Stretched Cartesian grids for solution of the incompressible Navier-Stokesequations

Two Cartesian grid stretching functions are investigated for solving the un steady incompressible Navier-Stokes equations using the pressure-velocity f ormulation. The first function is developed for the Fourier method and is a generalization of earlier work. This function concentrates more points at the centre of the computational box while allowing the box to remain finite . The second stretching function is for the second-order central finite dif ference scheme, which uses a staggered grid in the computational domain. Th is function is derived to allow a direct discretization of the Laplacian op erator in the pressure equation while preserving the consistent behaviour e xhibited by the uniform grid scheme. Both functions are analysed for their effects on the matrix of the discretized pressure equation. It is shown tha t while the second function does not spoil the matrix diagonal dominance, t he first one can. Limits to stretching of the first method are derived for the cases of mappings in one and two directions. A limit is also derived fo r the second function in order to prevent a strong distortion of a sine wav e. The performances of the two types of stretching are examined in simulati ons of periodic co-flowing jets and a time developing boundary layer. Copyr ight (C) 2000 John Whey & Sons, Ltd.