A fast finite difference method is proposed to solve the incompressible Navier-Stokes equations defined on a general domain. The method is based on the vorticity stream-function formulation and a fast Poisson solver defined on a general domain using the immersed interface method. The key to the new method is the fast Poisson solver for general domains and the interpolation scheme for the bounda...

Flame sheet problems are on the natural route to the numerical solution of detailed chemistry, laminar di usion ames, which, in turn, are important in many engineering applications. In order to model the ame structure more accurately, we use the vorticity-velocity formulation of the uid ow equations instead of the more traditional stream function-vorticity approach. The numerical solution of th...

We propose an analytical solution for the evolution of the spatial variability of wind-forced inertial energy in the presence of an oceanic mesoscale eddy field. The solution requires knowledge of only the stream function of the eddy field and the Rossby radii of the normal modes associated with the near-inertial oscillations. It also shows that, when the vorticity spectrum slope is shallower t...

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of parametric Navier–Stokes equations in stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients vorticity and function fields. In addition, studies use global POD basis space obtained from database time dependent full ...

In that report solution to incompressible Navier Stokes equations in non dimensional form will be presented. Standard fundamental methods: SIMPLE, SIMPLER (SIMPLE Revised) and Vorticity-Stream function approach are compared and results of them are analyzed for standard CFD test case Drived Cavity flow. Different aspect ratios of cavity and different Reynolds numbers are studied.

In this paper, we develop least-squares finite element methods (LSFEMs) for incompressible fluid flows with improved mass conservation. Specifically, we formulate a new locally conservative LSFEM for the velocity– vorticity–pressure Stokes system, which uses a piecewise divergence-free basis for the velocity and standard C 0 elements for the vorticity and the pressure. The new method, which we ...

This research includes of the numerical modeling of fluids in two-dimensional cavity. The cavity flow is an important theoretical problem. In this research, modeling was carried out based on an alternating direction implicit via Vorticity-Stream function formulation. It evaluates different Reynolds numbers and grid sizes. Therefore, for the flow field analysis and prove of the ability of the sc...

The roll of melting heat transfer on magnetohydrodynamic natural convection in a square enclosure with heating of bottom wall is examined numerically in this article. The dimensionless governing partial differential equations are transformed into vorticity and stream function formulation and then solved using the finite difference method (FDM). The effects of thermal Rayleigh number (Ra</em...

In the present paper heat transfer in a uid is considered. The Oberbeck-Boussinesq equations for stream function and vorticity are solved by a nite diierence method. In the presence of very strong convection puls type solutions occure. The results are applied in the design of microsensors and compared with experimental data.