TY - JOUR
T1 - Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using EMAC Formulation
AU - Ingimarson , Sean
AU - Neda , Monika
AU - Rebholz , Leo G.
AU - Reyes , Jorge
AU - Vu , An
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 176
EP - 198
PY - 2023
DA - 2023/01
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1008
UR - https://global-sci.org/intro/article_detail/ijnam/21353.html
KW - Navier-Stokes equations, EMAC formulation, projection methods.
AB - <p style="text-align: justify;">We consider a pressure correction temporal discretization for the incompressible
Navier-Stokes equations in EMAC form. We prove stability and error estimates for the case
of mixed finite element spatial discretization, and in particular that the Gronwall constant’s
exponential dependence on the Reynolds number is removed (for sufficiently smooth true solutions)
or at least significantly reduced compared to the commonly used skew-symmetric formulation. We
also show the method preserves momentum and angular momentum, and while it does not preserve
energy it does admit an energy inequality. Several numerical tests show the advantages EMAC
can have over other commonly used formulations of the nonlinearity. Additionally, we discuss
extensions of the results to the usual Crank-Nicolson temporal discretization.</p>