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.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

139
views

0
downloads

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

Suggestions

OpenMETU
Core

Forced oscillation of super-half-linear impulsive differential equations Oezbekler, A.; Zafer, Ağacık (Elsevier BV, 2007-09-01) By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered.
Value sets of Lattes maps over finite fields Küçüksakallı, Ömer (Elsevier BV, 2014-10-01) We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
Oscillation of nonlinear impulsive partial difference equations with continuous variables Agarwal, R. P.; KARAKOÇ, FATMA; Zafer, Ağacık (Informa UK Limited, 2012-01-01) By employing a difference inequality without impulses, we establish several sufficient conditions for the oscillation of solutions of a class of nonlinear impulsive partial difference equations with continuous variables.
Galois structure of modular forms of even weight Gurel, E. (Elsevier BV, 2009-10-01) We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Oscillation Criteria for Second-Order Forced Dynamic Equations with Mixed Nonlinearities Agarwal, Ravi P.; Zafer, A. (Springer Science and Business Media LLC, 2009) We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form (r(t)Phi(alpha)(x(Delta)))(Delta) + f(t,x(sigma)) = e(t), t is an element of [t(0), infinity)(T) with f (t, x) = q(t) Phi(alpha)(x) + Sigma(n)(i=1)q(i)(t)Phi(beta i)(x), Phi(*)(u) = vertical bar u vertical bar*(-1) u, where [t(0), infinity)(T) is a time scale interval with t(0) is an element of T, the functions r, q, q(i), e : [t(0), infinity)(T) -> R are right-dense contin...

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.