Luiz Felipe Mendes de Moura

Galerkin and Least Squares Methods to Solve a 3D Convection–Diffusion–Reaction Equation with Variable Coefficients

This study addresses how to implement the Galerkin finite element and least square finite element methods using auxiliary equations to solve the partial differential equation numerically, which models the convection–diffusion–reaction, set on a steady 3D domain. In the spatial discretization, hexahedral elements with eight (linear element) and 27 (quadratic element) nodes were used, in which Lagrange interpolation functions were adopted in local coordinates. Turning all the formulation of the problem of global coordinates into local coordinates, the Gauss–Legendre quadrature method was used to integrate coefficients of the element matrices numerically. In addition to the formulation by the two methods, a computer code was implemented to simulate the phenomenon proposed. By using analytical solutions, sundry numerical error analysis was performed from L2 norm (domain–average error) and L∞ norm (domain–top error), thus validating the numerical results. A real case is proposed and assessed.

A CONTROL-VOLUME FINITE-ELEMENT METHOD (CVFEM) FOR UNSTEADY, INCOMPRESSIBLE, VISCOUS FLUID FLOWS

A control-volume finite-element method (CVFEM), to simulate unsteady, incompressible, and viscous fluid flows, using nine-noded quadrilateral elements, has been developed. The Navier-Stokes equations in primitive variables u-v-p are the mathematical model of the flows. A technique of upwind, known as MAW, Mass-Weighted Interpolation, was extended for the finite element employed in this work. The set of nonlinear partial differential equations was integrated, and after using interpolation functions and time discretization, the algebraic system of equations was solved by using the frontal method of solution. Results obtained for some benchmark problems compared favorably with available results from the literature.A control-volume finite-element method (CVFEM), to simulate unsteady, incompressible, and viscous fluid flows, using nine-noded quadrilateral elements, has been developed. The Navier-Stokes equations in primitive variables u-v-p are the mathematical model of the flows. A technique of upwind, known as MAW, Mass-Weighted Interpolation, was extended for the finite element employed in this work. The set of nonlinear partial differential equations was integrated, and after using interpolation functions and time discretization, the algebraic system of equations was solved by using the frontal method of solution. Results obtained for some benchmark problems compared favorably with available results from the literature.

NUMERICAL SIMULATION of CONVECTION-DIFFUSION PROBLEMS BY THE CONTROL-VOLUME-BASED FINITE-ELEMENT METHOD

This work presents a numerical study of the tri-dimensional convection-diffusion equation by the control-volume-based on finite-element method using quadratic hexahedral elements. Considering that the equation governing this problem in its main variable may represent several properties, including temperature, turbulent kinetic energy, viscous dissipation rate of the turbulent kinetic energy, specific dissipation rate of the turbulent kinetic energy, or even the concentration of a contaminant in a given medium, among others, the wide applicability of this problem is thus evidenced. Three cases of temperature distributions will be studied specifically in this work, in addition to one case of pollutant dispersion upon analysis of the concentration of a contaminant in a fixed flow point. Some comparisons will be carried out against works found in the open literature, while others will be done according to each phenomenon characteristics.

A high frequency electronic transducer for multiphase flow measurements

This paper describes an electronic transducer for multiphase flow measurement. Its high sensitivity, good signal to noise ratio and accuracy are achieved through an electrical impedance sensor with a special guard technique. The transducer consists of a wide bandwidth and high slew rate differentiator where the lead inductance and stray capacitance effects are compensated. The sensor edge effect is eliminated by using a guard electrode based on the virtual ground potential of the operational amplifier. A theoretical modeling and a calibration method are also presented. The results obtained seem to confirm the validity of the proposed technique.

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.