Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using Emac Formulation

Accuracy of Projection Methods for the Incompressible Navier-Stokes Equations

Numerous papers have appeared in the literature over the past thirty years discussing projection-type methods for solving the incompressible Navier-Stokes equations. A recurring difficulty encountered is the proper choice of boundary conditions for the auxiliary variables in order to obtain at least second order accuracy in the computed solution. A further issue is the formula for the pressure ...

Improved Accuracy in Algebraic Splitting Methods for Navier-Stokes Equations

This paper studies a new alteration of Yosida algebraic splitting methods for the Navier-Stokes equations. By applying the usual or pressurecorrected Yosida splitting techniques to discretizations written in terms of velocity and pressure updates, we show that the accuracy is increased by one full order in ∆t without any additional cost in the respective methods. Proofs of the convergence resul...

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

On Error Estimates of the Pressure-correction Projection Methods for the Time-dependent Navier-stokes Equations

In this paper, we present a new pressure-correction projection scheme for solving the time-dependent Navier-Stokes equations, which is based on the Crank-Nicolson extrapolation method in the time discretization. Error estimates for the velocity and the pressure of semidiscretized scheme are derived by interpreting the projection scheme as second-order time discretization of a perturbed system w...

Numerical Methods for the Navier-Stokes equations