A MEEVC scheme with general boundary conditions and the ramifications for secondary conservation laws
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In [1] a spectral element formulation is presented which, in the absence of dissipative terms, conserves the total (kinetic) energy and enstrophy. Two essential ingredients of this paper are the introduction of a separate evolution equation for vorticity and the use of periodic boundary conditions. The extension of this MEEVC scheme to more general boundary conditions is not that trivial, as shown in [2]. In this presentation we will show that the evolution equation for the vorticity field can be replaced by the common relation between the velocity and vorticity field, while still satisfying the conservation properties of the original MEEVC scheme, [1]. In addition, this new formulation allows for more general boundary conditions in a much easier way than in [2]. Some of the consequences of these more general boundary conditions on the conservation laws will be presented.
