Math @ Duke

Publications [#246916] of JianGuo Liu
Papers Published
 Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes,
Journal of Computational Physics, vol. 124 no. 2
(1996),
pp. 368382 [doi]
(last updated on 2018/10/16)
Abstract: This paper discusses three basic issues related to the design of finite difference schemes for unsteady viscous incompressible flows using vorticity formulations: the boundary condition for vorticity, an efficient timestepping procedure, and the relation between these schemes and the ones based on velocitypressure formulation. We show that many of the newly developed global vorticity boundary conditions can actually be written as some local formulas derived earlier. We also show that if we couple a standard centered difference scheme with thirdor fourthorder explicit RungeKutta methods, the resulting schemes have no cell Reynolds number constraints. For high Reynolds number flows, these schemes are stable under the CFL condition given by the convective terms. Finally, we show that the classical MAC scheme is the same as Thom's formula coupled with secondorder centered differences in the interior, in the sense that one can define discrete vorticity in a natural way for the MAC scheme and get the same values as the ones computed from Thom's formula. We use this to derive an efficient fourthorder RungeKutta time discretization for the MAC scheme from the one for Thom's formula. We present numerical results for driven cavity flow at high Reynolds number (105). © 1996 Academic Press, Inc.


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