Resolution Requirements for Numerical Simulations of Transition

Abstract

~F l -r d r ( h l t W

Sufficient Stability Criteria and Uniform Stability of Difference Schemes

“…It is also noted that distortions at small scales inevitably cause large-scale distortions. It is noted in [30] in conclusion that the problem of overcoming the effects of spurious oscillations is not solved and is a difficult problem.…”

“…The problem of laminar-turbulent transition is one of practical importance. As was noted in [30], besides the well-known distortion of the velocity field by the scheme viscosity, a new unpleasant phenomenon was revealed recently: the appearance of spurious oscillations in the flow. This effect is the principal one for the direct numerical modeling of laminar-turbulent transition, and it is unfortunately almost impossible to control it.…”

On discretization error and its control in variational data assimilation

“…Discretization normally introduces diffusion and dispersion errors into any instability wave analysis thereby dissipating its energy and affecting its phase velocity (e.g. see Zang et al, 1989). Although the model is simple and the observations synthetic and uniformly distributed, the conclusions of this study should hold.…”

High-order ENO schemes applied to two- and three-dimensional compressible flow

“…Figure 1 presents the evolution of the vorticity thickness for third-order ENO on grids of size 322, 642, and 1282 and compares these results with those of a 1282 spectral calculation. (An analysis of the spectral coefficients of the latter coefficients, along the lines discussed in [26], indicates that the spectral result is accurate to better than 4 significant digits until about t -= 125, but that thereafter its accuracy deteriorates rapidly as the vortex roll-up produces scales, particularly in the streamwise direction, that are too small for the grid. )…”

“…3 We use undivided differences, Eq. (26), and prestored local matrix c, Eq. (28), to reduce cost and to reduce the effect of round-off errors.…”