An overview of projection methods for incompressible flows

Velocity-Correction Projection Methods For Incompressible Flows

Velocity-Correction Projection Methods for Incompressible Flows

We introduce and study a new class of projection methods—namely, the velocitycorrection methods in standard form and in rotational form—for solving the unsteady incompressible Navier–Stokes equations. We show that the rotational form provides improved error estimates in terms of the H1-norm for the velocity and of the L2-norm for the pressure. We also show that the class of fractional-step meth...

Projection Methods for the Calculation of Incompressible Unsteady Flows

A general formula for the second-order projection method for solution of unsteady incompressible Navier-Stokes equations is presented. It includes the fourand three-step projection methods. Also, RKCN (Runge-Kutta=Crank-Nicholson) three-step and four-step projection methods are presented, in which the three-stage Runge-Kutta and semi-implicit Crank-Nicholson techniques are employed to update th...

Normal Mode Analysis of Second-order Projection Methods for Incompressible Flows

A rigorous normal mode error analysis is carried out for two second-order projection type methods. It is shown that although the two schemes provide second-order accuracy for the velocity in L-norm, their accuracies for the velocity in H1-norm and for the pressure in L2-norm are different, and only the consistent splitting scheme introduced in [6] provides full second-order accuracy for all var...

Variational Multiscale Methods for incompressible flows

The numerical simulation of incompressible flow governed by the Navier-Stokes equations requires to deal with subgrid phenomena. Particularly in turbulent flows, the scale spectra are notably widened and need to be handled adequately to get a reasonable numerical solution. Separating the complete scale range into subranges enables a different treatment of any of these subranges. In the brevity ...