Computation of hyperbolic equations on complicated domains with patched and overset Chebyshev grids
SIAM Journal on Scientific and Statistical Computing
Solution of an inverse heat transfer problem by means of empirical reduction of modes
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Trust region model management in multidisciplinary design optimization
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Digital Picture Processing
Standardized pseudospectral formulation of the inviscid supsersonic blunt body problem
Journal of Computational Physics
On the outflow conditions for spectral solution of the viscous blunt-body problem
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
A novel Karhunen-Loève (KL) least-squares model for the supersonic flow of an inviscid, calorically perfect ideal gas about an axisymmetric blunt body employing shock-fitting is developed; the KL least-squares model is used to accurately select an optimal configuration which minimizes drag. Accuracy and efficiency of the KL method is compared to a pseudospectral method employing global Lagrange interpolating polynomials. KL modes are derived from pseudospectral solutions at Mach 3.5 from a uniform sampling of the design space and subsequently employed as the trial functions for a least-squares method of weighted residuals. Results are presented showing the high accuracy of the method with less than 10 KL modes. Close agreement is found between the optimal geometry found using the KL model to that found from the pseudospectral solver. Not including the cost of sampling the design space and building the KL model, the KL least-squares method requires less than half the central processing unit time as the pseudospectral method to achieve the same level of accuracy. A decrease in computational cost of several orders of magnitude as reported in the literature when comparing the KL method against discrete solvers is shown not to hold for the current problem. The efficiency is lost because the nature of the nonlinearity renders a priori evaluation of certain necessary integrals impossible, requiring as a consequence many costly reevaluations of the integrals.