Mimetic differences and pseudo symplectic Runge Kutta methods for incompressible Navier Stokes equations

• Mimetic methods • High order • Incompressible Navier Stokes • Pseudo symplectic • Skew-symmetric The control of aliasing errors arising from the non-linear convective terms in the incompressible Navier Stokes equation requires care when investigating turbulent flow regimes. Discretization schemes that fail to mirror the conservation properties such as global kinetic energy (which is inherent to the continuum form) can result in spurious numerical energy build-up for turbulent flow simulations. Mimetic difference methods that operate on a staggered grid satisfy a discrete version of the continuum conservation laws, thereby resulting in more accurate numerical simulations. The high order mimetic operators of Corbino-Castillo using a skew-symmetric formulation is considered in the present work. On the temporal side, pseudo symplectic methods are investigated to obtain global kinetic energy preserving numerical solutions of the NS equations in turbulent flow regimes. Numerical examples highlighting the implementation of the mimetic pseudo symplectic schemes are also presented.