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Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations
Date
2018-03-01
Author
Akbaş, Meral
Rebholz, L. G.
Zerfas, C.
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We study a velocity-vorticity scheme for the 2D incompressible Navier-Stokes equations, which is based on a formulation that couples the rotation form of the momentum equation with the vorticity equation, and a temporal discretization that stably decouples the system at each time step and allows for simultaneous solving of the vorticity equation and velocity-pressure system (thus if special care is taken in its implementation, the method can have no extra cost compared to common velocity-pressure schemes). This scheme was recently shown to be unconditionally long-time H-1 stable for both velocity and vorticity, which is a property not shared by any common velocity-pressure method. Herein, we analyze the scheme's convergence, and prove that it yields unconditional optimal accuracy for both velocity and vorticity, thus making it advantageous over common velocity-pressure schemes if the vorticity variable is of interest. Numerical experiments are given that illustrate the theory and demonstrate the scheme's usefulness on some benchmark problems.
Subject Keywords
Algebra and Number Theory
,
Computational Mathematics
URI
https://hdl.handle.net/11511/57999
Journal
CALCOLO
DOI
https://doi.org/10.1007/s10092-018-0246-7
Collections
Department of Sociology, Article
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M. Akbaş, L. G. Rebholz, and C. Zerfas, “Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations,”
CALCOLO
, pp. 0–0, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57999.