Eliandro Rodrigues Cirilo

Eliandro Rodrigues Cirilo, Alessandra Negrini Dalla Barba, Neyva Maria Lopes Romeiro et al.

In this paper we developed a numerical methodology to study some incompressible fluid flows without free surface, using the curvilinear coordinate system and whose edge geometry is constructed via parametrized spline. First, we discussed the representation of the Navier-Stokes and continuity equations on the curvilinear coordinate system, along with the auxiliary conditions. Then, we presented the numerical method -- a simplified version of MAC (\textit{Marker and Cell}) method -- along with the discretization of the governing equations, which is carried out using the finite differences method and the implementation of the FOU (\textit{First Order Upwind}) scheme. Finally, we applied the numerical methodology to the parallel plates problem, lid-driven cavity problem and atherosclerosis problem, and then we compare the results obtained with those presented in the literature. Keywords: finite differences, simplified MAC, curvilinear coordinates, parallel plates, did-driven cavity, atherosclerosis.

Eliandro Rodrigues Cirilo, Paulo Laerte Natti, Neyva Maria Lopes Romeiro et al.

This work developed a numerical procedure for a system of partial differential equations (PDEs) describing the propagation of solitons in ideal optical fibers. The validation of the procedure was implemented from the numerical comparison between the known analytical solutions of the PDEs system and those obtained by using the numerical procedure developed. It was discovered that the procedure, based on the finite difference method and relaxation Gauss-Seidel method, was adequate in describing the propagation of soliton waves in ideals optical fibers.

Eliandro Rodrigues Cirilo, Paulo Laerte Natti, Neyva Maria Lopes Romeiro et al.

In this work, considering a numerical procedure developed to solve a system of coupled nonlinear complex differential equations, which describes the solitons propagation in dielectric optical fibers, we optimize the numerical processing time, in relation to the relaxation parameter of the procedure, for relevant groups of values of the dielectric variables of the optic fiber. Key-words: optical soliton, processing time, optimization.

T. M. Saita, P. L. Natti, E. R. Cirilo et al.

The Luruaco Lake located in the Department of Atlántico, Colombia, is damaged by the discharge of untreated sewage, bringing risks to the health of all who use its waters. The present study aims to perform the numerical simulation of the concentration dynamics of fecal coliforms in the lake. The simulation of the hydrodynamic flow is carried out by means of a two-dimensional horizontal (2DH) model, given by a Navier-Stokes system. The simulation of fecal coliform transport is described by a convective-dispersive-reactive equation. These equations are solved numerically by the Finite Difference Method (FDM) and the Mark and Cell (MAC) method, in generalized coordinates. Regarding the construction of the computational mesh of the Luruaco Lake, the cubic spline and multiblock methods were used. The results obtained in the simulations allow a better understanding of the dynamics of fecal coliforms in the Luruaco Lake, showing the more polluted regions. They can also advise public agencies on identifying the emitters of pollutants in the lake and on developing an optimal treatment for the recovery of the polluted environment.

Neyva Maria Lopes Romeiro, Eliandro Rodrigues Cirilo, Paulo Laerte Natti

This work proposes a mathematical model on the water quality for Igapó I Lake, located in Londrina, Paraná. A qualitative analysis on the pollution of the lake is carried out through numerical simulations which provide informations for the understanding of the processes involved. For the hydrodynamic flow of the lake, a horizontal two-dimensional model is considered. The hydrodynamic velocity field is simulated by the Navier-Stokes and pressure equations, supposing an incompressible newtonian fluid. This hydrodynamic velocity field is inserted in the reactive-transport model. The reactive part of this model considers only the carbon-nitrogen cycle, described by the QUAL2E model. A qualitative and quantitative analysis of the numerical simulations conducted in function of the deficit of dissolved oxygen, of the biochemical oxygen demand and of the load of pollutants provided a better understanding of the hydrology and of the water quality in the Igapó I Lake.