A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier-Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110: 171-186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199-210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright (c) 2006 John Wiley & Sons, Ltd.

Numerical assessment of mass conservation on a MAC-type method for viscoelastic free surface flows

A numerical study of mass conservation of MAC-type methods is presented, for viscoelastic free-surface flows. We use an implicit formulation which allows for greater time steps, and therefore time marching schemes for advecting the free surface marker particles have to be accurate in order to preserve the good mass conservation properties of this methodology. We then present an improvement by using a Runge-Kutta scheme coupled with a local linear extrapolation on the free surface. A thorough study of the viscoelastic impacting drop problem, for both Oldroyd-B and XPP fluid models, is presented, investigating the influence of timestep, grid spacing and other model parameters to the overall mass conservation of the method. Furthermore, an unsteady fountain flow is also simulated to illustrate the low mass conservation error obtained.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

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

Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

Numerical simulation of viscous three-dimensional flow over aerospace vehicles using Euler/boundary-layer zonal approach

This paper presents a viscous three-dimensional simulations coupling Euler and boundary layer codes for calculating flows over arbitrary surfaces. The governing equations are written in a general non orthogonal coordinate system. The Levy-Lees transformation generalized to three-dimensional flows is utilized. The inviscid properties are obtained from the Euler equations using the Beam and Warming implicit approximate factorization scheme. The resulting equations are discretized and approximated by a two-point fmitedifference numerical scheme. The code developed is validated and applied to the simulation of the flowfield over aerospace vehicle configurations. The results present good correlation with the available data.

Three-dimensional transient complex free surface flows: Numerical simulation of XPP fluid

In this paper we present a finite difference MAC-type approach for solving three-dimensional viscoelastic incompressible free surface flows governed by the eXtended Pom-Pom (XPP) model, considering a wide range of parameters. The numerical formulation presented in this work is an extension to three-dimensions of our implicit technique [Journal of Non-Newtonian Fluid Mechanics 166 (2011) 165-179] for solving two-dimensional viscoelastic free surface flows. To enhance the stability of the numerical method, we employ a combination of the projection method with an implicit technique for treating the pressure on the free surfaces. The differential constitutive equation of the fluid is solved using a second-order Runge-Kutta scheme. The numerical technique is validated by performing a mesh refinement study on a pipe flow, and the numerical results presented include the simulation of two complex viscoelastic free surface flows: extrudate-swell problem and jet buckling phenomenon. © 2013 Elsevier B.V.

Técnica para dedução do modelo algébrico PTT, aplicações e análises numéricas em escoamentos bidimensionais

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

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Digestibility and metabolizable energy of maize gluten feed for dogs as measured by two different techniques

Maize gluten feed (MGF) is a co-product of wet milling of maize, and is composed of structures that remain after most starch, gluten and germ has been extracted from the grain. Although currently used in dog foods, its digestibility and energy values have not been documented. Two techniques were used to determine nutrient digestibility of MGF for dog foods. Both techniques used extruded diets fed to Beagle dogs, with six replicates per diet. The first study used a difference method in which 300 g/kg of a reference diet was replaced by MGF. Based on the difference method, the coefficient of total tract apparent digestibility (CTTAD) of MGF was 0.53 for dry matter (DM), 0.69 for crude protein (CP), 0.74 for fat, 0.99 for starch, and 0.55 for gross energy (GE). The calculated metabolizable energy (ME) of MGF was 7.99 MJ/kg (as-fed). The second study used a regression method and included a basal diet and a basal diet with 70, 140 and 210 g MGF/kg of diet (as a substitute for maize starch). Maize gluten feed inclusion resulted in a linear reduction of CTTAD of DM (R(2)=0.99; P<0.001), CP (R(2)=0.95; P=0.002), fat (R(2)=0.87; P=0.009). starch (R(2)=0.81; P<0.001), and GE (R(2)=0.99; P<0.001). Faecal production increased linearly from 56 g to 107 g/dog/d (R(2)=0.99; P<0.001), with a linear reduction of faecal DM (R(2)=0.99: P<0.001) and a linear increase in faecal lactic acid concentration (P<0.02). Both urine (R(2)=0.77; P=0.029) and faeces (R(2)=0.92: P=0.019) showed a linear reduction in pH. Results of ingredient MAD obtained by the regression and difference methods were close (6% or less of variation) for CP, fat, and starch, and also for ME content (1.4% higher for the difference method), but the two methods disagreed on calculated CTTAD of DM and organic matter. The high dietary fiber content of MGF (382 g/kg) may explain the low digestibility of this ingredient. Maize gluten feed could be a useful ingredient for formulations designed to have low energy or reduce the urine pH of dogs. (C) 2011 Elsevier B.V. All rights reserved.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. and third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

Critical points in logistic growth curves and treatment comparisons

Several biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the maintenance of a less productive phase results in uneconomical activity. In this report we present methods of determining critical points in logistic functions that separate the early stages of growth from the asymptotic phase, with the aim of establishing a stopping critical point in the growth and on this basis determine differences in treatments. The logistic growth model is fitted to experimental data of imbibition of arariba seeds (Centrolobium tomentosum). To determine stopping critical points the following methods were used: i) accelerating growth function, ii) tangent at the inflection point, iii) segmented regression; iv) modified segmented regression; v) non-significant difference; and vi) non-significant difference by simulation. The analysis of variance of the abscissas and ordinates of the breakpoints was performed with the objective of comparing treatments and methods used to determine the critical points. The methods of segmented regression and of the tangent at the inflection point lead to early stopping points, in comparison with other methods, with proportions ordinate/asymptote lower than 0.90. The non-significant difference method by simulation had higher values of abscissas for stopping point, with an average proportion ordinate/asymptote equal to 0.986. An intermediate proportion of 0.908 was observed for the acceleration function method.

Effective diffusion coefficients behavior in osmotic dehydration of apple slices considering shrinking and local concentration dependence

The mass transfer during osmotic dehydration of apple slices immersed in 40, 50 and 60% (w/w) aqueous sucrose solutions was investigated to evaluate the influence of solution concentration on diffusivities. In the mathematical model, the diffusion coefficients were functions of the local water and sucrose concentration. The mass transfer equations were, simultaneously, solved for water and sucrose using an implicit numerical method. Material coordinates following the shrinkage of the solid were used. The predicted concentration profiles were integrated and compared to experimental data, showing a reasonable agreement with the measured data. on average, the effective diffusion coefficients for water and sucrose decreased as the osmotic solution concentration increased; that is the behavior of the binary coefficients in water-sucrose solutions. However, the diffusivities expressed as a function of the local concentration in the slices varied between the treatments. Water diffusion coefficients showed a remarkable variation throughout the slice and unusual behavior, which was associated to the cellular structure changes observed in tissue immersed in osmotic solutions. Cell structure changes occurred in different ways: moderate plasmolysis at 40%, accentuated plasmolysis at 50% and generalized damage of the cells at 60%. Intact vacuoles were observed after a long time of exposure (30 h) to 40 and 50% solutions. Effects of the concentration on tissue changes make it difficult to generalize the behavior of diffusion coefficients.

Nutrient digestibility of degermed, dehulled corn, citrus pulp, and soy protein concentrate by barrows

This study was carried out to determine apparent ileal digestibility (AID) and apparent total tract digestibility (ATTD) of DM, CP, GE, and their respective digestible content of degermed dehulled corn (Zea mays), citrus pulp, and soy (Glycine max) protein concentrate by pigs using the difference method. Thirty-two barrows (28.1 +/- 1.6 kg of BW) were fed a corn-soybean meal basal diet or 1 of 3 diets formulated by replacing 30% of the basal diet with 30% of 1 of the test feedstuffs for 11 d. Chromic oxide (0.3%) was included in the diets. Feces were collected from days 7 to 11 by grab sampling and ileal digesta were collected after pigs were slaughtered on day 12. The AID of DM and AID and ATTD of GE of degermed corn (77.4, 88.7, and 77.7%) were greater (P < 0.05) than those observed in citrus pulp (50.3, 86.5, and 55.8%) and in soy protein concentrate (63.5, 85.1, and 59.4%), which did not differ (P > 0.05). The ATTD of CP, total digestible CP, and total DE of soy protein concentrate (87.5%, 500 g/kg, and 3739 kcal/kg) were higher (P < 0.05) than the values in degermed corn (81.7%, 57.5 g/kg, and 3330 kcal/kg), which were greater (P < 0.05) than those in citrus pulp (60.5%, 39.5 g/kg, and 3223 kcal/kg). Total and ileal digestible DM, AID of CP, and ileal DE of degermed corn (782 g/kg, 673 g/kg, 70.7%, and 2913 kcal/kg) and soy protein concentrate (778 g/kg, 570 g/kg, 78.7%, and 2878 kcal/kg) were similar (P > 0.05) and greater (P < 0.05) than those in citrus pulp (737 g/kg, 436 g/kg, 50.6%, and 2081 kcal/kg). Ileal digestible CP of degermed corn (49.8 g/kg) and citrus pulp (33.0 g/kg) did not differ (P > 0.05) but were smaller (P < 0.05) than the value found in soy protein concentrate (434 g/kg). The DM and energy from degermed corn are more efficiently digested by the pig than those from soy protein concentrate and citrus pulp. Soy protein concentrate was the best protein source evaluated in this study.

Optimization procedures in the design of continuous induction hardening and tempering installations for magnetic steel bars

An inverse problem concerning the industrial process of steel bars hardening and tempering is considered. The associated optimization problem is formulated in terms of membership functions and, for the sake of comparison, also in terms of quadratic residuals; both geometric and electromagnetic design variables have been considered. The numerical solution is achieved by coupling a finite difference procedure for the calculation of the electromagnetic and thermal fields to a deterministic strategy of minimization based on modified Flctcher and Reeves method. © 1998 IEEE.