Volume 2, Issue 4
A Numerical Study for a Velocity-Vorticity-Helicity Formulation of the 3D Time-Dependent Nse

KEITH J. GALVIN, HYESUK K. LEE, AND LEO G. REBHOLZ

Int. J. Numer. Anal. Mod. B, 2 (2011), pp. 355-368

Published online: 2011-02

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  • Abstract
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.
  • AMS Subject Headings

35Q30 65N30 76D05

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-2-355, author = {KEITH J. GALVIN, HYESUK K. LEE, AND LEO G. REBHOLZ}, title = {A Numerical Study for a Velocity-Vorticity-Helicity Formulation of the 3D Time-Dependent Nse}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2011}, volume = {2}, number = {4}, pages = {355--368}, abstract = {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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/317.html} }
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.
KEITH J. GALVIN, HYESUK K. LEE, AND LEO G. REBHOLZ. (2011). A Numerical Study for a Velocity-Vorticity-Helicity Formulation of the 3D Time-Dependent Nse. International Journal of Numerical Analysis Modeling Series B. 2 (4). 355-368. doi:
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