A Cartesian grid finite-difference method for 2D incompressible viscous flows in irregular geometries

Authors:
E. Sanmiguel-Rojas;J. Ortega-Casanova;C. del Pino;R. Fernandez-Feria
Affiliations:
Universidad Politécnica de Cartagena, E.T.S. Ingenieros Industriales, 30202 Cartagena, Murcia, Spain;Universidad de Málaga, E.T.S. Ingenieros Industriales, 29013 Málaga, Spain;Universidad de Málaga, E.T.S. Ingenieros Industriales, 29013 Málaga, Spain;Universidad de Málaga, E.T.S. Ingenieros Industriales, 29013 Málaga, Spain
Venue:
Journal of Computational Physics
Year:
2005

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Abstract

A method for generating a non-uniform Cartesian grid for irregular two-dimensional (2D) geometries such that all the boundary points are regular mesh points is given. The resulting non-uniform grid is used to discretize the Navier-Stokes equations for 2D incompressible viscous flows using finite-difference approximations. To that end, finite-difference approximations of the derivatives on a non-uniform mesh are given. We test the method with two different examples: the shallow water flow on a lake with irregular contour and the pressure driven flow through an irregular array of circular cylinders.