: JASON was asked to recommend ways in which the DOD/IC can handle present and future sensor data... more : JASON was asked to recommend ways in which the DOD/IC can handle present and future sensor data in fundamentally different ways, taking into account both the state-of-the-art, the potential for advances in areas such as data structures, the shaping of sensor data for exploitation, as well as methodologies for data discovery. This report examines the challenges associated with the analysis of large data and in particular compares DOD/IC requirements to those of several data intensive fields. JASON finds that DOD/IC data requirements are certainly significant, but not unmanageable given the capabilities of current and projected storage technology. The key challenge will be to adequately empower the analyst by matching analysis needs to data delivery modalities. The report also proposes various grand challenges that could be used to assess and prioritize future research efforts in data assimilation and fusion.
Numerical computation of the linear stability of the diffusion model for crystal growth simulation
We consider a computational scheme for determining the linear stability of a diffusion model aris... more We consider a computational scheme for determining the linear stability of a diffusion model arising from the simulation of crystal growth. The process of a needle crystal solidifying into some undercooled liquid can be described by the dual diffusion equations with appropriate initial and boundary conditions. Here U{sub t} and U{sub a} denote the temperature of the liquid and solid respectively, and {alpha} represents the thermal diffusivity. At the solid-liquid interface, the motion of the interface denoted by r and the temperature field are related by the conservation relation where n is the unit outward pointing normal to the interface. A basic stationary solution to this free boundary problem can be obtained by writing the equations of motion in a moving frame and transforming the problem to parabolic coordinates. This is known as the Ivantsov parabola solution. Linear stability theory applied to this stationary solution gives rise to an eigenvalue problem of the form.
We present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface s... more We present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number ${\approx }1.2$ , the density ratio (precisely $|A_0|\approx 0.67$ ) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of $3\, \%$ ): the incident shock travels from the lighter fluid to the heavy fluid or, inversely, from the heavy to the light fluid. After describing the computational problem we present results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. Turbulent statistics are developed in Part 2 (Lombardini, M., Pullin, D. I. & Meiron, D. I. J. Fluid Mech., vol. 748, 2014, pp. 113–142). A wave-diagram analysis of the radially symmetric flow highlights that the light...
Dynamic refinement algorithms for spectral element methods
Numerical simulation of morphological development during Ostwald ripening
Acta Metallurgica, 1988
A boundary integral technique is employed to determine the morphological evolution of a small num... more A boundary integral technique is employed to determine the morphological evolution of a small number of particles during Ostwald ripening in two dimensions. The approach allows the bodies to change shape consistent with interparticle diffusional interactions and the interfacial concentrations as given by the Gibbs-Thomson equation. It is shown that the strong interparticle diffusional interactions which occur at small interparticle separations can induce significant motions of the centers of mass of the particles. Such motion is shown to be a strong function of the spatial distribution of particles. The generality of the mechanism responsible for the particle migration suggests that particle motion is a generic aspect of the ripening process at high volume fractions of coarsening phase. It was found that significant shape distortions of particles during ripening requires particle arrangements which induce significant diffusional screening of regions of interface. Through particle ar...
Contributions to the computation of compressible turbulence
The shape of stationary dislocations
Physics Letters A, 1985
It is shown that the structure of the stationary dislocations which occur in a wide variety of pa... more It is shown that the structure of the stationary dislocations which occur in a wide variety of patterns in nonequilibrium systems is given by a self-similar solution of the universal Cross-Newell equation.
An experimental and numerical study of impinging, incompressible, axisymmetric, laminar jets is d... more An experimental and numerical study of impinging, incompressible, axisymmetric, laminar jets is described, where the jet axis of symmetry is aligned normal to the wall. Particle streak velocimetry ͑PSV͒ is used to measure axial velocities along the centerline of the flow field. The jet-nozzle pressure drop is measured simultaneously and determines the Bernoulli velocity. The flow field is simulated numerically by an axisymmetric Navier-Stokes spectral-element code, an axisymmetric potential-flow model, and an axisymmetric onedimensional stream-function approximation. The axisymmetric viscous and potential-flow simulations include the nozzle in the solution domain, allowing nozzle-wall proximity effects to be investigated. Scaling the centerline axial velocity by the Bernoulli velocity collapses the experimental velocity profiles onto a single curve that is independent of the nozzle-to-plate separation distance. Axisymmetric direct numerical simulations yield good agreement with experiment and confirm the velocity profile scaling. Potential-flow simulations reproduce the collapse of the data; however, viscous effects result in disagreement with experiment. Axisymmetric one-dimensional stream-function simulations can predict the flow in the stagnation region if the boundary conditions are correctly specified. The scaled axial velocity profiles are well characterized by an error function with one Reynolds-number-dependent parameter. Rescaling the wall-normal distance by the boundary-layer displacement-thickness-corrected diameter yields a collapse of the data onto a single curve that is independent of the Reynolds number. These scalings allow the specification of an analytical expression for the velocity profile of an impinging laminar jet over the Reynolds number range investigated of 200ഛ Re ഛ 1400.
We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface ... more We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air-CO 2 , air-SF 6 and H 2 -air. A canonical, threedimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ∼1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ∼0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semianalytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate.
ASCI Alliance Center for Simulation of Dynamic Response in Materials California Insitute of
galcit.caltech.edu
1. Material properties and chemical reactions The detailed reaction mechanism and rate constants ... more 1. Material properties and chemical reactions The detailed reaction mechanism and rate constants were completed for HMX (C4H8N8O8, cyclotetramethylene-tetranitramine) and RDX (C3H6N6O6, cyclotrimethylenetrinitramine) gas phase decomposition. This was a con- ...
International Journal for Multiscale Computational Engineering, 2007
The coupling of a dynamically adaptive Eulerian Cartesian detonation solver with hierarchical tim... more The coupling of a dynamically adaptive Eulerian Cartesian detonation solver with hierarchical time-step refinement to a Lagrangian thin-shell finite element solver with fracture and fragmentation capabilities is presented. The approach uses a level-set function to implicitly represent arbitrarily evolving solid structures on the Cartesian mesh. The auxiliary algorithm used to efficiently transform the shell solver mesh on the fly into a distance function is sketched briefly. We detail the derivation of the employed engineering combustion model that eliminates the numerical stiffness otherwise inherent to detonation waves and describe our approach to modeling fracture. The thin-shell solver utilizes a subdivision finite element discretization and achieves element separation with interface edges and a cohesive law. For method validation and benchmarking, the simulation of the deformation of a circular thin copper plate under impulsive pressure loading is presented. As a realistic computational application, we consider a three-dimensional setup in which the passage of an ethylene-oxygen detonation wave induces large plastic deformations and rupture of a thin-walled tubular specimen made of aluminum. Special attention is paid to the verification of the hydrodynamic loading conditions. The computational fluid-structure interaction results are found to be in agreement with experimental observations.
iv I am indebted to many for playing a role in my graduate career. Some helped me get started, so... more iv I am indebted to many for playing a role in my graduate career. Some helped me get started, some helped me finish, and many helped me along the way; Michael Aivazis, Marco
I am indebted to many for playing a role in my graduate career. Some helped me get started, some ... more I am indebted to many for playing a role in my graduate career. Some helped me get started, some helped me finish, and many helped me along the way; Michael Aivazis, Marco
The implulse approximation for the Richtmyer-Meshkov
The popular impulse approximation is applied to the Richtmyer-Meshkov problem for continuously st... more The popular impulse approximation is applied to the Richtmyer-Meshkov problem for continuously stratified fluids through the use of a model due to Saffman and Meiron. The predictions of the late time growth rate of the interface and interfacial circulation from a numerical implementation of the model are compared with calculations from the nonlinear Euler equations. It is shown that for weak incidentshocks the impulse approximation, known to be accurate for interfaces of infinitesimal amplitude and thickness, is also very accurate for problems with interfaces of finite amplitude and thickness. For stronger shocks, post-shockvalues of Atwood ratio, amplitude and layer thickness are used in the model to obtain accurate predictions of late time growth rate for high Atwood ratio configurations. Poor agreement is seen for low Atwood ratios. Examinations of vorticity distributions reveal that the impulse model does not predict the correct distribution for either high or low Atwo...
Parallel computing in computational fluid dynamics
ABSTRACT An abstract is not available.
High Performance Biocomputation
: This section summarizes the conclusions and recommendations of the 2004 JASON summer study comm... more : This section summarizes the conclusions and recommendations of the 2004 JASON summer study commissioned by the Department of Energy (DOE) to explore the opportunities and challenges presented by applying advanced computational power and methodology to problems in the biological sciences. JASON was tasked to investigate the current suite of computationally intensive problems as well as potential future endeavors. JASON was also tasked to consider bow advanced computational capability and capacity could best be brought to bear on bioscience problems and to explore how different computing approaches such as Grid computing, supercomputing, cluster computing or custom architectures might map onto interesting biological problems
Linearized Navier-Stokes Solution of the Richtmyer-Meshkov Instability
ABSTRACT Results are presented from a numerical investigation of the two-dimensional Richtmyer-Me... more ABSTRACT Results are presented from a numerical investigation of the two-dimensional Richtmyer-Meshkov instability, using a linearization about a fully-resolved, 1-D numerical solution of the Navier-Stokes equations. An asymptotically-stable, non-dissipative, fourth-order finite-difference scheme is used with local grid refinement to properly resolve the internal structure of all shocks and the contact zone. Detailed results are shown for the case of a single fluid with constant viscosity and heat conductivity, Pr = 3/4, and incident shock Mach number 1.2, across a range of contact-zone perturbation wavenumbers.
In his 1932 address to the British Society for the Advancement of Science the famed mathematician... more In his 1932 address to the British Society for the Advancement of Science the famed mathematician Sir Horace Lamb was said to have made the following seemingly prescient statement: ‘I am an old man now, and when I die and go to heaven, there are two matters on which I hope for enlightenment. One is quantum electrodynamics and the other is the turbulent motion of fluids. About the former, I am really rather optimistic’. Turbulent flow is a ubiquitous aspect of nature and its understanding has important implications for a wide variety of applications including weather prediction, industrial flows and aeronautics. Increasingly detailed and precise experiments combined with highly resolved numerical simulations have led to some insights, but despite over 100 years of research a full understanding of the detailed mechanics of turbulence and its implications for quantities of applied interest such as drag, lift and mixture fraction remains incomplete. For example, as understood by G. I. T...
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Papers by Dan Meiron