Commun. Comput. Phys.,
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Volume 4.

Synchronization of Weighted Essentially Non-Oscillatory Methods

Ellen M. Taylor 1, M. Pino Martin 1*

1 Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA.

Received 17 June 2007; Accepted (in revised version) 6 November 2007
Available online 27 February 2008


Weighted essentially non-oscillatory (WENO) methods have been developed to simultaneously provide robust shock-capturing in compressible fluid flow and avoid excessive damping of fine-scale flow features such as turbulence. Under certain conditions in compressible turbulence, however, numerical dissipation remains unacceptably high even after optimization of the linear component that dominates in smooth regions. Of the \emph{non}linear error that remains, we demonstrate that a large fraction is generated by a ``synchronization deficiency'' that interferes with the expression of theoretically predicted numerical performance characteristics when the WENO adaptation mechanism is engaged. This deficiency is illustrated numerically in simulations of a linearly advected sinusoidal wave and the Shu-Osher problem [J. Comput. Phys., 83 (1989), pp. 32-78]. It is shown that attempting to correct this deficiency through forcible synchronization results in violation of conservation. We conclude that, for the given choice of candidate stencils, the synchronization deficiency cannot be adequately resolved under the current WENO smoothness measurement technique.

AMS subject classifications: 76F65

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Key words: Direct numerical simulation, large eddy simulation, compressible turbulence, shock capturing.

*Corresponding author.
Email: (E. M. Taylor), (M. P. Martin)

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