A Karhunen–Loève least-squares technique for optimization of geometry of a blunt body in supersonic flow

On the outflow conditions for spectral solution of the viscous blunt-body problem

“…The boundary conditions at this boundary as observed in [7][8][9][10]41] to present a well-posed solution and consistent with low dissipative features of the spectral methods are:…”

“…In this study, the shock-fitting method is used to obtain the shock position, as it is a computational boundary, and postshock flow variables accurately. This is done by means of the Rankine-Hugoniot relations and the compatibility equation corresponding to the characteristic variable carrying information from inside toward the shock, as in [8][9][10]32,34,41]. The initial shock profile is approximated by the correlation of Billig [42].…”

Dynamical Behavior of Trains Excited by a Non-Gaussian Vector Valued Random Field

“…This modeling is based on a two steps decomposition. First, a Karhunen-Loève (KL) expansion is performed (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] for further details):…”

Track irregularities stochastic modeling

“…First, a spatial and statistical representation is achieved, which is based on a Karhunen-Loève (KL) expansion. This very efficient method, which has first been introduced by Pearson [8] in data analysis, has been applied in many works for the last decades (see, for instance [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]). It is indeed particularly interesting as it allows the uncorrelation of the projection coefficients of X on the KL vector basis, while optimally compacting the signal energy.…”