Numerical simulation of BOD5 dynamics in Igapó I lake, Londrina, Paraná, Brazil: Experimental measurement and mathematical modeling

Romeiro, Neyva Maria Lopes; Mangili, Fernanda Bezerra; Costanzi, Ricardo Nagamine; Cirilo, Eliandro Rodrigues; Natti, Paulo Laerte

doi:10.5433/1679-0375.2017v38n2p50

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…A vertical one-dimensional heat conduction equation depicts the water temperature changes adopting two-step operator-splitting method. Romeiro et al, 2017, analyzed the concentration of biochemical oxygen demand, BOD 5 to evaluate the water quality of the lake. The numerical simulation was done by aid of discretization in curvilinear coordinates of the geometry of lake, combining with FDM and FEM.…”

Section: Pollutant Transport and Resultsmentioning

confidence: 99%

Research on Numerical Modelling in Lake Dynamics

2019

IJITEE

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Lakes are natural water bodies, where flow from single or various rivers is impounded by a natural impediment. Lake water environmental problem has severe effect on human health and the socio-economic sustainable development. So, it's very important to find the more effective way of controlling the water pollution. Dynamics of lakes is the vast topic, which includes important concepts such as circulation of lakes, pollutant transport and interaction between lakes and hydrology. The hydrological dynamics of lake has been influenced by land cover modification, climate change, and increase in population and development activities within the catchment. Due to less velocity, lake impounds water for some time, and a significant characteristic of a lake is its retention time. Wind is the prevalent force in driving the circulation and in developing turbulent mixing in the lakes. Vertical mixing is caused by this turbulence. During circulation, summer and winter has different wind patterns. Strong wind would cause storm surge, which results in increased, mixing and transport in the surface water systems. Air temperature influence surface waters through heat flux and evaporation exchange between the air and the water. The Coriolis force is certain in large lakes due to earth rotation. Precipitation, tributaries inflow, runoffs, etc are lake water inputs. During numerical simulation of lakes, generally Boussinesq approximation and hydrostatic approximation are considered due to actual density distribution variations in water depth concepts respectively. It is essential to calibrate and verify the model before predictive applications anywhere. A simple numerical hydrodynamic model of a lake includes wind stress, bottom friction, Coriolis force, inflow, outflow, and the bottom topography of the lake. The hydrodynamic model has to be tested for stability, convergence, and sensitivity to parameters such as wind shear, wind direction, and vertical eddy viscosity effects. In this paper, the numerical simulation of lake dynamics has been discussed in detail.

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Section: Pollutant Transport and Resultsmentioning

confidence: 99%

Research on Numerical Modelling in Lake Dynamics

2019

IJITEE

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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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