An essentially non-oscillatory Crank-Nicolson procedure for incompressible Navier-Stokes equations

The article introduces an essentially non-oscillatory Crank-Nicolson (ENO-CN) scheme for the numerical solution of unsteady incompressible Navier-Stokes equations. ENO-CN utilizes the second-order upwind ENO scheme for the approximation of the convection term in the explicit step, while everything else is discretized by the central finite volume method. We also introduce a new projection method which can virtually eliminate splitting errors arising due to the velocity-pressure separation. It has been numerically verified that our resulting algorithm is non-oscillatory for arbitrary Reynolds numbers, its numerical dissipation is not observable, and the computed solution shows a second-order accuracy in both space and time for smooth solutions.