equations of fluid motion coupled with Maxwell's equations of electromagnetics. The study of fluid flows under the influence of a magnetic field and with no free electric charges or electric fields is known as magnetohydrodynamics. The magnetohydrodynamics approximation is considered for the formulation of the non-dimensional problem and for the characterization of similarity parameters. A finite-difference technique is used to discretize the equations. In particular, an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows is presented. The discretized conservation equations are solved in stream function-vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient in simulating low Reynolds number and magnetic Reynolds number problems. Numerical results demonstrating the applicability of this technique are also presented. The simulation of incompressible magneto hydrodynamic fluid flows is illustrated by numerical solution for two-dimensional cases. (c) 2007 Elsevier B.V. All rights reserved.

Aplicação da técnica de elementos finitos na estratificação de armazenadores térmicos com barreiras de meios porosos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some experiments with high order compact methods using a computer algebra software - Part II (non-uniform grid)

We generalize a procedure proposed by Mancera and Hunt [P.F.A. Mancera, R. Hunt, Some experiments with high order compact methods using a computer algebra software-Part 1, Appl. Math. Comput., in press, doi: 10.1016/j.amc.2005.05.015] for obtaining a compact fourth-order method to the steady 2D Navier-Stokes equations in the streamfunction formulation-vorticity using the computer algebra system Maple, which includes conformal mappings and non-uniform grids. To analyse the procedure we have solved a constricted stepped channel problem, where a fine grid is placed near the re-entrant corner by transformation of the independent variables. (c) 2006 Elsevier B.V. All rights reserved.

Stability and Local Toxicity Evaluation of a Liposomal Prilocaine Formulation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pharmacological and local toxicity studies of a liposomal formulation for the novel local anaesthetic ropivacaine

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Different criteria of feed formulation for broilers aged 43 to 49 days

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

PLGA nanoparticles containing praziquantel: effect of formulation variables on size distribution

Praziquantel has been shown to be highly effective against all known species of Schistosoma infecting humans. Spherical nanoparticulate drug carriers made of poly(D,L-lactide-co-glycolide) acid with controlled size were designed. Praziquantel, a hydrophobic molecule, was entrapped into the nanoparticles with theoretical loading varying from 10 to 30% (w/w). This investigates the effects of some process variables on the size distribution of nanoparticles prepared by emulsion-solvent evaporation method. The results show that sonication time, PLGA and drug amounts, PVA concentration, ratio between aqueous and organic phases, and the method of solvent evaporation have a significant influence on size distribution of the nanoparticles. (C) 2004 Elsevier B.V. All rights reserved.

Evaluation of the performance of a castor-oil based formulation in limiting pesticide residues in strawberry crops

A study was made to evaluate the effect of a castor oil-based detergent on strawberry crops treated with different classes of pesticides, namely deltamethrin, folpet, tebuconazole, abamectin and mancozeb, in a controlled environment. Experimental crops of greenhouse strawberries were cultivated in five different ways with control groups using pesticides and castor oil-based detergent. The results showed that the group 2, which was treated with castor oil-based detergent, presented the lowest amount of pesticide residues and the highest quality of fruit produced.

Notes on Newton-Euler formulation of robotic manipulators

The equations corresponding to Newton-Euler iterative method for the determination of forces and moments acting on the rigid links of a robotic manipulator are given a new treatment using composed vectors for the representation of both kinematical and dynamical quantities. It is shown that Lagrange equations for the motion of a holonomic system are easily found from the composed vectors defined in this note. Application to a simple model of an industrial robot shows that the method developed in these notes is efficient in solving the dynamics of a robotic manipulator. An example is developed, where it is seen that with the application of appropriate control moments applied to each arm of the robot, starting from a given initial position, it is possible to reach equilibrium in a final pre-assigned position.

Analysis of the Coupled Stretching-Bending Problem of Stiffened Plates by a BEM Formulation Based on Reissner's Hypothesis

In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.

A BEM formulation for analysing the coupled stretching-bending problem of plates reinforced by rectangular beams with columns defined in the domain

In this work, a boundary element formulation to analyse plates reinforced by rectangular beams, with columns defined in the domain is proposed. The model is based on Kirchhoff hypothesis and the beams are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The presented boundary element method formulation is derived by applying the reciprocity theorem to zoned plates, where beams are treated as thin sub-regions with larger rigidities. The integral representations derived for this complex structural element consider the bending and stretching effects of both structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed, being the bending tractions eliminated along interfaces. The in-plane tractions and the bending and in-plane displacements are approximated along the beam width, reducing the number of degrees of freedom. The columns are introduced into the formulation by considering domain points where tractions can be prescribed. Some examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with other numerical solutions.

Electrical load forecasting formulation by a fast neural network

The objective of this work is to develop a methodology for electric load forecasting based on a neural network. Here, backpropagation algorithm is used with an adaptive process that based on fuzzy logic and using a decaying exponential function to avoid instability in the convergence process. This methodology results in fast training, when compared to the conventional formulation of backpropagation algorithm. The results are presented using data from a Brazilian Electric Company, and shows a very good performance for the proposal objective.