A new structure-preserving discretization for incompressible Navier-Stokes equations
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We introduce a new structure-preserving discretization for incompressible Navier-Stokes equations. Differing from existing structure-preserving methods [1,2] which contains two staggered in time evolution equations, the proposed method possesses a single evolution equation and uses the Crank-Nicolson method for the temporal discretization. The method is mass, energy, and vorticity conserving and is enstrophy conserving in 2D. Applying no-slip boundary conditions becomes straightforward, circumventing the challenges discussed in [3]. Supplementary numerical results will be presented. [1] A. Palha, M. Gerritsma, A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations, J. Comput. Phys. 328 (2017) 200-220. [2] Y. Zhang, A. Palha, M. Gerritsma, L. G. Rebholz, A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains, J. Comput. Phys. 451 (2022) 110868. [3] G. G. Diego, A. Palha, M. Gerritsma, Inclusion of no-slip boundary conditions in the MEEVC scheme, J. Comput. Phys. 378 (2019) 615-633.
