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In this work, a review of the theoretical aspects and an assessment to validate a Computational Fluid Dynamics (CFD) opensource code for applications in aerospace problems are discussed. !e code uses a "nite volume method, with cell-centered implementation, and it is suitable for simulations of inviscid, laminar, and turbulent #ows. !e code considers two-dimensional cases with unstructured meshes and employs the turbulence model known as Spalart-Allmaras. !e implementation is detailed presenting the spatial discretization, including the upwind scheme, the linear reconstruction algorithm, and the calculation applying the method of gradients. !e temporal discretization considers the application of a multistage explicit algorithm using a 5 stages Runge-Kutta method. !e validation was done considering three cases of study: the inviscid shock tube, the laminar #at plate, and the #ow over a rocket fairing. !ese cases are simulated using the so$ware developed and the results are compared with analytical and experimental results. !e rocket fairing case is related to the analysis of the Brazilian VLS launch during its transonic #ight and it exempli"es the e%ect of the shock wave/boundary-layer interaction in its pressure distribution. !e simulation results present a good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

This work presents the application of a scalar finite element formulation for [E.sup.x] (TE-like) modes in anisotropic planar and channel waveguides with diagonal permittivity tensor, diffused in both transversal directions. This extended formulation considers explicitly both the variations of the refractive index and their spatial derivates inside of each finite element. Dispersion curves for [E.sup.x] modes in planar and channel waveguides are shown, and the results compared with solutions obtained by other formulations. Index terms - Finite element methods, nonhomogeneously loaded waveguides, optical strip waveguides, anisotropic media.

A MATHEMATICA notebook to compute the elements of the matrices which arise in the solution of the Helmholtz equation by the finite element method (nodal approximation) for tetrahedral elements of any approximation order is presented. The results of the notebook enable a fast computational implementation of finite element codes for high order simplex 3D elements reducing the overheads due to implementation and test of the complex mathematical expressions obtained from the analytical integrations. These matrices can be used in a large number of applications related to physical phenomena described by the Poisson, Laplace and Schrodinger equations with anisotropic physical properties. Index terms - Helmholtz equations, finite element methods, anisotropic media, software tools.

A procedure to model optical diffused-channel waveguides is presented in this work. The dielectric waveguides present anisotropic refractive indexes which are calculated from the proton concentration. The proton concentration inside the channel is calculated by the anisotropic 2D-linear diffusion equation and converted to the refractive indexes using mathematical relations obtained from experimental data. The arbitrary refractive index profile is modeled by a nodal expansion in the base functions. The TE and TM-like propagation properties (effective index) and the electromagnetic fields for well-annealed proton-exchanged (APE) [LiNbO.sub.3] waveguides are computed by the finite element method. Index terms - Finite element methods, nonhomogeneously loaded waveguides, optical strip waveguides, anisotropic media, diffusion processes.

LMAG-2D is an educational Finite-Element Analysis software package with CAD/CAE technology used to teach the finite element method to undergraduate and graduate students of electrical engineering. A user-friendly interface encapsulates the technical complexity of the method, allowing students and professionals, even in their first contact with this methodology, to appreciate its relevance to practical problems. LMAG-2D can be used to simulate complex two dimensional 'real-world' electrostatic, magnetostatic and electrokinetic models, with planar and axial symmetries. Linear and nonlinear phenomena can also be simulated.

In a periodic structure, the magnetic flux density profile of a hybrid undulator depends strongly on the characteristics of its permanent magnets. A simple procedure to select the best permanent magnets for periodic magnetic structures is presented here. We used a very simple apparatus for the magnetic field measurements. We tested by assembling periodic structure prototypes formed by brick-shaped permanent magnets. Index Terms--Free electron lasers, periodic structures, permanent magnets, undulators.