Velocity–vorticity–helicity formulation and a solver for the Navier–Stokes equations |
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Authors: | Maxim A Olshanskii Leo G Rebholz |
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Institution: | 1. Department of Mechanics and Mathematics, Moscow State M.V. Lomonosov University, Moscow 119899, Russia;2. Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, United States |
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Abstract: | For the three-dimensional incompressible Navier–Stokes equations, we present a formulation featuring velocity, vorticity and helical density as independent variables. We find the helical density can be observed as a Lagrange multiplier corresponding to the divergence-free constraint on the vorticity variable, similar to the pressure in the case of the incompressibility condition for velocity. As one possible practical application of this new formulation, we consider a time-splitting numerical scheme based on an alternating procedure between vorticity–helical density and velocity–Bernoulli pressure systems of equations. Results of numerical experiments include a comparison with some well-known schemes based on pressure–velocity formulation and illustrate the competitiveness on the new scheme as well as the soundness of the new formulation. |
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Keywords: | Incompressible Navier&ndash Stokes equations Finite element method Vorticity Helicity |
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