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

Cirilo, Eliandro Rodrigues; Barba, Alessandra Negrini Dalla; Natti, Paulo Laerte; Romeiro, Neyva Maria Lopes

doi:10.5433/1679-0375.2018v39n2p87

Cited by 5 publications

(5 citation statements)

References 17 publications

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“…In numerical model, the equations ( 1)-( 4) are discretized by means of the finite differences method (FDM). The term convective has nonlinearity, so we use the First Order Upwind (FOU) method that provides consistent numerical results for the model (Cirilo et al, 2018).…”

Section: Development Of Mathematical and Numerical Modelmentioning

confidence: 99%

“…The computational code is developed in Fortran 90 language. The hydrodynamic model is calculated using Mark and Cell method (Mckee et al, 2008;Cirilo et al, 2018), generating the velocity field of water flow. Simulation of faecal coliform injection through the three entrances (streams) is then performed separately, which allowed us to analyze the impact of each stream on lake pollution.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…In order to have the analytical mathematical model simulated computationally, the discretization of equations is carried out through the finite difference method (Evans et al, 1999;Fortuna, 2012). Given the dynamic complexity generated by the nonlinear terms of the hydrodynamic model, we use the First Order Upwind method and the Mark and Cell method (MAC) to solve the hydrodynamic model (Mckee et al, 2008;Cirilo et al, 2018). Thus we obtain the velocity fields of water flow, necessary to simulate the transport model of faecal coliforms concentration.…”

Section: Introductionmentioning

confidence: 99%

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A sewage management proposal for Luruaco lake, Colombia

Saita,

Natti,

Cirilo

et al. 2022

Preprint

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This study presents numerical simulations of faecal coliforms dynamics in Luruaco lake, located in Atlántico Department, Colombia. The velocity field is obtained through a twodimensional horizontal (2DH) model of Navier-Stokes equations system. The transport equation of faecal coliforms concentration is provided from a convective-diffusive-reactive equation. The lake's geometry is built through cubic spline and multiblock methods. The discretization method by Finite Differences and the First Order Upwind (FOU) are applied to the 2DH model. The Mark and Cell (MAC) method is used to determine numerically the velocity field of water flow. Numerical simulations are carried out for a 72-hour period in order to understand the influence of faecal coliforms injections from each tributary. From the qualitative and quantitative analysis of the factors that influence faecal coliforms dynamics, proposals are presented, which aims to reduce contamination in some regions of Lake Luruaco. The numerical 1

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Section: Development Of Mathematical and Numerical Modelmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A sewage management proposal for Luruaco lake, Colombia

Saita,

Natti,

Cirilo

et al. 2022

Preprint

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“…Lowercase acronyms are cardinal variations from the center P. As shown in Figure 2, the population densities S 1 and S 2 are calculated at the center of the cell. Note that storage shifted to population densities has a positive impact on numerical computation, reducing numerical instability (CIRILO et al, 2018;FERREIRA et al, 2001;FORTUNA, 2012;GRIEBEL;DORNSEIFER;NEUNHOEFFER, 1998;SAITA et al, 2021).…”

Section: Discretization Of the Telegraph Predator-prey Systemmentioning

confidence: 99%

Numerical convergence of a Telegraph Predator-Prey system

Luiz

Organista²,

Cirilo³

et al. 2022

Semina: Ciênc. Ex. Tech.

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Numerical convergence of a Telegraph Predator-Prey system is studied. This partial differential equation (PDE) system can describe various biological systems with reactive, diffusive, and delay effects. Initially, the PDE system was discretized by the Finite Differences method. Then, a system of equations in a time-explicit form and in a space-implicit form was obtained. The consistency of the Telegraph Predator-Prey system discretization was verified. Von Neumann stability conditions were calculated for a Predator-Prey system with reactive terms and for a Delayed Telegraph system. On the other hand, for our Telegraph Predator-Prey system, it was not possible to obtain the von Neumann conditions analytically. In this context, numerical experiments were carried out and it was verified that the mesh refinement and the model parameters, reactive constants, diffusion coefficients and delay constants, determine the stability/instability conditions of the discretized equations. The results of numerical experiments were presented.

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

Cited by 5 publications

References 17 publications

A sewage management proposal for Luruaco lake, Colombia

A sewage management proposal for Luruaco lake, Colombia

Numerical convergence of a Telegraph Predator-Prey system

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

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