Estaner Claro Romão

Numerical Simulation of Diffusive Processes in Heated Cylinder Using the Finite Volume and Finite Difference Methods

A comparative investigation of a series of numerical tests in the solution of heat transfer problems in the heated cylinder using radiation is presented. The numerical application, in steady state and cylindrical coordinates is studied through of Finite Volume and Finite Difference Methods. The numerical temperature profiles were compared with the analytical solution.

Efficient Alternative for Construction of the Linear System Stemming from Numerical Solution of Heat Transfer Problems via FEM

This paper proposes an efficient alternative to construction of the linear system coming from a solution via the Finite Element Method that is able to significantly decrease the time of construction of this system. From the presentation of the methodology used and a numerical application it will be clear that the purpose of this work is to be able to decrease 6-7 times (on average) the linear system building time.

3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

Efficiency of Solution Methods for Kepler’s Equation

This article discusses, in the case of eccentric orbits, some solution methods for Keplers equation, for instance: Newtons method, Halley method and the solution by Fourire-Bessel expansion. The efficiency of solution methods is evaluated according to the number of iterations that each method needs to lead to a solution within the specified tolerance. The solution using Fourier-Bessel series is not an iterative method, however, it was analyzed the number of terms required to achieve the accuracy of the prescribed solution.

Numerical Simulation by FDM of Unsteady Heat Transfer in Cylindrical Coordinates

In this paper the heat transfer problem in transient and cylindrical coordinates will be solved by the Crank-Nicolson method in conjunction the Finite Difference Method. To validate the formulation will study the numerical efficiency by comparisons of numerical results compared with two exact solutions.

3D Unsteady Heat Transfer in Multi-Connected Domains via LSFEM: A Case Study

This paper aims in particular to do a case study of the numerical efficiency of the application of LSFEM (Least Squares Finite Element Method) in the solution of heat conduction problems in multi-connected domains. To demonstrate this study two cases (the first with exact solution for comparison of results) are presented in the same multi-connected geometry, of easy construction, to facilitate the comparison of the results of this paper with future studies of other researchers.

3D Unsteady Convection Problems via LSFEM Solver

In this paper, an important study on the application of the α family of temporal discretization is presented. For spatial discretization, the Least Squares Finite Element Method (LSFEM) is used. It is expected that this study can be able to advance several other studies within the domain of numerical simulation of physical problems. It is important to note that for all applications we will use a mesh that is considered gross, with the purpose of presenting a method that is robust, precise and mainly computationally economic.

3D Unsteady Convection-Diffusion-Reaction via GFEM Solver

In this paper, an important study on the application of the α family of temporal discretization is presented. For spatial discretization the Galerkin Method (GFEM) was used. With the variation of the α coefficient in temporal discretization and through one numerical applications with exact solution, it will be possible to have an initial idea on how each one of the two suggested methods behaves. It is expected that this study can be able to advance several other studies within the domain of numerical simulation of physical problems. It is important to note that for all applications we will use a mesh that is considered gross, with the purpose of presenting a method that is robust, precise and mainly computationally economic.

Catastrophic Results for Equipment and Machine Driving Systems when High Impact during Operation Occurs

Energy is vital to machines and equipment basic functioning. On the other hand, it has an ambiguity determined by its detrimental side under other circumstances. This paper aims to present a review of simple laws of physics / mechanics in order to understand some benefits of using such energies (kinetic and potential energies), in order to process products or generating movement (mechanical energy). However, also shows its damaging side for driving systems, where such energies may generate catastrophes, usually due to high impacts. This last, which destroys complete or partial systems due to the absence of any robust / preventive protection. There is a safety manner (solution) to protect the systems, described along the text.

An Efficient Technique of Linearization towards Fourth Order Finite Differences for Numerical Solution of the 1D Burgers Equation

This work aims to solve the 1D Burgers equation, which represents a simplification of the Navier-Stokes equation, supposing the yielding only at x-direction and without pressure gradient. For such a solution, an implicit scheme (Cranck-Nicolson method) with a fourth order precision in space is utilized. The main contribution of this work is the application of a linearization technique of the non-linear term (advective term), and then, towards the analytical and numerical results from literature, validate and demonstrate it as being highly satisfactory.