Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation element methods of arbitrary order for the compressible Navier-Stokes equations. The new methods are similar to strong form, nodal discontinuous Galerkin spectral elements but conserve entropy for the Euler equations and are entropy stable for the Navier-Stokes equations. Shock capturing follows immediately by combining them with a dissipative companion operator via a comparison approach. Smooth and discontinuous test cases are presented that demonstrate their efficacy. Introduction.Next generation numerical algorithms for use in large eddy simulations (LES) and hybrid Reynolds-averaged Navier-Stokes (RANS)-LES simulations will undoubtedly rely on efficient high-order formulations. Although highorder techniques are well suited for LES, most lack robustness when the solution contains discontinuities or even underresolved physical features. Although a variety of stabilization techniques have been developed for second-order methods (e.g., total variation diminishing (TVD) limiters [35], and entropy stability [40]), extending these techniques to high-order formulations has been problematic. High-order essentially nonoscillatory (ENO) [20,36] and weighted ENO (WENO) [31,25] schemes provide a partial remedy to the problem; they achieve high-order design accuracy away from captured discontinuities and maintain sharp "nearly monotone" captured shocks. Unfortunately, nonoscillatory schemes experience instabilities in less than ideal circumstances (e.g., curvilinear mapped grids or expansion of flows into vacuum). Because nonoscillatory schemes are largely based on stencil biasing heuristics rather than stability analysis, there is little theory to guide further development efforts focused on

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The aerodynamic transfer of energy from glottal airflow to vocal fold tissue during phonation was explored using complementary synthetic and numerical vocal fold models. The synthetic model was fabricated using a flexible polyurethane rubber compound. The model size, shape, and material properties were generally similar to corresponding human vocal fold characteristics. Regular, self-sustained oscillations were achieved at a frequency of approximately 120 Hz. The onset pressure was approximately 1.2 kPa. A corresponding two-dimensional finite element model was developed using geometry definitions and material properties based on the synthetic model. The finite element model upstream and downstream pressure boundary conditions were based on experimental values acquired using the synthetic model. An analysis of the fully coupled fluid and solid numerical domains included flow separation and unsteady effects. The numerical results provided detailed flow data that was used to investigate aerodynamic energy transfer mechanisms. The results support the hypothesis that a cyclic variation of the orifice profile from a convergent to a divergent shape leads to a temporal asymmetry in the average wall pressure, which is the key factor for the achievement of self-sustained vocal fold oscillations. me rica.

Direct numerical simulations (DNS) of steady and pulsatile flow through 75% (by area reduction) stenosed tubes have been performed, with the motivation of understanding the biofluid dynamics of actual stenosed arteries. The spectral-element method, providing geometric flexibility and high-order spectral accuracy, was employed for the simulations. The steady flow results are examined here while the pulsatile flow analysis is dealt with in Part 2 of this study. At inlet Reynolds numbers of 500 and 1000, DNS predict a laminar flow field downstream of an axisymmetric stenosis and comparison to previous experiments show good agreement in the immediate post-stenotic region. The introduction of a geometric perturbation within the current model, in the form of a stenosis eccentricity that was 5% of the main vessel diameter at the throat, resulted in breaking of the symmetry of the post-stenotic flow field by causing the jet to deflect towards the side of the eccentricity and, at a high enough Reynolds number of 1000, jet breakdown occurred in the downstream region. The flow transitioned to turbulence about five diameters away from the stenosis, with velocity spectra taking on a broadband nature, acquiring a -5/3 slope that is typical of turbulent flows. Transition was accomplished by the breaking up of streamwise, hairpin vortices into a localized turbulent spot, reminiscent of the turbulent puff observed in pipe flow transition, within which r.m.s. velocity and turbulent energy levels were highest. Turbulent fluctuations and energy levels rapidly decayed beyond this region and flow relaminarized. The acceleration of the fluid through the stenosis resulted in wall shear stress (WSS) magnitudes that exceeded upstream levels by more than a factor of 30 but low WSS levels accompanied the flow separation zones that formed immediately downstream of the stenosis. Transition to turbulence in the case of the eccentric stenosis was found to be manifested as large temporal and spatial gradients of shear stress, with significant axial and circumferential variations in instantaneous WSS.

The aerodynamic generation of sound during phonation was studied using direct numerical simulations of the airflow and the sound field in a rigid pipe with a modulated orifice. Forced oscillations with an imposed wall motion were considered, neglecting fluid-structure interactions. The compressible, two-dimensional, axisymmetric form of the Navier-Stokes equations were numerically integrated using highly accurate finite difference methods. A moving grid was used to model the effects of the moving walls. The geometry and flow conditions were selected to approximate the flow within an idealized human glottis and vocal tract during phonation. Direct simulations of the flow and farfield sound were performed for several wall motion programs, and flow conditions. An acoustic analogy based on the Ffowcs Williams-Hawkings equation was then used to decompose the acoustic source into its monopole, dipole, and quadrupole contributions for analysis. The predictions of the farfield acoustic pressure using the acoustic analogy were in excellent agreement with results from the direct numerical simulations. It was found that the dominant sound production mechanism was a dipole induced by the net force exerted by the surfaces of the glottis walls on the fluid along the direction of sound wave propagation. A monopole mechanism, specifically sound from the volume of fluid displaced by the wall motion, was found to be comparatively weak at the frequency considered (125 Hz). The orifice geometry was found to have only a weak influence on the amplitude of the radiated sound.