The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results p...

The present study aimed to investigate two numerical solutions of the Navier-Stokes equations. For this purpose, the mentioned flow equations were written in two different formulations, namely (i) velocity-pressure and (ii) vorticity-stream function formulations. Solution algorithms and boundary conditions were presented for both formulations and the efficiency of each formulation was investiga...

We show that the two dimensional Navier–Stokes equations in the stream function and vorticity form with nonhomogeneous boundary conditions have a unique solution with a stream function having two space derivatives. 2005 Published by Elsevier Inc.

Abstract. We prove real analyticity of all the streamlines, including the free surface, of a gravityor capillary-gravity-driven steady flow of water over a flat bed, with a Hölder continuous vorticity function, provided that the propagating speed of the wave on the free surface exceeds the horizontal fluid velocity throughout the flow. Furthermore, if the vorticity possesses some Gevrey regular...

Finite element procedures and computations based on the velocity-pressure and vorticitystream function formulations of incompressible flows are presented. Two new multi-step velocity-pressure formulations are proposed and are compared with the vorticity-stream function and one-step formulations. The example problems chosen are the standing vortex problem and flow past a circular cylinder. Bench...

A numerical approach called “SIMPLER” is used to investigate the  flow and heat transfer characteristics in a square driven cavity. The two-dimensional incompressible Navier-Stokes equations were solved and the results are depicted as contour plots of stream function, vorticity, and total pressure for Reynolds numbers from 1 to 10000. At the higher values of Reynolds number, an inviscid core re...

In this study, a spectral collocation domain decomposition method is developed for the numerical solution of second and fourth order problems in circular domains. The method is applied to the Navier-Stokes equations and its performance is investigated in the cases of the stream function and the stream function-vorticity formulations.

An efficient and accurate algorithm for solving the two-dimensional (2D) incompressible Navier–Stokes equations on a disk with no-slip boundary conditions is described. The vorticitystream function formulation of these equations is used, and spatially the vorticity and stream functions are expressed as Fourier–Chebyshev expansions. The Poisson and Helmholtz equations which arise from the implic...

Computational fluid mechanics based on the finite element method has been developed so far following two distinct approaches (a) using a stream function, or stream functlon-vortlcity formulation [1,2], and (b) using a primitive variables formulation [3,4,5]. Within the first approach a stream function is defined such that the continuity equation is identically satisfied and the momentum equatio...