Open Access

ARTICLE

Solutions for Incompressible Viscous Flow in a Triangular Cavity using Cartesian Grid Method

by B. M. Pasquim¹, V. C. Mariani²

1 Department of Chemical Engineering, Pontifical Catholic University of Paraná, Rua Imaculada Conceição, 1155, Prado Velho, 80215-901, Curitiba, PR, Brazil.
2 Department of Mechanical Engineering, Pontifical Catholic University of Paraná, Rua Imaculada Conceição, 1155, Prado Velho, 80215-901, Curitiba, PR, Brazil. {viviana.mariani@pucpr.br}

Computer Modeling in Engineering & Sciences 2008, 35(2), 113-132. https://doi.org/10.3970/cmes.2008.035.113

Abstract

This study presents a Cartesian grid method and its application to solve a steady flow in a lid-driven triangular two-dimensional cavity. The evolution of stream function and vorticity inside a triangular lid-driven cavity, when the Reynolds number changes from 1 to 6000, is presented. For space discretization on the interior of triangular cavity orthogonal Cartesian grid is used. Then, using this grid, trapezoidal volumes appear in the interface between solid and fluid. For a suitable treatment of these volumes the Eulerian-Lagrangian methodology is used. The Navier-Stokes equations are solved numerically using finite-volume method. On the basis of the numerical studies reported here it seems that the method under investigation has no difficulty at capturing the formation of primary, secondary and tertiary vortices as Reynolds number increases. It is observed also that the interior of the primary vortex has almost constant stream function and vorticity for reasonably large Reynolds number. Highly accurate benchmark results are provided including new global quantities as the kinetic energy and the enstrophy.

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Keywords

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