the numerical method presented by safaiy et al. [1] is reformulated with finite volume method in its most general form and tested on non-orthogonal flow problems. navier-stokes equations are solved for the solution of stream function and vorticity. numerical solutions of the driven skewed cavity flow, solved using a fine grid (513×513) mesh, are presented for reynolds number of 100 and 1000 for...

In this paper, we simulate steady inviscid flows over a cylinder using potential and stream functions, including entropy and vorticity corrections for incompressible, subsonic, transonic and supersonic flows. The present hierarchical formulation is equivalent to Euler equations satisfying conservation of mass, momentum and energy. Standard numerical schemes and iterative algorithms are used for...

Model equations describing large scale buoyant convection in an enclosure are formulated with the vorticity and stream function as dependent variables. The mathematical model, based on earlier work of the authors, is unique in two respects. First, it neglects viscous and thermal conductivity effects. Second the fluid is taken to be thermally expandable: large density variations are allowed whil...

The physical mechanisms for vortex breakdown which, it is proposed here, rely on the production of a negative azimuthal component of vorticity, are elucidated with the aid of a simple, steady, inviscid, axisymmetric equation of motion. Most studies of vortex breakdown use as a starting point an equation for the azimuthal vorticity (Squire 1960), but a departure in the present study is that it i...

After casting Euler-$\alpha$ equations into vorticity-stream function formula, we obtain some very useful estimates from the properties of vorticity formula in exterior domain. Basing on these estimates, one can have got global existence and uniqueness solutions to 2D domain provided that initial data is regular enough.

The semi-geostrophic equations are used in meteorology. They appear as a variant of the two-dimensional Euler incompressible equations in vorticity form, where the Poisson equation that relates the stream function and the vorticity field is just replaced by the fully non linear elliptic Monge-Ampère equation. This work gathers new results concerning the semi-geostrophic equations: Existence and...

Ahstract~~alculations for the two-dimensional driven cavity incompressible flow problem are presented. A p-type Jinite element scheme for the fully coupled stream function-vorticity formulation of the Navier-Stokes equations is used. Graded meshes are used to resolve vortex flow features and minimize the impact of comer singularities. Incremental continuation in the Reynolds number allows solut...

Hydrodynamic equations for ideal incompressible fluid are written in terms of generalized stream function. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation contains arbitrary function which is determined by inflow conditions given on the boundary. To determine unique solution, velocity and vorticity (but not onl...

This paper presents a study of the behavior of several di erence approximations for the incompressible Navier-Stokes equations as a function of the computational mesh resolution. In particular, the under-resolved case is considered. The methods considered include a Godunov projection method, a primitive variable ENO method, an upwind vorticity stream-function method, centered di erence methods ...

Two dimensional motion of an incompressible second grade fluid in a porous medium with Hall effects has been considered. Exact solutions are obtained via inverse method when vorticity distribution is proportional to stream function ψ, perturbed by a quadratic term.