Direct numerical simulation of mixing processes (Rayleigh-Taylor and Richtmyer-Meshkov instabilities) is computationally expensive due to the need to resolve turbulent structures on small scales. Hence, it is common practice in both academia and industry to use phenomenological models that explicitly model the mixing processes within a host hydrodynamic code. For such schemes to be self-consistent, the mixing should be dominated by the mass introduced by the dedicated mixing model, with minimal contribution from the numerical methods of the host code. In this report, several diagnostic statistics are described that allow for the assessment of the production of mix and a determination of the quality of a mixing model. These diagnostics are implemented within an existing two-dimensional finite element hydrocode, containing an implementation of Youngs' turbulent mix model, and used to assess the mixing scheme against a number of two-fluid test problems.

References

References
1.
Youngs
,
D. L.
,
1994
, “
Numerical Simulation of Mixing by Rayleigh-Taylor and Richtmyer-Meshkov Instabilities
,”
Laser Part. Beams
,
12
, pp. 725–750.10.1017/S0263034600008557
2.
Youngs
,
D. L.
,
1995
, “
Representation of the Molecular Mixing Process in a Two-Phase Flow Turbulent Mixing Model
,”
5th International Workshop on the Physics of Compressible Turbulent Mixing
,
World Scientific
,
Singapore
, pp.
83
88
.
3.
Hansom
,
J. C. V.
,
Rosen
,
P. A.
,
Goldack
,
T. J.
,
Oades
,
K.
,
Fieldhouse, P.
,
Cowperthwaite
,
N.
,
Youngs
,
D. L.
,
Mawhinney
,
N.
, and
Baxter
,
A. J.
,
1990
, “
Radiation Driven Planar Foil Instability and Mix Experiments at the AWE HELEN Laser
,”
Laser Part. Beams
,
8
, pp.
51
71
.10.1017/S0263034600007825
4.
Llor
,
A.
, 2005, “Statistical Hydrodynamic Models for Developing Mixing Instability Flows,”
Lect. Notes Phys.
,
681
, pp. 17–28.
5.
Besnard
,
D.
,
Harlow
,
F. H.
,
Rauenzahn
,
R. M.
, and
Zemach
,
C.
,
1992
, “
Turbulence Transport Equations for Variable-Density Turbulence and Their Relationship to Two-Field Models
,” Los Alamos National Laboratory, Report No. LA–12303-MS.
6.
Youngs
,
D. L.
,
1989
, “
Modeling Turbulent Mixing by Rayleigh-Taylor Instability
,”
Phys. D
,
37
, pp.
270
287
.10.1016/0167-2789(89)90135-8
7.
Smeeton
,
V. S.
, and
Youngs
,
D. L.
,
1988
, “
Experimental Investigation of Turbulent Mixing by Rayleigh-Taylor Instability
,” AWE, Report No. O 35/87.
8.
Winslow
,
A. M.
,
1966
, “
Numerical Solution of the Quasilinear Poisson Equation in a Non-Uniform Triangular Mesh
,”
J. Comput. Phys.
,
1
, pp.
149
–172.10.1016/0021-9991(66)90001-5
9.
Lombardini
,
M.
,
Hill
,
D. J.
,
Pullin
,
D. I.
, and
Meiron
,
D. I.
,
2011
, “
Atwood Ratio Dependence of Richtmyer-Meshkov Flows Under Reshock Conditions Using Large-Eddy Simulations
,”
J. Fluid Mech.
,
670
, pp.
439
–480.10.1017/S0022112010005367
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