TY - JOUR
T1 - A Numerical Study for a Velocity-Vorticity-Helicity Formulation of the 3D Time-Dependent Nse
AU - KEITH J. GALVIN, HYESUK K. LEE, AND LEO G. REBHOLZ
JO - International Journal of Numerical Analysis Modeling Series B
VL - 4
SP - 355
EP - 368
PY - 2011
DA - 2011/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/317.html
KW - Navier-Stokes equations
KW - Finite element method
KW - Velocity-Vorticity-Helicity formulation
AB - We study a finite element method for the 3D Navier-Stokes equations in velocity-vorticity-helicity formulation, which solves directly for velocity, vorticity, Bernoulli pressure and
helical density. Moreover, the algorithm strongly enforces solenoidal constraints on both the velocity 
(to enforce the physical law for conservation of mass) and vorticity (to enforce the mathematical
law that div(curl)= 0). We prove unconditional stability of the velocity, and with the use of a
(consistent) penalty term on the difference between the computed vorticity and curl of the computed 
velocity, we are also able to prove unconditional stability of the vorticity in a weaker norm.
Numerical experiments are given that confirm expected convergence rates, and test the method
on a benchmark problem.