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

Authors

  • Eliandro Rodrigues Cirilo Universidade Estadual de Londrina
  • Alessandra Negrini Dalla Barba Universidade Estadual de Londrina
  • Paulo Laerte Natti Universidade Estadual de Londrina http://orcid.org/0000-0002-5988-2621
  • Neyva Maria Lopes Romeiro Universidade Estadual de Londrina

DOI:

https://doi.org/10.5433/1679-0375.2018v39n2p87

Keywords:

Finite Differences, Simplified MAC, Curvilinear Coordinates, Parallel Plates, Did-Driven Cavity, Atherosclerosis

Abstract

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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Author Biographies

Eliandro Rodrigues Cirilo, Universidade Estadual de Londrina

Prof. Dr. Depto. Matemática, UEL

Alessandra Negrini Dalla Barba, Universidade Estadual de Londrina

Me. em Matemática Aplicada, PGMAC/UEL

Paulo Laerte Natti, Universidade Estadual de Londrina

 Prof. Dr. Depto. Matemática, UEL

Neyva Maria Lopes Romeiro, Universidade Estadual de Londrina

Profa. Dra. Depto. Matemática, UEL

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Published

2018-12-29

How to Cite

Cirilo, E. R., Barba, A. N. D., Natti, P. L., & Romeiro, N. M. L. (2018). A numerical model based on the curvilinear coordinate system for the MAC method simplified. Semina: Ciências Exatas E Tecnológicas, 39(2), 87–98. https://doi.org/10.5433/1679-0375.2018v39n2p87

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Original Article

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