Some implementations of projection methods for Navier-Stokes equations

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 ...

Numerical Methods for the Navier-Stokes equations

A bridge between projection methods and SIMPLE type methods for incompressible Navier-Stokes equations

A bridge is built between projection methods and SIMPLE type methods (Semi-Implicit Method for Pressure-Linked Equation). A general second-order accurate projection method is developed for the simulation of incompressible unsteady flows by employing a non-linear update of pressure term as n∇ pn+1 + (I − n)∇ pn , where n is a coefficient matrix, which may depend on the grid size, time step and e...

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...

On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes

We present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible NavierStokes equations. The error analysis is accomplished by interpreting the respective projection schemes as second-order time discretizations of a perturbed system which approximates the Navier-Stokes equations. Numerical results in agreement with the error a...