Mathematical Science

In this thesis, we study algorithms for the 2D NS-α model of incompressible flow. These schemes conserve both discrete energy and discrete enstrophy in the absence of viscous and external forces, and otherwise admit exact balances for them analogous to those of true fluid flow. This model belongs to a very small group that conserves both of these quantities in the continuous case, and in this work, we develop finite element algorithms for the vorticity-stream formulation of this model that will preserve numerical energy and enstrophy in the computed solutions. i