An energy, momentum and angular momentum conserving scheme for a regularization model of incompressible flow
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We introduce a new regularization model for incompressible fluid flow, which is a regularization of the EMAC formulation of the Navier-Stokes equations (NSE) that we call EMAC-Reg. The EMAC formulation has proved to be a useful formulation because it conserves energy, momentum and angular momentum even when the divergence constraint is only weakly enforced. However it is still a NSE formulation and so cannot resolve higher Reynolds number flows without very fine meshes. By carefully introducing regularization into the EMAC formulation, we create a model more suitable for coarser mesh computations but that still conserves the same quantities as EMAC, i.e., energy, momentum, and angular momentum. We show that EMAC-Reg, when equipped with a finite element spatial discretization, is well-posed, conserves all the important quantities that EMAC does, and is optimally accurate. Numerical results are provided that show EMAC-Reg is a robust coarse mesh model.
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