Adaptive Mesh Refinement (AMR) Simulations of Richtmyer-Meshkov Instability with Re-Shock

Man Long Wong 1, Daniel Livescu 2 and Sanjiva K. Lele 1

1 Stanford University, 2 Los Alamos National Laboratory

References1. Man Long Wong, Sanjiva K. Lele. "High-Order Localized Dissipation

Weighted Compact Nonlinear Scheme for Shock-and Interface-Capturing in Compressible Flows." Journal of Computational Physics (2017)

2. Man Long Wong, Sanjiva K. Lele. "Multiresolution Feature Detection in Adaptive Mesh Refinement with High-Order Shock-and Interface-Capturing Scheme." 46th AIAA Fluid Dynamics Conference (2016)

3. John D Schwarzkopf, Daniel Livescu, Robert A Gore, Rick M Rauenzahn, J Raymond Ristorcelli. “Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids.” Journal of Turbulence (2011)

Numerical Methods

• In-house AMR solver HAMeRS built on the SAMRAI library by LLNL

• 6th-order localized dissipation shock-capturing scheme WCNS [1]

• 6th-order finite difference scheme for diffusive/viscous flux• TVD-RK3 scheme for time integration• Adaptive refinement in both space and time• 3 levels of adaptive meshes (two levels of AMR)• Gradient and wavelet sensors [2] to identify regions of

interest for refinementAcknowledgements

This research is supported by Los Alamos National Laboratory (LANL) (LANL agreement number: 431679). We also acknowledge LANL for providing computer time to complete the numerical simulations.

Introduction

Richtmyer-Meshkov (RM) instability is a fundamentalhydrodynamic flow instability that occurs when a shock wavepasses through a material interface between fluids of differentdensities. The instability is initiated from the misalignment in thepressure and density gradients across the shock wave and materialinterface. The study of turbulence from RM instability is veryimportant for understanding supernova explosion in astrophysics,supersonic/hypersonic combustion and inertial confinementfusion in engineering applications.

Problem Description

Grid Base Grid Resolution Refinement Ratios Finest Grid Spacing

B 640 × 32 × 32 1: 2, 1: 4 0.0977𝑚𝑚

C 1280 × 64 × 64 1: 2, 1: 4 0.0488𝑚𝑚

D 2560 × 128 × 128 1: 2, 1: 4 0.0244𝑚𝑚

Visualization of Mass Fraction Field Budget of Turbulent Mass Flux

Analysis of BHR3[3] Closure Model

Grid Convergence Study

𝑊 = න4 < 𝑌𝑆𝐹6 >< 𝑌𝑎𝑖𝑟 >𝑑𝑥 Θ = < 𝑌𝑆𝐹6 ⋅ 𝑌𝑎𝑖𝑟 >𝑑𝑥

< 𝑌𝑆𝐹6 >< 𝑌𝑎𝑖𝑟 > 𝑑𝑥

Mixing width, W Mixedness, Θ

Integrated turbulent kinetic energy, TKE Reynolds number, 𝑅𝑒

Conclusion

High-fidelity adaptive mesh refinement simulations of the RMinstability were conducted. Good grid convergence of statisticalquantities is obtained from the simulations. The simulation data isused to validate a second moment closure model. It is shown thatthe model can capture the shape of the unclosed terms well but isimperfect in estimating the magnitude of the terms.

Just after re-shock (𝑡 = 1.2𝑚𝑠) End of simulation (𝑡 = 1.75𝑚𝑠)

Just after re-shock (𝑡 = 1.2𝑚𝑠)Just before re-shock (𝑡 = 1.1𝑚𝑠)

End of simulation (𝑡 = 1.75𝑚𝑠)

Model/exact ≈ 0.05 Model/exact ≈ 0.1

Model/exact ≈ 8 Model/exact ≈ 6• 𝑀𝑠ℎ𝑜𝑐𝑘 = 1.45

• 𝐴𝑡 =𝜌𝑆𝐹6−𝜌𝑎𝑖𝑟

𝜌𝑆𝐹6+𝜌𝑎𝑖𝑟= 0.68

• Perturbation wavelength ≈ 1𝑚𝑚

Video of AMR simulation: