This paper presents an investigation into the use of a moving mesh algorithm for solving unsteady turbulent mixing problems. The growth of a shock induced mixing zone following reshock, using an initial setup comparable to that of existing experimental work, is used to evaluate the behavior of the numerical scheme for single-mode Richtmyer–Meshkov instability (SM-RMI). Subsequently the code is used to evaluate the growth rate for a range of different initial conditions. The initial growth rate for three-dimensional (3D) SM Richtmyer–Meshkov is also presented for a number of different initial conditions. This numerical study details the development of the mixing layer width both prior to and after reshock. The numerical scheme used includes an arbitrary Lagrangian–Eulerian grid motion which is successfully used to reduce the mesh size and computational time while retaining the accuracy of the simulation results. Varying initial conditions shows that the growth rate after reshock is independent of the initial conditions for a SM provided that the initial growth remains in the linear regime.

References

References
1.
Richtmyer
,
R. D.
,
1960
, “
Taylor Instability in Shock-Acceleration of Compressible Fluids
,”
Commun. Pure. Appl. Math.
,
13
(2), pp.
297
319
.10.1002/cpa.3160130207
2.
Meshkov
,
E. E.
,
1972
, “
Instability of the Interface of Two Gases Accelerated by a Shock Wave
,”
Fluid Dyn.
,
4
(
5
), pp.
101
104
.10.1007/BF01015969
3.
Barnes
,
C. W.
,
Batha
,
S. H.
,
Dunne
,
A. M.
,
Magelssen
,
G. R.
,
Rothman
,
S.
,
Day
,
R. D.
,
Elliott
,
N. E.
,
Haynes
,
D. A.
,
Holmes
,
R. L.
,
Scott
,
J. M.
,
Tubbs
,
D. L.
,
Youngs
,
D. L.
,
Boehley
,
T. R.
, and
Jaanimagi
,
P.
,
2002
, “
Observation of Mix in a Compressible Plasma in a Convergent Cylindrical Geometry
,”
Phys. Plasmas
,
9
(
11
), pp.
4431
4434
.10.1063/1.1511730
4.
Lindl
,
J. D.
,
McCrory
,
R. L.
, and
Campbell
,
E. M.
,
1992
, “
Progress Toward Ignition and Burn Propagation in Inertial Confinement Fusion
,”
Phys. Today
,
45
(
9
), pp.
32
40
.10.1063/1.881318
5.
Latini
,
M.
,
Schilling
,
O.
, and
Don
,
W. S.
,
2007
, “
High-Resolution Simulations and Modeling of Reshocked Single-Mode Richtmyer–Meshkov Instability: Comparison to Experimental Data and to Amplitude Growth Model Predictions
,”
Phys. Fluids
,
19
, p. 024104.10.1063/1.2472508
6.
Collins
,
B. D.
, and
Jacobs
,
J. W.
,
2002
, “
PLIF Flow Visualization and Measurement of the Richtmyer–Meshkov Instability of an Air/SF6 Interface
,”
J. Fluid Mech.
,
464
, pp.
113
136
.10.1017/S0022112002008844
7.
Sod
,
G. A.
,
1978
, “
A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws
,”
J. Comput. Phys.
,
27
(1), pp.
1
31
.10.1016/0021-9991(78)90023-2
8.
Thornber
,
B.
,
Bilger
,
R. W.
,
Masri
,
A. R.
, and
Hawkes
,
E. R.
,
2011
, “
An Algorithm for LES of Premixed Compressible Flows Using the Conditional Moment Closure Model
,”
J. Comput. Phys.
,
230
(20), pp.
7687
7705
.10.1016/j.jcp.2011.06.024
9.
Allaire
,
G.
,
Clerc
,
S.
, and
Kokh
,
S.
,
2002
, “
A Five-Equation Model for the Simulation of Interfaces Between Compressible Fluids
,”
J. Comput. Phys.
,
181
(2), pp.
577
616
.10.1006/jcph.2002.7143
10.
Kim
,
K. H.
, and
Kim
,
C.
,
2005
, “
Accurate, Efficient and Monotonic Numerical Methods for Multi-Dimensional Compressible Flows Part II: Multi-Dimensional Limiting Process
,”
J. Comput. Phys.
,
208
(2), pp.
570
615
.10.1016/j.jcp.2005.02.022
11.
Shu
,
C. W.
,
1988
, “
Total-Variation-Diminishing Time Discretizations
,”
SIAM J. Sci. Stat. Comput.
,
9
(6), pp.
1073
1084
.10.1137/0909073
12.
Thornber
,
B.
,
Drikakis
,
D.
,
Youngs
,
D. L.
, and
Williams
,
R. J. R.
,
2008
, “
On Entropy Generation and Dissipation of Kinetic Energy in High-Resolution Shock-Capturing Schemes
,”
J. Comput. Phys.
,
227
(10), pp.
4853
4872
.10.1016/j.jcp.2008.01.035
13.
Thornber
,
B.
,
Mosedale
,
A.
,
Drikakis
,
D.
,
Youngs
,
D. L.
, and
Williams
,
R. J. R.
,
2008
, “
An Improved Reconstruction Method for Compressible Flows With Low Mach Number Features
,”
J. Comput. Phys.
,
227
(10), pp.
4873
4894
.10.1016/j.jcp.2008.01.036
14.
Toro
,
E. F.
,
2009
,
Riemann Solvers and Numerical Methods for Fluid Dynamics
,
3rd ed.
,
Springer
,
Berlin
, Germany.
15.
Mosedale
,
A.
, and
Drikakis
,
D.
,
2007
, “
Assessment of Very High Order of Accuracy in Implicit LES Models
,”
ASME J. Fluid. Eng.
,
129
(12), pp.
1497
1503
.10.1115/1.2801374
16.
Liska
,
R.
, and
Wendroff
,
B.
,
2003
, “
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations
,”
SIAM J. Sci. Comput.
,
25
(
3
), pp.
995
1017
.10.1137/S1064827502402120
17.
Gowardhan
,
A. A.
,
Ristorcelli
,
J. R.
, and
Grinstein
,
F. F.
,
2011
, “
The Bipolar Behavior of the Richtmyer–Meshkov Instability
,”
Phys. Fluids
,
23
, p. 071701.10.1063/1.3610959
18.
Balakumar
,
B. J.
,
Orlicz
,
G. C.
,
Tomkins
,
C. D.
, and
Prestridge
,
K. P.
,
2008
, “
Simultaneous Particle-Image Velocimetry-Planar Laser-Induced Fluorescence Measurements of Richtmyer–Meshkov Instability Growth in a Gas Curtain With and Without Reshock
,”
Phys Fluids
,
20
(
12
), p.
124103
.10.1063/1.3041705
19.
Thornber
,
B.
,
Drikakis
,
D.
,
Youngs
,
D. L.
, and
Williams
,
R. J. R.
,
2012
, “
Physics of the Single-Shocked and Reshock Richtmyer–Meshkov Instability
,”
J. Turb.
,
13
.10.1080/14685248.2012.658916
20.
Thornber
,
B.
,
Drikakis
,
D.
,
Youngs
,
D. L.
, and
Williams
,
R. J. R.
,
2010
, “
The Influence of Initial Conditions on Turbulent Mixing Due to Richmyer–Meshkov Instability
,”
J. Fluid. Mech.
,
654
, pp.
99
139
.10.1017/S0022112010000492
21.
Mikaelian
,
K. O.
,
1989
, “
Turbulent Mixing Generated by Rayleigh–Taylor and Richtmyer–Meshkov Instability
,”
Physica. D
,
36
(3), pp.
343
357
.10.1016/0167-2789(89)90089-4
22.
Charakhch'an
,
A. A.
,
2000
, “
Richtmyer–Meshkov Instability of an Interface Between Two Media Due to Passage of Two Successive Shocks
,”
J. Appl. Mech. Tech. Phys
,
41
(
1
), pp.
23
31
.10.1007/BF02465232
You do not currently have access to this content.