TY - JOUR
T1 - A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations
AU - Palha da Silva Clérigo, A.
AU - Gerritsma, M.
PY - 2017
Y1 - 2017
N2 - In this work we present a mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured triangular grids. The essential ingredients to achieve this are: (i) a velocity–vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular triangular grids.
AB - In this work we present a mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured triangular grids. The essential ingredients to achieve this are: (i) a velocity–vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular triangular grids.
KW - Energy conserving discretization
KW - Enstrophy conserving discretization
KW - Incompressible Navier–Stokes equations
KW - Mimetic discretization
KW - Spectral element method
UR - http://www.scopus.com/inward/record.url?scp=84992428921&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2016.10.009
DO - 10.1016/j.jcp.2016.10.009
M3 - Article
SN - 0021-9991
VL - 328
SP - 200
EP - 220
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -