Math @ Duke

Publications [#268291] of John E. Dolbow
Papers Published
 Kim, TY; Dolbow, JE; Fried, E, The NavierStokesαβ equations as a platform for a spectral multigrid method to solve the NavierStokes equations,
Computers & Fluids, vol. 44 no. 1
(2011),
pp. 102110, ISSN 00457930 [doi]
(last updated on 2018/02/22)
Abstract: This paper describes a spectral multigrid method for spatially periodic homogeneous and isotropic turbulent flows. The method uses the NavierStokes αβ equations to accelerate convergence toward solutions of the NavierStokes equations. The NavierStokesαβ equations are solved on coarse grids at various levels and the NavierStokes equations are solved on the " nest grid" The method uses CrankNicolson timestepping for the viscous terms, explicit timestepping for the remaining terms, and Richardson iteration to solve linear systems encountered at each time step and on each grid level. To explore the computational efficiency of the method, comparisons are made with results obtained from an analogous spectral multigrid method for the NavierStokes equations. These comparisons are based on computing work units and residuals for multigrid cycles. Most importantly, we examine how choosing different values of the length scales α and β entering the NavierStokesαβ equations influence the efficiency and accuracy of these multigrid schemes. © 2010 Elsevier Ltd.


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