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

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.