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# Quantification of Computational Uncertainty for Molecular and Continuum Methods in Thermo-Fluid Sciences

[+] Author and Article Information
Dimitris Drikakis

Fluid Mechanics and Computational Sciences Department,  Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK;Computation-Based Science and Technology Centre,  The Cyprus Institute, P.O. Box 27456, 1645 Nicosia, Cyprus

Nikolaos Asproulis1

Fluid Mechanics and Computational Sciences Department,  Cranfield University, Cranfield, Bedfordshire, MK43 0AL, United Kingdom e-mail: n.asproulis@cranfield.ac.uk

1

Corresponding author.

Appl. Mech. Rev 64(4), 040801 (Aug 20, 2012) (14 pages) doi:10.1115/1.4006213 History: Received June 14, 2011; Revised February 03, 2012; Published April 27, 2012; Online August 20, 2012

## Abstract

This paper presents a review of computational uncertainties in scientific computing, as well as quantification of these uncertainties in the context of numerical simulations for thermo-fluid problems. The need for defining a measure of the numerical error that takes into account errors arising from different numerical building blocks of the simulation methods is discussed. In the above context, the effects of grid resolution, initial and boundary conditions, numerical discretization, and physical modeling constraints are presented.

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## Figures

Figure 4

Averaged relative errors compared to the very fine hexahedral mesh [40]

Figure 5

Maximum value of the axial velocity standard deviation along the central line for different grid resolutions [59]

Figure 6

Comparison of the present LES predictions for the average axial velocity against DNS and experimental data [59]

Figure 7

Effects of Riemann solver and numerical reconstruction schemes on the LES results for the average axial jet velocity distribution: HLLC and CBS Riemann Solvers; 9th-order WENO and 5th-order MUSCL schemes [59]

Figure 8

Average velocity distribution (labeled as ‘All’) obtained by averaging all LES solutions. The numerical error bar is the sum of the estimated error and the standard-error-of-the-mean [59].

Figure 9

Convergence of the PC analysis for the mean μ and standard deviation σ of the shock position xshock of the BL system [81]

Figure 10

Schematic representation of the backward-facing step and mean value and standard deviation of the horizontal velocity profile along the height of the channel at x = 21 for a backward-facing step flow at Re = 600 [82]

Figure 3

Fractional error in density for dense-fluid Poiseuille flow in a channel as a function of the transverse channel co-ordinate, y. The dashed line denotes Eq. 17 and the solid line indicates MD simulation results [14]

Figure 2

Fractional error in velocity for dense-fluid Poiseuille flow in a channel as a function of the transverse channel co-ordinate, y. The dashed line denotes Eq. 18 and the solid line denotes MD simulation results [14]

Figure 1

Variations of bulk viscosity as function of the cut-off distance [29]

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