Simulação numérica da dinâmica de coliformes fecais no lago Luruaco, Colômbia

Saita, Tatiana Mari; Natti, Paulo Laerte; Cirilo, Eliandro Rodrigues; Romeiro, Neyva Maria Lopes; Candezano, Miguel Antonio Caro; Acuña, Rafael B.; Moreno, Luis

doi:10.5540/tema.2017.018.03.435

Cited by 11 publications

(18 citation statements)

References 11 publications

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“…The first problem relates to the study of the flow between two parallel plates, the second deals with the flow in a square cavity with upper wall moving and the third refers to atherosclerosis. The mesh, for each problem studied, it was generated exactly as described in DE BORTOLI, 2006;SAITA et al 2017). The edges were built by Spline, and the mesh via numerical solution of the grid generation equations.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The metrics enabled mapping of the physical domain for the computational, implying in the perform of the required geometric compensations. In this work we build the mesh as detailed in (CIRILO; DE BORTOLI, 2006;SAITA et al 2017) and the board was obtained via the parametrized Spline method. Moreover, mathematical compensations is also carried out, by chain rule, in the governing equations of the studied physical problem.…”

Section: Curvilinear Governing Equationsmentioning

confidence: 99%

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A numerical model based on the curvilinear coordinate system for the MAC method simplified

Cirilo

Barba

Natti

et al. 2018

Semin., Scienc. Exact Technol.

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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 (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 (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.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Curvilinear Governing Equationsmentioning

confidence: 99%

A numerical model based on the curvilinear coordinate system for the MAC method simplified

Cirilo

Barba

Natti

et al. 2018

Semin., Scienc. Exact Technol.

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“…Note that the resolution of the complex linear system can be performed by other procedures, such as Cholesky decomposition, conjugate gradient, tridiagonal matrix algorithm (TDMA), modified strongly implicit procedure (MSI), among others. We chose the Relaxation Gauss-Seidel method because of its mathematical simplicity and easy computational implementation ( Smith, 2004;Sperandio, Mendes, & Monken, 2006;Romeiro, Castro, Cirilo, & Natti, 2011;Ferreira et al, 2012;Pardo, Natti, Romeiro, & Cirilo, 2011;Ladeia, Romeiro, Natti, & Cirilo, 2013;Saita et al, 2017;Romeiro, Mangili, Costanzi, Cirilo, & Natti, 2017;Cirilo, Barba, Romeiro, & Natti, 2018;Cirilo, Petrovskii, Romeiro, & Natti, 2019;Agrawal, 2019). We show that our procedure converges.…”

Section: Numerical Model For the Propagation Of Solitons In Optical Fibersmentioning

confidence: 99%

Numerical stability of solitons waves through splices in quadratic optical media

et al. 2020

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The propagation of soliton waves is simulated through splices in quadratic optical media, in which fluctuations of dielectric parameters occur. A new numerical scheme was developed to solve the complex system of partial differential equations (PDE) that describes the problem. Our numerical approach to solve the complex problem was based on the mathematical theory of Taylor series of complex functions. In this context, we adapted the Finite Difference Method (FDM) to approximate derivatives of complex functions and resolve the algebraic system, which results from the discretization, implicitly, by means of the relaxation Gauss-Seidel method. The mathematical modeling of local fluctuations of dielectric properties of optical media was performed by Gaussian functions. By simulating soliton wave propagation in optical fibers with Gaussian fluctuations in their dielectric properties, it was observed that the perturbed soliton numerical solution presented higher sensitivity to fluctuations in the dielectric parameter β, a measure of the nonlinearity intensity in the fiber. In order to verify whether the fluctuations of β parameter in the splices of the optical media generate unstable solitons, the propagation of a soliton wave, subject to this perturbation, was simulated for large time intervals. Considering various geometric configurations and intensities of the fluctuations of parameter β, it was found that the perturbed soliton wave stabilizes, i.e., the amplitude of the wave oscillations decreases as the values of propagation distance increases. Therefore, the propagation of perturbed soliton wave presents numerical stability when subjected to local Gaussian fluctuations (perturbations) of the dielectric parameters of the optical media.

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“…Different techniques have been used for the representation of domains of irregular regions, such as structured and unstructured meshes, generalized or hybrid meshes, among other techniques, that have advantages and disadvantages in terms of flexibility and ability to represent objects under study (THOMPSON et al, 1985;THOMPSON et al, 1997;THOMPSON et al, 1998;MALISKA, 2004;BORTOLI, 2006;KOOMULLIL et al, 2008;LAIPING et al, 2013;SAITA et al, 2017;BELINELLI et al, 2020;MAGANIN et al, 2020;ROMEIRO et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

“…Mathematically, any geometry, described in Cartesian system, can be transformed into a generalized system, allowing better adaptation in computational modeling BORTOLI, 2006;MALISKA, 2004;ROMEIRO et al, 2011;PARDO et al, 2012;SAITA et al, 2017;ROMEIRO et al, 2017;CIRILO et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional mesh generator and quality analysis of elements on the curvilinear coordinates system

et al. 2021

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Through mathematical models, it is possible to turn a problem of the physical domain to the computational domain. In this context, the paper presents a two-dimensional mesh generator in generalized coordinates, which uses the parametric linear spline method and partial differential equations. The generator is automated and able to treat real complex domains and, consequently, more realistic problems. However, there is a possibility that lower quality elements may be introduced into the computational mesh. Thus, metrics are investigated that identify elements considered to be of lower quality. Experiments are carried out to verify the efficiency of the adopted metrics, considering meshes with single block, and multi-blocks. According to the experiments, the work allowed the detection of elements of lower quality, contributing to the realization of an adequate modeling of geometries

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Simulação numérica da dinâmica de coliformes fecais no lago Luruaco, Colômbia

Cited by 11 publications

References 11 publications

A numerical model based on the curvilinear coordinate system for the MAC method simplified

A numerical model based on the curvilinear coordinate system for the MAC method simplified

Numerical stability of solitons waves through splices in quadratic optical media

Two-dimensional mesh generator and quality analysis of elements on the curvilinear coordinates system

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