Combined compact difference method for solving the incompressible Navier–Stokes equations

This paper presents a numerical method for solving the two‐dimensional unsteady incompressible Navier–Stokes equations in a vorticity–velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two‐dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourth‐order five‐ to six‐alternating‐stage Runge–Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid‐mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three‐dimensional cases in which full boundary layer transition happens. Copyright © 2011 John Wiley & Sons, Ltd.     

Disentangling the effects of phonation and articulation: Hemispheric asymmetries in the auditory N1m response of the human brain

Background  

The cortical activity underlying the perception of vowel identity has typically been addressed by manipulating the first and second formant frequency (F1 & F2) of the speech stimuli. These two values, originating from articulation, are already sufficient for the phonetic characterization of vowel category. In the present study, we investigated how the spectral cues caused by articulation are reflected in cortical speech processing when combined with phonation, the other major part of speech production manifested as the fundamental frequency (F0) and its harmonic integer multiples. To study the combined effects of articulation and phonation we presented vowels with either high (/a/) or low (/u/) formant frequencies which were driven by three different types of excitation: a natural periodic pulseform reflecting the vibration of the vocal folds, an aperiodic noise excitation, or a tonal waveform. The auditory N1m response was recorded with whole-head magnetoencephalography (MEG) from ten human subjects in order to resolve whether brain events reflecting articulation and phonation are specific to the left or right hemisphere of the human brain.