Begell House
International Journal for Uncertainty Quantification
International Journal for Uncertainty Quantification
2152-5080
8
5
2018
Uncertainty quantification for incident helium flux in plasma-exposed tungsten
In this work, the surface response of a tungsten plasma-facing component was simulated by a cluster-dynamics code, Xolotl, with a focus on quantifying the impact of uncertainty in one of the input parameters to Xolotl, namely the incident helium flux. The simulated conditions involve a tungsten surface exposed to 100 eV helium ion implantations with a flux of either 4x10^22 or 4x10^25 He m^(-2)s^(-1). Two sources were used to describe the implanted helium depth distribution in tungsten, either molecular dynamics (MD) or a binary collision approximation code, the Stopping and Range of Ions in Matter (SRIM). The aim of this work is to evaluate and examine uncertain predictions on the helium retention based on these two different modeling methodologies that either neglect electronic energy loss or the crystalline structure of the solid, respectively. An embedded model-form error approach was pursued here in order to arrive at predictions that account for variability due to the two different data sources, and the impact of this model-form uncertainty in incident helium flux on Xolotl output was presented for the two implantation fluxes.
Brian
Wirth
University of Tennesee, Knoxville
0
DATA ASSIMILATION FOR NAVIER-STOKES USING THE LEAST-SQUARES FINITE-ELEMENT METHOD
We investigate theoretically and numerically the use of the least-squares finite-element method (LSFEM) to approach
data-assimilation problems for the steady-state, incompressible Navier-Stokes equations. Our LSFEM discretization is
based on a stress-velocity-pressure (S-V-P) first-order formulation, using discrete counterparts of the Sobolev spaces
H(div)×H1×L2 for the variables respectively. In general, S-V-P formulations are promising when the stresses are of special interest, e.g., for non-Newtonian, multiphase or turbulent flows. Resolution of the system is via minimization of a least-squares functional representing the magnitude of the residual of the equations. A simple and immediate approach to extend this solver to data assimilation is to add a data-discrepancy term to the functional. Whereas most data assimilation techniques require a large number of evaluations of the forward simulation and are therefore very
expensive, the approach proposed in this work uniquely has the same cost as a single forward run. However, the question arises: what is the statistical model implied by this choice? We answer this within the Bayesian framework, establishing the latent background covariance model and the likelihood. Further we demonstrate that−in the linear case−the method is equivalent to application of the Kalman filter, and derive the posterior covariance. We practically demonstrate the capabilities of our method on a backward-facing step case. Our LSFEM formulation (without data) is shown to have good approximation quality, even on relatively coarse meshes−in particular with respect to mass conservation and reattachment location. Adding limited velocity measurements from experiment, we show that the method is able to correct for discretization error on very coarse meshes, as well as correct for the influence of unknown and uncertain boundary conditions.
Alexander
Schwarz
Institut für Mechanik, University of Duisburg-Essen, Universitätsstraße 15, 45141 Essen,
Germany
Richard P.
Dwight
Aerodynamics Group, Faculty of Aerospace, TU Delft, P.O. Box 5058, 2600GB Delft, The
Netherlands
383-403
CUBIC INTUITIONISTIC FUZZY AGGREGATION OPERATORS
The objective of this manuscript is to present some series of aggregation operators under the cubic intuitionistic fuzzy
set (CIFS) and their suitable properties. Firstly an operational law, score function, and accuracy function between
the cubic intuitionistic fuzzy numbers (CIFNs) under the P-order and R-order are defined and hence based on them, some weighted averaging and geometric aggregation operators, namely, cubic intuitionistic fuzzy weighted, ordered weighted, hybrid averaging, and geometric aggregation operators are proposed. A decision-making method based on these operators is proposed for ranking the different sets of the alternative under CIFS domain. Finally, an illustrative example is given to demonstrate the proposed approach.
Gagandeep
Kaur
School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University)
Patiala 147004, Punjab, India
Harish
Garg
School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University)
Patiala 147004, Punjab, India
405-427