# Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder

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## Abstract

Two-dimensional numerical simulations of the Richtmyer–Meshkov unstable “shock-jet” problem are conducted using both large-eddy simulation (LES) and unsteady Reynolds-averaged Navier–Stokes (URANS) approaches in an arbitrary Lagrangian–Eulerian hydrodynamics code. Turbulence statistics are extracted from LES by running an ensemble of simulations with multimode perturbations to the initial conditions. Detailed grid convergence studies are conducted, and LES results are found to agree well with both experiment and high-order simulations conducted by Shankar et al. (Phys Fluids 23, 024102, 2011). URANS results using a *k*–*L* approach are found to be highly sensitive to initialization of the turbulence lengthscale *L* and to the time at which *L* becomes resolved on the computational mesh. It is observed that a gradient diffusion closure for turbulent species flux is a poor approximation at early times, and a new closure based on the mass-flux velocity is proposed for low-Reynolds-number mixing.

## Keywords

Richtmyer–Meshkov instability Turbulent mixing Large-eddy simulation## Notes

### Acknowledgments

The authors would like to specifically acknowledge and thank Bob Tipton for his input and notes regarding the similarity analysis contained in Appendix 2. The authors would also like to thank Britton Olson, Mike Wickett, Oleg Schilling, Andy Cook, Bill Cabot, Mark Ulitsky, Bryan Johnson, Ivan Otero, Frank Graziani, Rob Rieben, and Brian Pudliner for their helpful input and support in the preparation of the present work.

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