Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Numerical study of the atmospheric flow over a coastal cliff

This work presents a numerical method suitable for the study of the development of internal boundary layers (IBL) and their characteristics for flows over various types of coastal cliffs. The IBL is an important meteorological occurrence for flows with surface roughness and topographical step changes. A two-dimensional flow program was used for this study. The governing equations were written using the vorticity-velocity formulation. The spatial derivatives were discretized by high-order compact finite differences schemes. The time integration was performed with a low storage fourth-order Runge-Kutta scheme. The coastal cliff (step) was specified through an immersed boundary method. The validation of the code was done by comparison of the results with experimental and observational data. The numerical simulations were carried out for different coastal cliff heights and inclinations. The results show that the predominant factors for the height of the IBL and its characteristics are the upstream velocity, and the height and form (inclination) of the coastal cliff. Copyright (C) 2010 John Wiley & Sons, Ltd.

A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Comparison of two extraction methods for evaluation of volatile constituents patterns in commercial whiskeys: Elucidation of the main odour-active compounds

An analytical procedure based on manual dynamic headspace solid-phase microextraction (HS-SPME) method and the conventional extraction method by liquid–liquid extraction (LLE), were compared for their effectiveness in the extraction and quantification of volatile compounds from commercial whiskey samples. Seven extraction solvents covering a wide range of polarities and two SPME fibres coatings, has been evaluated. The highest amounts extracted, were achieved using dichloromethane (CH2Cl2) by LLE method (LLECH2Cl2)(LLECH2Cl2) and using a CAR/PDMS fibre (SPMECAR/PDMS) in HS-SPME. Each method was used to determine the responses of 25 analytes from whiskeys and calibration standards, in order to provide sensitivity comparisons between the two methods. Calibration curves were established in a synthetic whiskey and linear correlation coefficient (r ) were greater than 0.9929 for LLECH2Cl2LLECH2Cl2 and 0.9935 for SPMECAR/PDMS, for all target compounds. Recoveries greater than 80% were achieved. For most compounds, precision (expressed by relative standard deviation, R.S.D.) are very good, with R.S.D. values lower than 14.78% for HS-SPME method and than 19.42% for LLE method. The detection limits ranged from 0.13 to 19.03 μg L−1 for SPME procedure and from 0.50 to 12.48 μg L−1 for LLE. A tentative study to estimate the contribution of a specific compound to the aroma of a whiskey, on the basis of their odour activity values (OAV) was made. Ethyl octanoate followed by isoamyl acetate and isobutyl alcohol, were found the most potent odour-active compounds.

Desenvolvimento de esquema de controle com realimentação visual para um robô manipulador

This work proposes a kinematic control scheme, using visual feedback for a robot arm with five degrees of freedom. Using computational vision techniques, a method was developed to determine the cartesian 3d position and orientation of the robot arm (pose) using a robot image obtained through a camera. A colored triangular label is disposed on the robot manipulator tool and efficient heuristic rules are used to obtain the vertexes of that label in the image. The tool pose is obtained from those vertexes through numerical methods. A color calibration scheme based in the K-means algorithm was implemented to guarantee the robustness of the vision system in the presence of light variations. The extrinsic camera parameters are computed from the image of four coplanar points whose cartesian 3d coordinates, related to a fixed frame, are known. Two distinct poses of the tool, initial and final, obtained from image, are interpolated to generate a desired trajectory in cartesian space. The error signal in the proposed control scheme consists in the difference between the desired tool pose and the actual tool pose. Gains are applied at the error signal and the signal resulting is mapped in joint incrementals using the pseudoinverse of the manipulator jacobian matrix. These incrementals are applied to the manipulator joints moving the tool to the desired pose

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.

Methods and tools for encoding the WordNet.Br sentences, concept glosses, and conceptual-semantic relations

This paper presents the overall methodology that has been used to encode both the Brazilian Portuguese WordNet (WordNet.Br) standard language-independent conceptual-semantic relations (hyponymy, co-hyponymy, meronymy, cause, and entailment) and the so-called cross-lingual conceptual-semantic relations between different wordnets. Accordingly, after contextualizing the project and outlining the current lexical database structure and statistics, it describes the WordNet.Br editing GUI that was designed to aid the linguist in carrying out the tasks of building synsets, selecting sample sentences from corpora, writing synset concept glosses, and encoding both language-independent conceptual-semantic relations and cross-lingual conceptual-semantic relations between WordNet.Br and Princeton WordNet © Springer-Verlag Berlin Heidelberg 2006.

Numerical correction for the diffuse solar irradiance by the melo-escobedo shadowring measuring method

The present paper deals with numerical corrections factors proposed as a function of the clearness index in order to correct the diffuse solar irradiance measured with the Melo-Escobedo Shadowring Measuring Method (ME shadowring). The global irradiance was measured by an Eppley - PSP pyranometer ; direct normal irradiance by an Eppley-NIP pyrheliometer fitted to a ST-3 sun tracking device and the diffuse irradiance by an Eppley-PSP pyranometer fitted to a ME shadowring. The validations were performed by the MBE and RMSE statistical indicators. The results showed that the numerical correction factors were appropriate to correct the shadowring diffuse irradiance.

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.