We prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. The data prescribed is the rearrangement class of the vorticity field. The corresponding stream function satisfies a semilinear elliptic partial differential equation. The result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

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 consider a finite element method based on biorthogonal or quasi-biorthogonal systems for the biharmonic problem. The method is based on the primal mixed finite element method due to Ciarlet and Raviart for the biharmonic equation. Using different finite element spaces for the stream function and vorticity, this approach leads to a formulation only based on the stream function. We prove optim...

 Abstract : The meshless local Petrov-Galerkin method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for a driven cavity flow for moderate Reynolds numbers using different point distributions. The L2-...

Meshfree point collocation method is developed for the stream-vorticity formulation of two-dimensional incompressible Navier– Stokes equations. Particular emphasis is placed on the novel formulation of effective vorticity condition on no-slip boundaries. The moving least square approximation is employed to construct shape functions in conjunction with the framework of point collocation method. ...

A stability condition is provided for a class of vorticity boundary formulas used with the second order finite-difference numerical scheme for the vorticity-stream function formulation of the unsteady incompressible Navier-Stokes equations. These local vorticity boundary formulas are derived using the no-slip boundary condition for the velocity. A new form of these long-stencil formulas is need...