Velocity-Correction 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...

An unconditionally stable rotational velocity-correction scheme for incompressible flows

We present an unconditionally stable splitting scheme for incompressible Navier-Stokes equations based on the rotational velocity-correction formulation. The main advantages of the scheme are: (i) it allows the use of time step sizes considerably larger than the widely-used semi-implicit type schemes: the time step size is only constrained by accuracy; (ii) it does not require the velocity and ...

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...

Error analysis of fully discrete velocity-correction methods for incompressible flows

A fully discrete version of the velocity-correction method, proposed by Guermond and Shen (2003) for the time-dependent Navier-Stokes equations, is introduced and analyzed. It is shown that, when accounting for space discretization, additional consistency terms, which vanish when space is not discretized, have to be added to establish stability and optimal convergence. Error estimates are deriv...