Synchronization of Weighted Essentially Non-Oscillatory Methods (Communications in Computational Physics, 2008)
Weighted essentially non-oscillatory (WENO) methods have been developed to simultaneously provide robust shock-capturing in compressible fluid flow andavoid excessive damping of fine-scale flow features such as turbulence. Under certain conditions in compressible turbulence, however, numerical dissipation remainsunacceptably high even after optimization of the linear component that dominatesin smooth regions. Of the nonlinear error that remains, we demonstrate that a largefraction is generated by a "synchronization deficiency" that interferes with the expression of theoretically predicted numerical performance characteristics when the WENOadaptation 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 deficiencythrough forcible synchronization results in violation of conservation. We concludethat, for the given choice of candidate stencils, the synchronization deficiency cannotbe adequately resolved under the current WENO smoothness measurement technique.