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Economic competitiveness is driving industry to new frontiers of engineering design. Robustness and reliability-bused design, multidisciplinary-simulation-based design, increased complexity and sophistication of our design, and optimization-aided design are four such areas that are seriously challenging our ability to keep pace with the need to adequately model the systems we seek to design--in spite of the exponential growth of computing power. An emerging consensus within the community is that the effective development of computationally benign models (metamodels) will help us navigate the challenging road ahead. The process of constructing metamodels for computationally expensive models, such as finite element, aerodynamic, and heat-transfer models, is representative of the tasks we must address. Among the available metamodeling techniques, radial basis functions (RBFs) have recently generated much interest for their effectiveness and versatility. Radial basis functions offer numerous advantages over the traditional response surface methodology, including their ability to effectively generate multidimensional interpolative approximations. However, we show how the typical RBF approach lacks the critical flexibility required to handle the wide variety of complex models arising from the use of advanced techniques, such as uncertainty handling and multiobjective optimization, often encountered in modern design. Furthermore, in this paper we propose a novel approach---the extended radial basis function (E-RBF) approach--that provides the designer with significant flexibility and freedom in the metamodeling process, compared to conventional RBFs. Examples are provided that demonstrate the effectiveness of the new approach and explore its potential superiority to traditional RBF and response surface methodologies. Initial investigation indicates that the E-RBF possesses unique and novel properties not available in any other single method.

The flow over two-dimensional geometries is studied via unsteady numerical simulations that are three dimensional, with periodic conditions applied along the spanwise coordinate. This framework is well accepted for direct numerical simulations (DNS), large-eddy simulations, and detached-eddy simulations (DES), but is here combined with standard Reynolds-averaged Navier-Stokes (RANS) turbulence models. This strategy, which is not new, is referred to as unsteady RANS (URANS). Limited previous evidence suggested that, in URANS, three dimensionality is suppressed by high eddy-viscosity levels. However, three dimensionality proves fairly easy to sustain with adequate initial conditions, in all three cases studied here: stalled airfoil, circular cylinder, and a rounded square, except that for one case three dimensionality failed to last from random-based initial perturbations and was sustained only when using a DES field as initial condition. It is much less fine grained and chaotic than in the classical turbulence-resolving methods (from DNS to DES). Three-dimensional URANS gives clear improvements over two-dimensional URANS. It is less costly than DES, but is not as accurate. URANS also displays a troublesome sensitivity to the spanwise period and to the turbulence model. The approach is interesting and will appear spontaneously in many applications, but remains only partly understood.

The flow around infinite swept wings is computed using a Reynolds-averaged Navier-Stokes method coupled to a boundary layer and a transition prediction method based on the [e.sup.N] approach. This approach applies the two N factor [e.sup.N] strategy, which allows the differentiation between excited Tollmien-Schlichting waves of constant frequency and stationary crossflow waves of constant spanwise wave number. The applicability is documented by comparing computations with infinite swept-wing experiments on four configurations, where one configuration was tested in two different wind tunnels. The limiting N factors for both types of waves are a priori unknown. Hence, firstly the limiting N factors, which represent the stability limit, are deduced from the measured transition locations. Subsequently, iterative computations are executed to determine the transition location using the coupled system, Navier-Stokes, boundary-layer, and two N factor [e.sup.N] method in combination with the stability limit. The correlation between experimentally observed and computed transition locations is shown to be good for all considered wind-tunnel studies.

Within a parametric study on brush-type trailing-edge extensions, the noise reduction potential of several design concepts was determined. The obtained database represents the first phase of an ongoing project with the long-term objective to develop scaling laws for a future application of such devices as add-on solutions for today's aircraft components. The experiments comprised both acoustic and aerodynamic measurements on a zero-lift generic plate model (Re=2.1 x [10.sup.6] to 7.9 x [10.sup.6]) in DLR's open jet Aeroaconstic Wind Tunnel Braunschweig. Noise data were taken by means of a directional microphone system. Measurement results indicate a significant source noise reduction potential in excess of 10 dB, depending on the configuration. Two relevant noise reduction mechanisms were identified: 1) the suppression of narrowband bluntness noise, as well as 2) the reduction of broadband turbulent boundary-layer trailing-edge noise.

Instability of the three-dimensional boundary layer on a yawed circular cylinder placed in a uniform flow is investigated experimentally by introducing acoustic disturbances from a point near the attachment line. To exemplify the flow dominated by streamline-curvature instability rather than crossflow instability, which has been often observed in many swept-wing flows, is the aim here. In upstream regions of the disturbance wedge originating from the point source, both streamline-curvature and crossflow disturbances are superposed on each other and yield complicated amplitude distributions. A newly proposed method enables the decomposition of the distorted amplitude distribution into contributions from the two instability modes. Detailed observations, however, show that the crossflow mode decays with the distance from the source much faster than the streamline-curvature mode and allows the latter to be dominant in a region further downstream. A fundamental characteristic of the streamline-curvature instability wave is confirmed by examining its phase distribution in the spanwise and normal directions. Wave numbers and spatial growth rates are in good agreement with theoretical predictions.

The Harten, Lax, and van Leer with contact restoration (HLLC) scheme has been modified and extended in conjunction with time-derivative preconditioning to compute flow problems at all speeds. It is found that a simple modification of signal velocities in the HLLC scheme based on the eigenvalues of the preconditioned system is only needed to reduce excessive numerical diffusion at the low Mach number. The modified scheme has been implemented and used to compute a variety of flow problems in both two and three dimensions on unstructured grids. Numerical results obtained indicate that the modified HLLC scheme is accurate, robust, and efficient for flow calculations across the Mach-number range.