Andrew W. Cook

The mixing transition in Rayleigh-Taylor instability

A large-eddy simulation technique is described for computing Rayleigh–Taylor instability. The method is based on high-wavenumber-preserving subgrid-scale models, combined with high-resolution numerical methods. The technique is verified to match linear stability theory and validated against direct numerical simulation data. The method is used to simulate Rayleigh–Taylor instability at a grid resolution of

Enthalpy Diffusion in Multicomponent Flows

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High-Reynolds number Rayleigh–Taylor turbulence

. The growth rate is found to depend on the mixing rate. A mixing transition is observed in the flow, during which an inertial range begins to form in the velocity spectrum and the rate of growth of the mixing zone is temporarily reduced. By measuring growth of the layer in units of dominant initial wavelength, criteria are established for reaching the hypothetical self-similar state of the mixing layer. A relation is obtained between the rate of growth of the mixing layer and the net mass flux through the plane associated with the initial location of the interface. A mix-dependent Atwood number is defined, which correlates well with the entrainment rate, suggesting that internal mixing reduces the layers growth rate.

Tera-Scalable Algorithms for Variable-Density Elliptic Hydrodynamics with Spectral Accuracy

The enthalpy diffusion flux in the multicomponent energy equation is a well known yet frequently neglected term. It accounts for energy changes, associated with compositional changes, resulting from species diffusion. Enthalpy diffusion is important in flows where significant mixing occurs between species of dissimilar molecular weight. The term plays a critical role in preventing local violations of the entropy condition. In simulations of nonpremixed combustion, omission of the enthalpy flux can lead to anomalous temperature gradients, which may cause mixing regions to exceed ignition conditions. The term can also play a role in generating acoustic noise in turbulent mixing layers. Euler solvers that rely on numerical diffusion to mix fluids cannot accurately predict the temperature in mixed regions. On the other hand, Navier-Stokes solvers that incorporate enthalpy diffusion can provide much more accurate results.

A subgrid-scale model for the scalar dissipation rate in nonpremixed combustion

The turbulence generated in the variable density Rayleigh–Taylor mixing layer is studied using the high-Reynolds number fully resolved 30723 numerical simulation of Cabot and Cook (Nature Phys. 2 (2006), pp. 562–568). The simulation achieves bulk Reynolds number, Re = H Ḣ/ν = 32,000, turbulent Reynolds number, Re t = [ktilde] 2/νϵ = 4600, and Taylor Reynolds number, R λ = 170. The Atwood number, A, is 0.5, and the Schmidt number, Sc, is 1. Typical density fluctuations, while modest, being one quarter the mean density, lead to non-Boussinesq effects. A comprehensive study of the variable density energy budgets for the kinetic energy, mass flux and density specific volume covariance equations is undertaken. Various asymmetries in the mixing layer, not seen in the Boussinesq case, are identified and explained. Hypotheses for the variable density turbulent transport necessary to close the second moment equations are studied. It is found that, even though the layer width becomes temporally self-similar relatively fast, the transient effects in the energy spectrum remain important for the duration of the simulation. Thus, the dissipation does not track the spectral energy cascade rate and the integral lengthscale does not follow the expected Kolmogorov scaling, [ktilde] 3/2/ϵ. As a result, the popular eddy diffusivity expression, ν t ∼[ktilde] 2/ϵ, does not model the temporal variation of the turbulent transport in any of the moment equations. An eddy diffusivity based on a lengthscale related to the layer width is found to work well in a gradient transport hypothesis for the turbulent transport; however, that lengthscale is a global quantity and does not lead to pointwise, local closure. Therefore, although the transient effects may vanish asymptotically, it is suggested that, even long after the onset of the self-similar growth, two separate lengthscale equations (or equivalent) are needed in a moment closure strategy for Rayleigh–Taylor turbulence: one for the turbulent transport and the other for the dissipation. Despite the fact that the intermediate scales are nearly isotropic, the small scales have a persistent anisotropy; this is due to a cancellation between the viscous and nonlinear effects, so that the anisotropic buoyancy production remains important at the smallest scales.

CHAMBER DESIGN FOR THE LASER INERTIAL FUSION ENERGY (LIFE) ENGINE

We describe Miranda, a massively parallel spectral/compact solver for variabledensity incompressible flow, including viscosity and species diffusivity effects. Miranda utilizes FFTs and band-diagonal matrix solvers to compute spatial derivatives to at least 10th-order accuracy. We have successfully ported this communicationintensive application to BlueGene/L and have explored both direct block parallel and transpose-based parallelization strategies for its implicit solvers. We have discovered a mapping strategy which results in virtually perfect scaling of the transpose method up to 65,536 processors of the BlueGene/L machine. Sustained global communication rates in Miranda typically run at 85% of the theoretical peak speed of the BlueGene/L torus network, while sustained communication plus computation speeds reach 2.76 TeraFLOPS. This effort represents the first time that a high-order variable-density incompressible flow solver with species diffusion has demonstrated sustained performance in the TeraFLOPS range.

Hyperviscosity for unstructured ALE meshes

A subgrid-scale model is discussed for the scalar dissipation rate in nonpremixed turbulent reacting flows. The model contains a coefficient which is determined by assuming a form for the scalar energy spectrum. The model is tested a priori using Direct Numerical Simulation (DNS) results for a temporal reacting mixing layer. The estimated dissipation rates are in good agreement with dissipation rates computed directly from the DNS data. Furthermore, the assumed spectrum methodology is found to accurately predict the model coefficient, including its spatial and temporal variations.

BlueGene/L applications: Parallelism On a Massive Scale

Abstract The Laser Inertial Fusion Energy (LIFE) concept is being designed to operate as either a pure fusion or hybrid fusion-fission system. The present work focuses on the pure fusion option. A key component of a LIFE engine is the fusion chamber subsystem. It must absorb the fusion energy, produce fusion fuel to replace that burned in previous targets, and enable both target and laser beam transport to the ignition point. The chamber system also must mitigate target emissions, including ions, x-rays and neutrons and reset itself to enable operation at 10-15 Hz. Finally, the chamber must offer a high level of availability, which implies both a reasonable lifetime and the ability to rapidly replace damaged components. An integrated design that meets all of these requirements is described herein.

Scaling physics and material science applications on a massively parallel Blue Gene/L system

An artificial viscosity, originally designed for Eulerian schemes, is adapted for use in arbitrary Lagrangian–Eulerian simulations. Changes to the Eulerian model (dubbed ‘hyperviscosity’) are discussed, which enable it to work within a Lagrangian framework. New features include a velocity-weighted grid scale and a generalised filtering procedure, applicable to either structured or unstructured grids. The model employs an artificial shear viscosity for treating small-scale vorticity and an artificial bulk viscosity for shock capturing. The model is based on the Navier–Stokes form of the viscous stress tensor, including the diagonal rate-of-expansion tensor. A second-order version of the model is presented, in which Laplacian operators act on the velocity divergence and the grid-weighted strain-rate magnitude to ensure that the velocity field remains smooth at the grid scale. Unlike sound-speed-based artificial viscosities, the hyperviscosity model is compatible with the low Mach number limit. The new model outperforms a commonly used Lagrangian artificial viscosity on a variety of test problems.

Scaling the incompressible Richtmyer-Meshkov instability

BlueGene/L (BG/L), developed through a partnership between IBM and Lawrence Livermore National Laboratory (LLNL), is currently the worlds largest system both in terms of scale, with 131,072 processors, and absolute performance, with a peak rate of 367 Tflop/s. BG/L has led the last four Top500 lists with a Linpack rate of 280.6 Tflop/s for the full machine installed at LLNL and is expected to remain the fastest computer in the next few editions. However, the real value of a machine such as BG/L derives from the scientific breakthroughs that real applications can produce by successfully using its unprecedented scale and computational power. In this paper, we describe our experiences with eight large scale applications on BG/ L from several application domains, ranging from molecular dynamics to dislocation dynamics and turbulence simulations to searches in semantic graphs. We also discuss the challenges we faced when scaling these codes and present several successful optimization techniques. All applications show excellent scaling behavior, even at very large processor counts, with one code even achieving a sustained performance of more than 100 Tflop/s, clearly demonstrating the real success of the BG/L design.