Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability
Finite-difference weighted essentially non-oscillatory (WENO) simulations of the reshocked two-dimensional single-mode Richtmyer-Meshkov instability using third-, fifth- and ninth-order spatial flux reconstruction and uniform spatial grid resolutions corresponding to 128, 256 and 512 points per initial perturbation wavelength are presented. The dependence of the density, vorticity, simulated density Schlieren and baroclinic production fields, mixing layer width, circulation deposition, mixing profiles, chemical products and mixing fractions, energy spectra, statistics, probability distribution functions, effective turbulent kinetic energy and enstrophy production/dissipation rates, numerical Reynolds numbers, and effective numerical viscosity on the order and resolution is comprehensively investigated to long evolution times. The results are interpreted using the computed implicit numerical diffusion arising from the truncation errors in the characteristic projection-based WENO method. It is quantitatively shown that simulations with higher order and higher resolution have lower numerical dissipation. The sensitivity of the quantities considered to the order and resolution is further amplified following reshock, when the energy deposition on the evolving interface by the second shock-interface interaction induces the formation of small-scale structures. Simulations using lower orders of reconstruction and on coarser grids preserve large-scale structures and flow symmetry to late times, while simulations using higher orders of reconstruction and on finer grids exhibit fragmentation of the structures, symmetry breaking and increased mixing. The investigation demonstrates that similar flow features are qualitatively and quantitatively captured by either approximately doubling the order or the resolution. Additionally, the computational scaling shows that increasing the order is more advantageous than doubling the resolution for the complex shock-driven hydrodynamic flow and WENO method considered here. The present investigation suggests that the ninth-order WENO method is well-suited for the simulation and analysis of complex multi-scale flows and mixing generated by shock-induced hydrodynamic instabilities.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 883610
- Report Number(s):
- UCRL-TR-220015; TRN: US200615%%175
- Country of Publication:
- United States
- Language:
- English
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