Efficient discretizations for the EMAC formulation of the incompressible Navier-Stokes equations
For computational fluid dynamics researchers, this work offers an efficient discretization strategy that balances computational cost and conservation properties, though the improvement is incremental.
The paper studies linearizations of the EMAC formulation for incompressible Navier-Stokes equations, showing that a Newton linearization with two steps per time step effectively preserves conservation laws and provides accurate long-time solutions, outperforming skew-symmetrized linearization and traditional formulations.
We study discretizations of the incompressible Navier-Stokes equations, written in the newly developed energy-momentum-angular momentum conserving (EMAC) formulation. We consider linearizations of the problem, which at each time step will reduce the computational cost, but can alter the conservation properties. We show that a skew-symmetrized linearization delivers the correct balance of (only) energy and that the Newton linearization conserves momentum and angular momentum, but conserves energy only up to the nonlinear residual. Numerical tests show that linearizing with 2 Newton steps at each time step is very effective at preserving all conservation laws at once, and giving accurate answers on long time intervals. The tests also show that the skew-symmetrized linearization is significantly less accurate. The tests also show that the Newton linearization of EMAC finite element formulation compares favorably to other traditionally used finite element formulation of the incompressible Navier-Stokes equations in primitive variables.