1,432 research outputs found
Quantification of errors in large-eddy simulations of a spatially-evolving mixing layer
A stochastic approach based on generalized Polynomial Chaos (gPC) is used to
quantify the error in Large-Eddy Simulation (LES) of a spatially-evolving
mixing layer flow and its sensitivity to different simulation parameters, viz.
the grid stretching in the streamwise and lateral directions and the subgrid
scale model constant (). The error is evaluated with respect to the
results of a highly resolved LES (HRLES) and for different quantities of
interest, namely the mean streamwise velocity, the momentum thickness and the
shear stress. A typical feature of the considered spatially evolving flow is
the progressive transition from a laminar regime, highly dependent on the inlet
conditions, to a fully-developed turbulent one. Therefore the computational
domain is divided in two different zones (\textit{inlet dependent} and
\textit{fully turbulent}) and the gPC error analysis is carried out for these
two zones separately. An optimization of the parameters is also carried out for
both these zones. For all the considered quantities, the results point out that
the error is mainly governed by the value of the constant. At the end of
the inlet-dependent zone a strong coupling between the normal stretching ratio
and the value is observed. The error sensitivity to the parameter values
is significantly larger in the inlet-dependent upstream region; however, low
error values can be obtained in this region for all the considered physical
quantities by an ad-hoc tuning of the parameters. Conversely, in the turbulent
regime the error is globally lower and less sensitive to the parameter
variations, but it is more difficult to find a set of parameter values leading
to optimal results for all the analyzed physical quantities
Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods
In this work, we consider the Biot problem with uncertain poroelastic
coefficients. The uncertainty is modelled using a finite set of parameters with
prescribed probability distribution. We present the variational formulation of
the stochastic partial differential system and establish its well-posedness. We
then discuss the approximation of the parameter-dependent problem by
non-intrusive techniques based on Polynomial Chaos decompositions. We
specifically focus on sparse spectral projection methods, which essentially
amount to performing an ensemble of deterministic model simulations to estimate
the expansion coefficients. The deterministic solver is based on a Hybrid
High-Order discretization supporting general polyhedral meshes and arbitrary
approximation orders. We numerically investigate the convergence of the
probability error of the Polynomial Chaos approximation with respect to the
level of the sparse grid. Finally, we assess the propagation of the input
uncertainty onto the solution considering an injection-extraction problem.Comment: 30 pages, 15 Figure
Efficient uncertainty quantification in aerospace analysis and design
The main purpose of this study is to apply a computationally efficient uncertainty quantification approach, Non-Intrusive Polynomial Chaos (NIPC) based stochastic expansions, to robust aerospace analysis and design under mixed (aleatory and epistemic) uncertainties and demonstrate this technique on model problems and robust aerodynamic optimization. The proposed optimization approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes the stochastic measures which are minimized simultaneously to ensure the robustness of the final design to both aleatory and epistemic uncertainties. For model problems with mixed uncertainties, Quadrature-Based and Point-Collocation NIPC methods were used to create the response surfaces used in the optimization process. For the robust airfoil optimization under aleatory (Mach number) and epistemic (turbulence model) uncertainties, a combined Point-Collocation NIPC approach was utilized to create the response surfaces used as the surrogates in the optimization process. Two stochastic optimization formulations were studied: optimization under pure aleatory uncertainty and optimization under mixed uncertainty. As shown in this work for various problems, the NIPC method is computationally more efficient than Monte Carlo methods for moderate number of uncertain variables and can give highly accurate estimation of various metrics used in robust design optimization under mixed uncertainties. This study also introduces a new adaptive sampling approach to refine the Point-Collocation NIPC method for further improvement of the computational efficiency. Two numerical problems demonstrated that the adaptive approach can produce the same accuracy level of the response surface obtained with oversampling ratio of 2 using less function evaluations. --Abstract, page iii
Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification
We present an enriched formulation of the Least Squares (LSQ) regression
method for Uncertainty Quantification (UQ) using generalised polynomial chaos
(gPC). More specifically, we enrich the linear system with additional equations
for the gradient (or sensitivity) of the Quantity of Interest with respect to
the stochastic variables. This sensitivity is computed very efficiently for all
variables by solving an adjoint system of equations at each sampling point of
the stochastic space. The associated computational cost is similar to one
solution of the direct problem. For the selection of the sampling points, we
apply a greedy algorithm which is based on the pivoted QR decomposition of the
measurement matrix. We call the new approach sensitivity-enhanced generalised
polynomial chaos, or se-gPC. We apply the method to several test cases to test
accuracy and convergence with increasing chaos order, including an aerodynamic
case with stochastic parameters. The method is found to produce accurate
estimations of the statistical moments using the minimum number of sampling
points. The computational cost scales as , instead of
of the standard LSQ formulation, where is the number of stochastic
variables and the chaos order. The solution of the adjoint system of
equations is implemented in many computational mechanics packages, thus the
infrastructure exists for the application of the method to a wide variety of
engineering problems
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