Hierarchically semiseparable (HSS) matrix techniques are emerging in constructing superfast direct solvers for both dense and sparse linear systems. Here, we develop a set of novel parallel algorithms for key HSS operations that are used for solving large linear systems. These are parallel rank-revealing QR factorization, HSS constructions with hierarchical compression, ULV HSS factorization, and HSS solutions. The HSS tree-based parallelism is fully exploited at the coarse level. The BLACS and ScaLAPACK libraries are used to facilitate the parallel dense kernel operations at the fine-grained level. We appply our new solvers for discretized Helmholtz equations for multifrequency seismic imaging and iteratively solve time-harmonic seismic inverse boundary value problems. In particular, we use the HSS algorithms to solve the dense Schur complement systems associated with the root separator of the separator tree obtained from nested dissection of the graph of discretized Helmholtz equations. We demonstrate that the new approach is much faster and uses much less memory than the LU factorization algorithm for both two-dimensional and three-dimensional problems, using up to 8912 processing cores. This is the first work in parallelizing HSS algorithms and conducting detailed performance analysis on a large parallel machine. This also lays a good foundation for developing scalable sparse structured factorization algorithms for general sparse linear systems.

Inclusion of the nozzle geometry with a turbulent inflow boundary condition is essential for realistic jet noise simulations. In the current study, a digital filter-based turbulent inflow condition, extended in a new way to non-uniform curvilinear grids, is implemented to achieve this. The proposed method has several key features desirable for jet noise simulations, with some limitations. To validate the method, a quasi-incompressible zeropressure-gradient flat plate turbulent boundary layer is simulated at a high Reynolds number. The boundary layer produced by the current method is shown to agree reasonably well with theory and a recycling-based turbulence injection method. The length of the adjustment region necessary for synthetic inlet turbulence to recover from modeling errors is estimated. A low Reynolds number wall-resolved jet simulation including a round nozzle geometry is performed. The method is shown to be effective in producing sustained turbulence on a non-uniform, non-Cartesian grid at a barely turbulent Reynolds number. The effect of variation of the inlet integral length scales on the recovery of turbulent fluctuations is studied and recommendations are made for choosing these parameters. A possible spurious noise source is identified near the turbulent inlet for the current method. It is shown that this spurious noise does not affect the acoustic field outside of the jet significantly, though it is recommended to attenuate this noise artificially by using a sponge zone.Downloaded by CORNELL UNIVERSITY on July 30, 2015 | http://arc.aiaa.org |

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Accurate predictions of jet noise produced by realistic nozzles with complicated geometries (e.g. chevrons) require the inclusion of walls in large eddy simulations (LES). However, the additional cost of resolving the near-wall turbulence at realistic Reynolds numbers is prohibitively expensive. To make such simulations more economical, a wall model based on the logarithmic velocity profile is described in detail and implemented in a high-order finite difference LES application using generalized curvilinear coordinates. Simulations of a high Reynolds number (Reθ = 13, 000) nearly incompressible zero pressure gradient flat plate boundary layer are completed for validation and justification of the proposed methodology. The subgrid scale (SGS) model choice is also examined. Implicit LES using a low-pass spatial filter and the dynamic Smagorinsky model are evaluated on an a posteriori basis. Lastly, a series of comparatively coarse grids are tested to more critically evaluate the methodology's ability to reduce simulation costs. This is essential as jet noise simulations can remain prohibitively expensive even with a suitable wall modeling approach. Overall, the numerical results show reasonable agreement for the flow in the outer portions of the boundary layer when compared to experimental data and theoretical estimates. NomenclatureB log-law integration constant C f skin friction coefficient C s Smagorinsky constant F, G, H fluxes in the generalized curvilinear coordinates J Jacobian transformation between physical Cartesian and generalized curvilinear coordinates L r reference length M Mach number P fluid static pressure P r t turbulent Prandtl number Q vector of conservative variables Q i SGS heat flux Re δ99iReynolds number based on inflow boundary layer thickness, ρU ∞ δ 99i /µ

Computational aeroacoustics (CAA) has emerged as a tool to complement theoretical and experimental approaches for robust and accurate prediction of sound levels from aircraft airframes and engines. CAA, unlike computational fluid dynamics (CFD), involves the accurate prediction of smallamplitude acoustic fluctuations and their correct propagation to the far field. In that respect, CAA poses significant challenges for researchers because the computational scheme should have high accuracy, good spectral resolution, and low dispersion and diffusion errors. A high-order compact finite difference scheme, which is implicit in space, can be used for such simulations because it fulfills the requirements for CAA. Usually, this method is parallelized using a transposition scheme; however, that approach has a high communication overhead. In this paper, we discuss the use of a parallel tridiagonal linear system solver based on the truncated SPIKE algorithm for reducing the communication overhead in our large eddy simulations. We report experimental results collected on two parallel computing platforms.