Finite difference schemes for incompressible flows in vorticity formulations

High-order finite difference schemes for incompressible flows

This paper presents a new high order approach to the numerical solution of the incompressible Stokes and Navier-Stokes equations. The class of schemes developed is based upon a velocity-pressure-pressure gradient formulation which allows: (i) high order finite difference stencils to be applied on nonstaggered grids; (ii) high order pressure gradient approximations to be made using standard Padé...

Simple finite element method in vorticity formulation for incompressible flows

A very simple and eÆcient nite element method is introduced for two and three dimensional viscous incompressible ows using the vorticity formulation. The method relies on recasting traditional nite element method in the spirit of the high order accurate nite di erence methods introduced by the authors in [10]. Optimal accuracy of arbitrary order can be achieved using standard nite element or sp...

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Modified finite difference schemes for geophysical flows

Finite Difference Schemes for Incompressible Flows in the Velocity Impulse Density Formulation

together with perspectives on the application of real space renormalization procedures to vortex methods based on We consider finite difference schemes based on the impulse density variable. We show that the original velocity—impulse density the impulse density. formulation of Oseledets is marginally ill-posed for the inviscid flow, At a first sight, the impulse density formulation also proand ...