We quantify initial-data uncertainties on a shock accelerated heavy-gas cylinder by two-dimensional well-resolved direct numerical simulations. A high-resolution compressible multicomponent flow simulation model is coupled with a polynomial chaos expansion to propagate the initial-data uncertainties to the output quantities of interest. The initial flow configuration follows previous experimental and numerical works of the shock accelerated heavy-gas cylinder. We investigate three main initial-data uncertainties, (i) shock Mach number, (ii) contamination of SF6 with acetone, and (iii) initial deviations of the heavy-gas region from a perfect cylindrical shape. The impact of initial-data uncertainties on the mixing process is examined. The results suggest that the mixing process is highly sensitive to input variations of shock Mach number and acetone contamination. Additionally, our results indicate that the measured shock Mach number in the experiment of Tomkins et al [“

An experimental investigation of mixing mechanisms in shock-accelerated flow
,” J. Fluid. Mech.611, 131 (2008)] and the estimated contamination of the SF6 region with acetone [S. K. Shankar, S. Kawai, and S. K. Lele, “
Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder
,” Phys. Fluids23, 024102 (2011)
] exhibit deviations from those that lead to best agreement between our simulations and the experiment in terms of overall flow evolution.

1.
R. D.
Richtmyer
, “
Taylor instability in shock acceleration of compressible fluids
,”
Commun. Pure Appl. Math.
13
,
297
(
1960
).
2.
E. E.
Meshkov
, “
Instability of the interface of two gases accelerated by a shock wave
,”
Fluid Dyn.
4
,
101
(
1969
).
3.
D.
Arnett
, “
The role of mixing in astrophysics
,”
Appl. J. Suppl.
127
,
213
(
2000
).
4.
P.
Amendt
,
J. D.
Colvin
,
R. E.
Tipton
,
D. E.
Hinkel
, and
M. J.
Edwards
, “
Indirect-drive noncryogenic double-shell ignition targets for the National Ignition Facility: Design and analysis
,”
Phys. Plasmas
9
,
2221
(
2002
).
5.
J.
Yang
,
T.
Kubota
, and
E. E.
Zukoski
, “
Applications of shock-induced mixing to supersonic combustion
,”
AIAA J.
31
,
854
(
1993
).
6.
J.-F.
Haas
and
B.
Sturtevant
, “
Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities
,”
J. Fluid Mech.
181
,
41
(
1987
).
7.
M. A.
Jones
and
J. W.
Jacobs
, “
A membraneless experiment for the study of Richtmyer-Meshkov instability of a shock-accelerated gas interface
,”
Phys. Fluids
9
,
3078
(
1997
).
8.
C.
Tomkins
,
S.
Kumar
,
G.
Orlicz
, and
K.
Prestridge
, “
An experimental investigation of mixing mechanisms in shock-accelerated flow
,”
J. Fluid Mech.
611
,
131
(
2008
).
9.
S. K.
Shankar
,
S.
Kawai
, and
S. K.
Lele
, “
Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder
,”
Phys. Fluids
23
,
024102
(
2011
).
10.
B. D.
Collins
and
J. W.
Jacobs
, “
PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface
,”
J. Fluid Mech.
464
,
113
(
2002
).
11.
S.
Balasubramanian
, private communication (
2012
).
12.
S.
Balasubramanian
,
G. C.
Orlicz
,
K. P.
Prestridge
, and
B. J.
Balakumar
, “
Experimental study of initial condition dependence on Richtmyer-Meshkov instability in the presence of reshock
,”
Phys. Fluids
24
,
034103
(
2012
).
13.
A. W.
Cook
, “
Enthalpy diffusion in multicomponent flows
,”
Phys. Fluids
21
,
055109
(
2009
).
14.
B.
Larrouturou
and
L.
Fezoui
, “
On the equations of multi-component perfect or real gas inviscid flow
,”
Lect. Notes Math.
1402
,
69
(
1989
).
15.
R. P.
Fedkiw
,
B.
Merriman
, and
S.
Osher
, “
High accuracy numerical methods for thermally perfect gas flows with chemistry
,”
J. Comput. Phys.
132
,
175
(
1997
).
16.
P. L.
Roe
, “
Approximate Riemann solvers, parameter, and difference schemes
,”
J. Comput. Phys.
43
,
357
(
1981
).
17.
X. Y.
Hu
,
Q.
Wang
, and
N. A.
Adams
, “
An adaptive central-upwind weighted essentially non-oscillatory scheme
,”
J. Comput. Phys.
229
,
8952
(
2010
).
18.
E. F.
Toro
,
Riemann Solvers and Numerical Methods for Fluid Dynamics
(
Springer
,
Berlin
,
1999
).
19.
S.
Gottlieb
and
C.-W.
Shu
, “
Total variation diminishing Runge-Kutta schemes
,”
Math. Comput.
67
,
73
(
1998
).
20.
V. K.
Tritschler
,
X. Y.
Hu
,
S.
Hickel
, and
N. A.
Adams
, “
Numerical simulation of a Richtmyer-Meshkov instability with an adaptive central-upwind 6th-order WENO scheme
,”
Phys. Scr.
T155
,
014016
(
2013
).
21.
V. K.
Tritschler
,
S.
Hickel
,
X. Y.
Hu
, and
N. A.
Adams
, “
On the Kolmogorov inertial subrange developing from Richtmyer-Meshkov instability
,”
Phys. Fluids
25
,
071701
(
2013
).
22.
B. M.
Adams
,
M. S.
Ebeida
,
M. S.
Eldred
,
J. D.
Jakeman
,
L. P.
Swiler
,
W. J.
Bohnhoff
,
K. R.
Dalbey
,
J. P.
Eddy
,
K. T.
Hu
, and
D. M.
Vigil
, “
DAKOTA a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis
,” Technical Report SAND2011-9106 (
Sandia National Laboratories
,
2011
), see http://dakota.sandia.gov/docs/dakota/3.0/Users3.0.pdf.
23.
S. K.
Shankar
,
S.
Kawai
, and
S. K.
Lele
, “
Numerical simulation of multicomponent shock accelerated flows and mixing using localized artificial diffusivity method
,” AIAA Paper No. 2010-352,
2010
.
24.
S. K.
Shankar
, private communication (
2013
).
25.
R. C.
Reid
,
J. M.
Pransuitz
, and
B. E.
Poling
,
The Properties of Gases and Liquids
(
McGraw-Hill
,
New York
,
1987
).
26.
J. D.
Ramshaw
, “
Self-consistent effective binary diffusion in multicomponent gas mixtures
,”
J. Non-Equilib. Thermodyn.
15
,
295
(
1990
).
27.
S.
Chapman
and
T. G.
Cowling
,
The Mathematical Theory of Non- Uniform Gases: An Account of the Kinetic Theory of Viscosity
(
Cambridge University Press
,
Cambridge
,
1990
).
You do not currently have access to this content.