Mixing with applications to inertial-confinement-fusion implosions.

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.

Linear augmented Slater-type orbital method for free standing clusters.

We have developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for electronic-structure calculations on free-standing atomic clusters. As with other linear methods we solve the Schrödinger equation using a mixed basis set consisting of numerical functions inside atom-centered spheres and matched onto tail functions outside. The tail functions are Slater-type orbitals, which are localized, exponentially decaying functions. To solve the Poisson equation between spheres, we use a finite difference method replacing the rapidly varying charge density inside the spheres with a smoothed density with the same multipole moments. We use multigrid techniques on the mesh, which yields the Coulomb potential on the spheres and in turn defines the potential inside via a Dirichlet problem. To solve the linear eigen-problem, we use ScaLAPACK, a well-developed package to solve large eigensystems with dense matrices. We have tested the method on small clusters of palladium.

Turbulent mixing with physical mass diffusion.

Simulated mixing rates of the Rayleigh-Taylor instability for miscible fluids with physical mass diffusion are shown to agree with experiment; for immiscible fluids with physical values of surface tension the numerical data lie in the center of the range of experimental values. The simulations are based on an improved front tracking algorithm to control numerical surface tension and on improved physical modeling to allow physical values of mass diffusion or surface tension. Compressibility, after correction for variable density effects, has also been shown to have a strong influence on mixing rates. In summary, we find significant dependence of the mixing rates on scale breaking phenomena. We introduce tools to analyze the bubble merger process and confirm that bubble interactions, as in a bubble merger model, drive the mixing growth rate.

Dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts.

Dynamic behavior of mixing fronts plays a crucial role in multifluid turbulent mixing. In this paper, we derive an analytic solution for the dynamic evolution of mixing fronts driven by constant acceleration Rayleigh-Taylor (RT) and impulsive acceleration Richtmyer-Meshkov instabilities, from a simple physics model expressed as a pair of ordinary differential equations. An approximate closed form asymptotic evaluation of the RT solution is obtained, through terms of order O(1), as t--> infinity. This three term expansion, including lower order terms, is used to interpret experimental and simulation data. Our solutions improve on previous analyses in their agreement with experimental data, in that we can fit both the slope and the intercept of the Z(b) vs Agt(2) experimental plots by adjusting parameters in our model. Since the experimental data are close to self-similar, the improvement due to the lower order contributions in the asymptotic expansion is modest. We also apply this analysis to simulation data, for which preasymptotic data exist. We reexamine previous simulation data and determine an improved growth rate alpha(b)=0.0625. The present paper provides concepts and tools to explore the preasymptotic aspects of these data.

A comparison of experimental, theoretical, and numerical simulation Rayleigh-Taylor mixing rates.

We present a Rayleigh-Taylor mixing rate simulation with an acceleration rate falling within the range of experiments. The simulation uses front tracking to prevent interfacial mass diffusion. We present evidence to support the assertion that the lower acceleration rate found in untracked simulations is caused, at least to a large extent, by a reduced buoyancy force due to numerical interfacial mass diffusion. Quantitative evidence includes results from a time-dependent Atwood number analysis of the diffusive simulation, which yields a renormalized mixing rate coefficient for the diffusive simulation in agreement with experiment.

A three-dimensional renormalization group bubble merger model for Rayleigh-Taylor mixing.

In this paper we formulate a model for the merger of bubbles at the edge of an unstable acceleration driven (Rayleigh-Taylor) mixing layer. Steady acceleration defines a self-similar mixing process, with a time-dependent inverse cascade of structures of increasing size. The time evolution is itself a renormalization group (RNG) evolution, and so the large time asymptotics define a RNG fixed point. We solve the model introduced here at this fixed point. The model predicts the growth rate of a Rayleigh-Taylor chaotic fluid mixing layer. The model has three main components: the velocity of a single bubble in this unstable flow regime, an envelope velocity, which describes collective excitations in the mixing region, and a merger process, which drives an inverse cascade, with a steady increase of bubble size. The present model differs from an earlier two-dimensional (2-D) merger model in several important ways. Beyond the extension of the model to three dimensions, the present model contains one phenomenological parameter, the variance of the bubble radii at fixed time. The model also predicts several experimental numbers: the bubble mixing rate, alpha(b)=h(b)/Agt(2) approximately 0.05-0.06, the mean bubble radius, and the bubble height separation at the time of merger. From these we also obtain the bubble height to the radius aspect ratio. Using the experimental results of Smeeton and Youngs (AWE Report No. O 35/87, 1987) to fix a value for the radius variance, we determine alpha(b) within the range of experimental uncertainty. We also obtain the experimental values for the bubble height to width aspect ratio in agreement with experimental values. (c) 2002 American Institute of Physics.

Transverse magnetic defect modes in two-dimensional triangular-lattice photonic crystals.

We present a numerical study of the localized transverse magnetic (TM) defect modes in a two-dimensional, triangular-lattice photonic crystal. The sample consists of an array of circular, air cylinders in a dielectric medium (GaAs). The defect modes were calculated by using a parallel version of the finite-difference time-domain method on the Yee mesh. To validate our computations the results for the transverse electric case were checked against experimental results and the numerical results using a different method. We study the spatial symmetry for TM modes, obtained by changing the dipole excitation frequency. Also, we vary the defect-cylinder radius to tune the resonant frequency across the band gap. The TM mode is found to be highly localized at the defect in the photonic lattice.

Conservative front tracking and level set algorithms.

Hyperbolic conservation laws are foundational for many branches of continuum physics. Discontinuities in the solutions of these partial differential equations are widely recognized as a primary difficulty for numerical simulation, especially for thermal and shear discontinuities and fluid-fluid internal boundaries. We propose numerical algorithms that will (i) track these discontinuities as sharp internal boundaries, (ii) fully conserve the conserved quantities at a discrete level, even at the discontinuities, and (iii) display one order of numerical accuracy higher globally (at the discontinuity) than algorithms in common use. A significant improvement in simulation capabilities is anticipated through use of the proposed algorithms.