Turbulent fluid flow interacts nonlinearly with a number of processes, including reactive flow (chemistry), radiation, and the transport of particles embedded in the flow. Subgrid scale modeling of these nonlinear processes is a major challenge to computational science. To this end, turbulent mixing of dissimilar fluids is a driver. Here we study validation issues for a class of turbulent mixing simulations. In previous work, we have obtained agreement between simulation and experiment. The present paper addresses a remaining issue, the role of meniscus related boundary effects for immiscible fluids in the validation process. Validation and even verification has been controversial for turbulent mixing flows, as commonly used numerical models are diffusive and the resulting numerical diffusion modifies the parameters of the problem and its solution. Numerical diffusion of concentration and temperature is well documented in the scientific literature for Eulerian simulations. Lagrangian simulations, which might appear to avoid this problem, are subject to mesh tangling, ensuing regridding and use of Arbitrary Lagrangian Eulerian codes to substitute for a pure Lagrangian algorithm. In practice, Lagrangian methods are potentially subject to the same numerical diffusion issues when used to study complex interface instabilities.

Approximate one-dimensional (1D) as well as 2D and 3D simulations are playing an important supporting role in the design and analysis of future experiments at National Ignition Facility. This paper is mainly concerned with 1D simulations, used extensively in design and optimization. We couple a 1D buoyancy-drag mix model for the mixing zone edges with a 1D inertial confinement fusion simulation code. This analysis predicts that National Ignition Campaign (NIC) designs are located close to a performance cliff, so modeling errors, design features (fill tube and tent) and additional, unmodeled instabilities could lead to significant levels of mix. The performance cliff we identify is associated with multimode plastic ablator (CH) mix into the hot-spot deuterium and tritium (DT). The buoyancy-drag mix model is mode number independent and selects implicitly a range of maximum growth modes. Our main conclusion is that single effect instabilities are predicted not to lead to hot-spot mix, while combined mode mixing effects are predicted to affect hot-spot thermodynamics and possibly hot-spot mix. Combined with the stagnation Rayleigh-Taylor instability, we find the potential for mix effects in combination with the ice-to-gas DT boundary, numerical effects of Eulerian species CH concentration diffusion, and ablation-driven instabilities. With the help of a convenient package of plasma transport parameters developed here, we give an approximate determination of these quantities in the regime relevant to the NIC experiments, while ruling out a variety of mix possibilities. Plasma transport parameters affect the 1D buoyancy-drag mix model primarily through its phenomenological drag coefficient as well as the 1D hydro model to which the buoyancy-drag equation is coupled.

We determine the dependence of key Inertial Confinement Fusion (ICF) hot spot simulation properties on the deuterium-tritium fuel adiabat, here modified by addition of energy to the cold shell. Variation of this parameter reduces the simulation to experiment discrepancy in some, but not all, experimentally inferred quantities. Using simulations with radiation drives tuned to match experimental shots N120321 and N120405 from the National Ignition Campaign (NIC), we carry out sets of simulations with varying amounts of added entropy and examine the sensitivities of important experimental quantities. Neutron yields, burn widths, hot spot densities, and pressures follow a trend approaching their experimentally inferred quantities. Ion temperatures and areal densities are sensitive to the adiabat changes, but do not necessarily converge to their experimental quantities with the added entropy. This suggests that a modification to the simulation adiabat is one of, but not the only explanation of the observed simulation to experiment discrepancies. In addition, we use a theoretical model to predict 3D mix and observe a slight trend toward less mixing as the entropy is enhanced. Instantaneous quantities are assessed at the time of maximum neutron production, determined dynamically within each simulation. These trends contribute to ICF science, as an effort to understand the NIC simulation to experiment discrepancy, and in their relation to the high foot experiments, which features a higher adiabat in the experimental design and an improved neutron yield in the experimental results.

The purpose of this note is to summarize recent progress of the authors in understanding turbulent mixing. We consider both Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities and mixing. Numerical simulations, theory and analysis of experimental data are combined to reach our conclusions. Three challenges that serve to organize our results are: (I) To compare to experiment when most experiments did not measure initial conditions. (II) To remove the effect of models and base science on fundamental equations. (III) To investigate high or infinite Reynolds (Re) regime for which the existing laboratory experiments may have diminished relevance. The results summarized here raise the possibility of verification and validation (V&V)/uncertainty quantification (UQ) for high Re simulations of RT/RM mixing.

Hydro instabilities have been identified as a potential cause of performance degradation in inertial confinement fusion (ICF) experiments. We study instabilities associated with a single Richtmyer–Meshkov (RM) interface in a circular geometry, idealized from an ICF geometry. In an ICF application, atomic level mix, as an input to nuclear burn, is an important, but difficult to compute, variable. We find numerical convergence for this important quantity, in a purely hydro study, with only a mild dependence on the Reynolds number of the flow, in the high Reynolds number limit. We also find that mixing properties show a strong sensitivity to turbulent transport parameters; this sensitivity translates into an algorithmic dependence and a nonuniqueness of solutions for nominally converged solutions. It is thus a complication to any verification and validation program. To resolve the nonuniqueness of the solution, we propose a validation program with an extrapolation component, linking turbulent transport quantities in experimental regimes to mildly perturbed turbulent transport values in ICF Reynolds number regimes. In view of the observed solution nonuniqueness, the validation program and its justification from the results presented here, has a fundamental significance.

In the context of the classical Rayleigh-Taylor hydrodynamical instability, we examine the much debated question of models for initial conditions and the possible influence of unrecorded long wave length contributions to the instability growth rate α.

We present the highlights of and supplementary material related to two recent studies yielding verification and validation of a new approach to the simulation of turbulent mixing. The verification is based on (i) a mesh refinement study of the circular Richtmyer-Meshkov unstable flow, (ii) comparison of the code to a well-documented code and (iii) comparison to a simple analytic model. The validation is based on the simulation's agreement with the Rayleigh-Taylor unstable experiments of Smeeton-Youngs and of Mueschke-Andrews. The mesh refinement verification gives convergence for such molecular level variables as the probability density functions for concentration, temperature and a chemical reaction rate. The validation study, beyond obtaining nearly perfect agreement with experiment, explores the various factors in the simulations that lead to the agreement and to differences between the two experiments. The important variables are fluid transport parameters, dimensionless groups (not widely recognized to be significant) to characterize the dominant short-wavelength initial perturbations and experimentally measured (long-wavelength) initial perturbations.

We are concerned with the chaotic flow fields of turbulent mixing. Chaotic flow is found in an extreme form in multiply shocked Richtmyer-Meshkov unstable flows. The goal of a converged simulation for this problem is to obtain converged solutions for such micro solution features as the joint probability distributions of the temperature and species concentration, as well as the macro features such as the edges of the mixing region. Here we introduce parameterized subgrid models of mass and thermal diffusion, to define LES that replicate the micro features observed in the DNS. The Schmidt numbers and Prandtl numbers are chosen to represent typical liquid and gas parameter values. The viscosity, and thus the Reynolds number, is allowed to vary through a range of values, to allow exploration of both DNS and LES regimes. Our main result is to explore the dependence of these solutions on mesh and Reynolds number.

Recent work of the authors and colleagues on the turbulent mixing of compressible fluids is developed and extended with an emphasis on the multiscale aspects of this work. Specifically, we study an interplay between micro and macro aspects of mixing.

We study Rayleigh–Taylor instability in both the moderately compressible and weakly compressible regimes. For the two-dimensional single mode case, we find that the dimensionless terminal velocities (and associated Froude numbers) are nearly constant over most of this region of parameter space, as the thermodynamic parameters describing the equation of state are varied. The phenomenological drag coefficient which occurs in the single mode buoyancy-drag equation is directly related to the terminal velocities and has a similar behavior. Pressure differences and interface shape, however, display significant dependence on the equation of state parameters even for the weakly compressible flows. For three-dimensional multimode mixing, we expect accordingly that density stratification rather than drag will provide the leading compressibility effect. We develop an analytical model to account for density stratification effects in multimode self-similar mixing. Our theory is consistent with and extends numerically based conclusions developed earlier which also identify density stratification as the dominant compressibility effect for multimode three-dimensional mixing.

The interaction of shock waves with spherical and perturbed spherical layers provides an interesting and important class of problems. We present recent results for these and related planar geometry problems. We address the following issues:1. The accuracy of different numerical solution methods.2. The magnitude of numerical solution errors and their causes.3. The development of the instabilities.4. Reduced descriptions for chaotic flows.(c) 2004 Elsevier Ltd. All rights reserved.

In this paper, a model for the unstable mixing of n parallel or concentric incompressible fluid layers is proposed. The approach in constructing this model is pairwise, based on a known two-incompressible-fluid mixing model. The problem complexity increases significantly in going from two to three fluids, but the increase in complexity is relatively small thereafter. We present a detailed study of the n=3 problem, which displays all of the difficult modeling issues applicable to arbitrary n⩾3 while still being reasonably tractable.

This paper follows our earlier work on axisymmetric flows [1–4] where algorithms, theories, experiments, simulations, applications, and validations were presented. Here we study the effectiveness and efficiency of explicit front tracking by comparing the L1-error for spherical shock refraction simulations with and without tracking. We find that front tracking reduces the level of mesh refinement needed to achieve a specified error tolerance by a significant factor compared to corresponding methods without tracking, thus substantially reducing the computational time as well as memory usage for simulations with contacts or material interfaces.

Numerical simulations of a spherical shock refraction have been successfully conducted by a front tracking method. We demonstrate the efficiency of the front tracking algorithm by comparing the L 1-error of spherical simulations by tracked and untracked methods. We find that the tracked algorithm is about 64 (256) times faster than the corresponding method without tracking the interface for a 2d (3d) simulation.

A new algorithm is introduced for upscaling relative permeabilities, and tested in simulations of two-dimensional reservoir displacement processes. The algorithm is similar to existing algorithms for computing upscaled relative permeabilities from subgrid simulations, but uses new boundary conditions for the pressure field. The new 'effective flux boundary conditions' were introduced in a previous paper and provide a more accurate estimate of flux through high permeability channels. The algorithm was tested in conjunction with uniform grid coarsening and upscaled absolute permeabilities for a broad range of coarsenings. The permeability fields were highly heteroge-neous and layered, and were obtained from synthetic data and from conditioned realizations of actual oil reservoirs. The algorithm was tested for a wide variety of grid aspect ratios, and for both viscous-and gravity-dominated flow. Typical fine grids were of the order of 100×100 cells; the coarsest scaled-up grids were on the order of 5×5 cells. The quality of scale up was evaluated by comparing oil cut curves for the fine and coarse grid simulations. We consistently obtained excellent agreement, even at the coarsest levels of scale up.