Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations

2018-03-01
Akbaş, Meral
Rebholz, L. G.
Zerfas, C.
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.

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Citation Formats
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.