The pressure-correction projection method for the incompressible Navier-Stokes equation is approached as a preconditioned Richardson iterative method for the pressure- Schur complement equation. Typical pressure correction methods perform only one iteration and suffer from a splitting error that results in a spurious numerical boundary layer, and a limited order of convergence in time. We investigate the benefit of performing more than one iteration. We show that that not only performing more iterations attenuates the effects of the splitting error, but also that it can be more computationally efficient than reducing the time step, for the same level of accuracy. We also devise a stopping criterion that helps achieve a desired order of temporal convergence, and implement our method with multi-stage and multi-step time integration schemes. In order to further reduce the computational cost of our iterative method, we combine it with an Aitken acceleration scheme. Our theoretical results are validated and illustrated by numerical test cases for the Stokes and Navier-Stokes equations, using Implicit-Explicit Backwards Difference Formula and Runge-Kutta time integration solvers. The test cases comprises a now classical manufactured solution in the projection method literature and a modified version of a more recently proposed manufactured solution.

Congratulations to John Aoussou on his recent graduation! John received an SM from Mechanical Engineering and CDO program for his research on “An Iterative Pressure-Correction Method for the Unsteady Incompressible Navier-Stokes Equation” with our MSEAS group at MIT.

Congratulations to Matt Swezey on his recent graduation! Matt received Master of Naval Architecture and Marine Engineering and a Master of Mechanical Engineering for his research on “Ocean Acoustic Uncertainty for Submarine Applications”.

Florian Feppon has received the Wunsch Foundation Silent Hoist and Crane Award for Outstanding Graduate Research. The honor was presented at the Mechanical Engineering Student Awards Luncheon on Friday, May 13, 2016. An honor well-deserved. Congratulations Florian!

Abstract The impact of horizontal resolution (1/12 to 1/50 degree) on Gulf Stream separation and penetration is analyzed in a series of identical North Atlantic HYCOM configurations. The specific questions that will be addressed are as follows: When does a solution converge or is “good enough”? Are the mesoscale and sub-mesoscale eddy activity representative of interior quasigeostrophic (QG) or surface quasigeostrophic (SQG) turbulence? How well do the simulations compare to observations? We will show that the increase in resolution (1/50 degree) does lead to a substantial improvement in the Gulf Stream representation (surface and interior) when compared to observations and the results will be discussed in terms of ageostrophic contributions and power spectra.