Numerical Algorithms for Turbulent Mixing Simulations

The desirable features of algorithms for the direct, implicit large-eddy, and largeeddy numerical simulation of compressible turbulent mixing are discussed. Issues specific to turbulence and mixing induced by interfacial instabilities are briefly reviewed. A high-resolution, Eulerian numerical algorithm for compressible turbulent mixing simulations currently in use at the Lawrence Livermore National Laboratory (LLNL) is described−the weighted essentially non-oscillatory (WENO) method. The method is applied to the two-dimensional reshocked Richtmyer-Meshkov instability using third-, fifth-, and ninth-order reconstruction, and the dependence of quantities on both the grid resolution and order of spatial flux reconstruction is investigated. It is shown that certain large-scale quantities exhibit little sensitivity to both the resolution and order prior to reshock, but exhibit much greater sensitivity following reshock. The dependence of various quantities determined by the entire range of resolved scales (such as energy spectra and mixing characteristics) on the resolution and order is also discussed. It is concluded that lower-order reconstruction and lower resolution result in excessively large numerical dissipation. The implications of these results for simulating experiments and assessing turbulent transport and mixing models are briefly discussed.