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research-article  
Panagiotis Tsilifis
J. Verif. Valid. Uncert   doi: 10.1115/1.4040802
The recently introduced basis adaptation method for Homogeneous (Wiener) Chaos expansions is explored in a new context where the rotation/projection matrices are computed by discovering the active subspace where the random input exhibits most of its variability. In the case of 1-dimensional active subspaces, the methodology can be applicable to generalized Polynomial Chaos expansions, thus enabling the efficient computation of the chaos coefficients in expansions with arbitrary input distribution. Besides the significant computational savings, additional attractive features such as high accuracy in computing statistics of interest are also demonstrated.
TOPICS: Chaos, Computation, Polynomials, Statistics as topic, Rotation
research-article  
Luis Eca, Guilherme Vaz and Martin Hoekstra
J. Verif. Valid. Uncert   doi: 10.1115/1.4040803
This article presents grid refinement studies for statistically steady, two-dimensional flows of an incompressible fluid: a flat plate at Reynolds numbers equal to $10^7$, $10^8$ and $10^9$ and the NACA 0012 airfoil at angles of attack of 0, 4 and 10 degrees with $Re=6 \times 10^6$. Results are based on the numerical solution of the Reynolds-Averaged Navier-Stokes equations supplemented by one of three eddy-viscosity turbulence models of choice: the one-equation model of Spalart \& Allmaras and the two-equation models $k-\omega$ SST and $k-\sqrt{k}L$. Sets of geometrically similar structured grids with the same number of cells but different near-wall spacings are used to generate a data set that allows more than one estimation of the numerical uncertainty for similar grid densities . The selected flow quantities include functional (integral), surface and local flow quantities. An extra set of grids significantly more refined than those proposed for the estimation of the numerical uncertainty is generated for each test case. These extra solutions are used to obtain an approximation of the exact solution that allows the assessment of the performance of the numerical uncertainty estimations performed for the basis data set. However, it must be stated that with grids up to 2.5 (plate) and 8.46 (airfoil) million cells in two-dimensions, the asymptotic range is not attained for many of the selected flow quantities. All this data is available online to the community.
TOPICS: Flow (Dynamics), Turbulence, Eddies (Fluid dynamics), Viscosity, Dimensions, Reynolds number, Navier-Stokes equations, Approximation, Errors, Flat plates, Incompressible fluids, Reynolds-averaged Navier–Stokes equations, Uncertainty, Airfoils

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