Publications

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  Liou, M.-S., and Scandaliato, A.L. • Computational Fluid Dynamics 2008, Springer Berlin Heidelberg, p.391-396, 2009

  Compact differencing can deliver high-order accuracy using only a limited span of stencils, but incurring a costly matrix inversion. Hence, use of a stable implicit time discretization becomes favorable in order to offset the computation cost by allowing a large time step. A practical way to reduce the burden of inverting a large matrix from multidimensional problems is to split the implicit operator into a series of smaller operators. Undesirable consequences can surface, such as (1) loss of stability, and/or (2) loss of accuracy. Here, we propose a consistent implicit compact method and study the stability and accuracy of steady and unsteady solutions.

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  Scandaliato, A.L., and Liou, M.-S. • Commun. Comput. Phys., Vol. 12, No.4, p. 1096-1120, 2012

  In this paper we study the effectiveness of using known high-order upwind-biased interpolation procedures, weighted essentially non-oscillatory (WENO) scheme [1] and its variations[2][3], and monotonicity preserving (MP) scheme [4], in conjunction with AUSM-family, specifically AUSM+-UP [5], for Euler equations. Key difficulties become apparent with these high-order formulations that require special attention beyond any seen in low-order formulations (third-order and below). In addition, four reflective boundary conditions are compared for their effects on residual convergence and near boundary oscillations. Notes are made on the importance of interpolating with characteristics variables. Results of using the Roe flux with an entropy fix and Lax-Friedrichs scheme are also included for comparison. Finally, a measure for quantifying the efficiency of high order solution is proposed, showing that a maximum return is reached at some moderate order of accuracy, provided sufficient grid resolution is available.

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  Scandaliato, A.L., and Liou, M.-S. • 49th AIAA Aerospace Sciences Meeting, Orlando FL, AIAA-2011-1279, 2011

  In this paper we investigate the issues encountered in the state-of-the-art practice for sonic boom calculation, specifically the near-field flow fidelity, the axial-symmetry criteria for wave-form propagation, and the sensitivity of perceived loudness to wave-form. This work has been carried out with the intent for inclusion in a shape optimization framework for aerodynamic design and analysis for low boom supersonic transport. Using an adaptive Cartesian meshing method for solving the Euler equations, Cart3D1, we analyze the effects of both grid refinement and pressure sampling distance away from an aircraft on the extrapolated sonic boom signature and perceived loudness. In this study, two delta-wing models and the NASA experimental F-15-Active aircraft are used to test the sonic boom propagation procedure and loudness calculation. Convergence of the ground pressure signature with respect to the near-field sampling distance from the aircraft is achieved rather quickly. The perceived loudness (PLdB) is tested for its sensitivity to changes in signature shape; our study reveals a surprising insensitivity to the near-field sampling distance, axial-symmetry condition, and mesh size. Finally, to gain further insight into the link between the ground signature and loudness, we construct several nominal signature models and assess the effectiveness of the controlling parameters.

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