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Computational astrophysical fluid dynamics

The field of astrophysical fluid dynamics (AFD) is described as an emerging discipline which derives historically from both the theory of stellar evolution and space plasma physics. The fundamental physical assumption behind AFD is that fluid equations of motion accurately describe the evolution of plasmas on scales that are large in comparison with particle interaction length scales. Particular attention is given to purely fluid models of large-scale astrophysical plasmas. The role of computer simulation in AFD research is also highlighted and a suite of general-purpose application codes for AFD research is discussed. The codes are called ZEUS-2D and ZEUS-3D and solve the equations of AFD in two and three dimensions, respectively, in several coordinate geometries for general initial and boundary conditions. The topics of bipolar outflows from protostars, galactic superbubbles and supershells, and extragalactic radio sources are addressed.

Norman, Michael L.↗

A mixed method Poisson solver for three-dimensional self-gravitating astrophysical fluid dynamical systems

A key ingredient in the simulation of self-gravitating astrophysical fluid dynamical systems is the gravitational potential and its gradient. This paper focuses on the development of a mixed method multigrid solver of the Poisson equation formulated so that both the potential and the Cartesian components of its gradient are self-consistently and accurately generated. The method achieves this goal by formulating the problem as a system of four equations for the gravitational potential and the three Cartesian components of the gradient and solves them using a distributed relaxation technique combined with conventional full multigrid V-cycles. The method is described, some tests are presented, and the accuracy of the method is assessed. We also describe how the method has been incorporated into our three-dimensional hydrodynamics code and give an example of an application to the collision of two stars. We end with some remarks about the future developments of the method and some of the applications in which it will be used in astrophysics.

Duncan, Comer↗

Parallel Multiscale Algorithms for Astrophysical Fluid Dynamics Simulations

Our goal is to develop software libraries and applications for astrophysical fluid dynamics simulations in multidimensions that will enable us to resolve the large spatial and temporal variations that inevitably arise due to gravity, fronts and microphysical phenomena. The software must run efficiently on parallel computers and be general enough to allow the incorporation of a wide variety of physics. Cosmological structure formation with realistic gas physics is the primary application driver in this work. Accurate simulations of e.g. galaxy formation require a spatial dynamic range (i.e., ratio of system scale to smallest resolved feature) of 104 or more in three dimensions in arbitrary topologies. We take this as our technical requirement. We have achieved, and in fact, surpassed these goals.

Norman, Michael L.↗

A new approach to the study of the turbulence layer

Turbulent thermal convection is of considerable importance in fluid dynamical transport phenomena occurring, for example, in the planetary boundary layer of the Earth, the interiors of stars, and accretion disks. In particular, during a significant portion of the evolutionary phase of many stars having convectively unstable cores or outer envelopes, a substantial fraction of energy is transported from the central layers to the outer layers by thermal convection. Moreover, as much of the interior of a star is in highly turbulent motion, a complete theory of stellar structure and evolution requires the explicit consideration of turbulence in order to have expressions for the turbulent quantities arising in the stellar structure equations, and particularly, the turbulent fluxes that appear in the total flux conservation equation, such as the convective flux, kinetic energy flux, etc. A reliable quantification of these fluxes continues to present a challenge in astrophysical fluid dynamics, primarily because astrophysical turbulence is almost always fully-developed and nearly inviscid, and therefore governed by strong nonlinear interactions that distribute the energy among a very wide spectrum of eddies with scales ranging from the characteristic dimension of the flow to those sufficiently small to be affected by viscous dissipation. Furthermore, astrophysical flows are invariably compressible, anisotropic, and inhomogeneous, which requires the consideration of the dynamics of longitudinal modes and their interaction with the transverse modes, as well as complicated boundary conditions. In order to reach a compromise between analytical and numerical tractability and the basic physics of turbulent convection, we have constructed a model of stationary turbulent convection that yields various turbulence statistics, including the convective flux, that are required in stellar evolution models.

Levenson, Ruth A.↗

Pentium Pro inside: A treecode at 430 Gigaflops on ASCI Red - 1

As an entry for the 1997 Gordon Bell performance prize, we present results from two methods of solving the gravitational N-body problem on the Intel Teraflops system at Sandia National Laboratory (ASCI Red). The first method, an O(N2) algorithm, obtained 635 Gigaflops for a 1 million particle problem on 6800 Pentium Pro processors. The second solution method, a tree-code which scales as O(N log N), sustained 170 Gigaflops over a continuous 9.4 hour period on 4096 processors, integrating the motion of 322 million mutually interacting particles in a cosmology simulation, while saving over 100 Gigabytes of raw data. Additionally, the tree-code sustained 430 Gigaflops on 6800 processors for the first 5 time-steps of that simulation. This tree-code solution is approximately 105 times more efficient than the O(N2) algorithm for this problem. As an entry for the 1997 Gordon Bell price/performance prize, we present two calculations from the disciplines of astrophysics and fluid dynamics. The simulations were performed on two 16 Pentium Pro processor Beowulf-class computers (Loki and Hyglac) constructed entirely from commodity personal computer technology, at a cost of roughly $50k each in September, 1996. The price of an equivalent system in August 1997 is less than $30. At Los Alamos, Loki performed a gravitational tree-code N-body simulation of galaxy formation using 9.75 million particles, which sustained an average of 879 Mflops over a ten day period, and produced roughly 10 Gbytes of raw data.

Warren, M. S.↗

Spacelab 3 Mission Science Review

Papers and abstracts of the presentations made at the symposium are given as the scientific report for the Spacelab 3 mission. Spacelab 3, the second flight of the National Aeronautics and Space Administration's (NASA) orbital laboratory, signified a new era of research in space. The primary objective of the mission was to conduct applications, science, and technology experiments requiring the low-gravity environment of Earth orbit and stable vehicle attitude over an extended period (e.g., 6 days) with emphasis on materials processing. The mission was launched on April 29, 1985, aboard the Space Shuttle Challenger which landed a week later on May 6. The multidisciplinary payload included 15 investigations in five scientific fields: material science, fluid dynamics, life sciences, astrophysics, and atmospheric science.

Fichtl, George H.↗

Supercomputing in Aerospace

Topics addressed include: numerical aerodynamic simulation; computational mechanics; supercomputers; aerospace propulsion systems; computational modeling in ballistics; turbulence modeling; computational chemistry; computational fluid dynamics; and computational astrophysics.

Kutler, Paul↗

Finite Element Method for Capturing Ultra-relativistic Shocks

While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.

Richardson, G. A.↗

Marshall Space Flight Center Faculty Fellowship Program

The Faculty Fellowship program was revived in the summer of 2015 at NASA Marshall Space Flight Center, following a period of diminished faculty research activity here since 2006 when budget cuts in the Headquarters' Education Office required realignment. Several senior Marshall managers recognized the need to involve the Nation's academic research talent in NASA's missions and projects to the benefit of both entities. These managers invested their funds required to establish the renewed Faculty Fellowship program in 2015, a 10-week residential research involvement of 16 faculty in the laboratories and offices at Marshall. These faculty engineers and scientists worked with NASA collaborators on NASA projects, bringing new perspectives and solutions to bear. This Technical Memorandum is a compilation of the research reports of the 2015 Marshall Faculty Fellowship program, along with the Program Announcement (appendix A) and the Program Description (appendix B). The research touched on seven areas-propulsion, materials, instrumentation, fluid dynamics, human factors, control systems, and astrophysics. The propulsion studies included green propellants, gas bubble dynamics, and simulations of fluid and thermal transients. The materials investigations involved sandwich structures in composites, plug and friction stir welding, and additive manufacturing, including both strength characterization and thermosets curing in space. The instrumentation projects involved spectral interfero- metry, emissivity, and strain sensing in structures. The fluid dynamics project studied the water hammer effect. The human factors project investigated the requirements for close proximity operations in confined spaces. Another team proposed a controls system for small launch vehicles, while in astrophysics, one faculty researcher estimated the practicality of weather modification by blocking the Sun's insolation, and another found evidence in satellite data of the detection of a warm-hot intergalactic medium filament. Our goal is to continue the Faculty Fellowship effort with Center funds in succeeding summers.

Six, N. F.↗

A comparative study of computational methods in cosmic gas dynamics

Many theoretical investigations of fluid flows in astrophysics require extensive numerical calculations. The selection of an appropriate computational method is, therefore, important for the astronomer who has to solve an astrophysical flow problem. The present investigation has the objective to provide an informational basis for such a selection by comparing a variety of numerical methods with the aid of a test problem. The test problem involves a simple, one-dimensional model of the gas flow in a spiral galaxy. The numerical methods considered include the beam scheme, Godunov's method (G), the second-order flux-splitting method (FS2), MacCormack's method, and the flux corrected transport methods of Boris and Book (1973). It is found that the best second-order method (FS2) outperforms the best first-order method (G) by a huge margin.

Van Albada, G. D.↗

The impact of supercomputers on experimentation: A view from a national laboratory

The relative roles of large scale scientific computers and physical experiments in several science and engineering disciplines are discussed. Increasing dependence on computers is shown to be motivated both by the rapid growth in computer speed and memory, which permits accurate numerical simulation of complex physical phenomena, and by the rapid reduction in the cost of performing a calculation, which makes computation an increasingly attractive complement to experimentation. Computer speed and memory requirements are presented for selected areas of such disciplines as fluid dynamics, aerodynamics, aerothermodynamics, chemistry, atmospheric sciences, astronomy, and astrophysics, together with some examples of the complementary nature of computation and experiment. Finally, the impact of the emerging role of computers in the technical disciplines is discussed in terms of both the requirements for experimentation and the attainment of previously inaccessible information on physical processes.

Peterson, V. L.↗

The impact of supercomputers on experimentation - A view from a National Laboratory

The relative roles of large-scale scientific computers and physical experiments in several science and engineering disciplines are discussed. Increasing dependence on computers is shown to be motivated both by the rapid growth in computer speed and memory, which permits accurate numerical simulation of complex physical phenomena, and by the rapid reduction in the cost of performing a calculation, which makes computation an increasingly attractive complement to experimentation. Computer speed and memory requirements are presented for selected areas of such disciplines as fluid dynamics, aerodynamics, aerothermodynamics, chemistry, atmospheric sciences, astronomy, and astrophysics, together with some examples of the complementary nature of computation and experiment. Finally, the impact of the emerging role of computers in the technical disciplines is discussed in terms of both the requirements for experimentation and the attainment of previously inaccessible information on physical processes.

Peterson, V. L.↗

The Impact of Supercomputers on Experimentation: A View from a National Laboratory

The relative roles of large-scale scientific computers and physical experiments in several science and engineering disciplines are discussed. Increasing dependence on computers is shown to be motivated both by the rapid growth in computer speed and memory, which permits accurate numerical simulation of complex physical phenomena, and by the rapid reduction in the cost of performing a calculation, which makes computation an increasingly, attractive complement to experimentation. Computer speed and memory requirements are presented for selected areas of such disciplines as fluid dynamics, aerodynamics, aerothermodynamics, chemistry, atmospheric sciences, astronomy, and astrophysics, together with some examples of the complementary nature of computation and experiment. Finally the impact of the emerging role of computers in the technical disciplines is discussed in terms of both the requirements for experimentation and the attainment of previously inaccessible information on physical processes.

Peterson, V.L.↗

Microgravity laboratory simulations of planetary and stellar circulations

This paper summarizes experiments on thermal convection in a rotating differentially heated spherical shell of liquid that were carried out in the microgravity laboratory of Spacelab III. In these experiments, dielectric polarization forces were used to generate a radially-directed buoyancy force. This enabled the simulation of a number of geophysically and astrophysically important situations in which sphericity and rotation both impose strong constraints on the global scale fluid dynamics. Recent theoretical and numerical interpretations of the original data are discussed. Further laboratory experiments in the areas of geophysical and g-jitter fluid dynamics are suggested.

Hart, John E.↗

Sensitivity analysis in multipole-accelerated panel methods for potential flow

In the design of an airframe, the effect of changing the geometry on resulting computations is necessary for design optimization. The geometry is defined in terms of a series of design variables, including design variables to define the wing planform, tail, canard, pylon, and nacelle. Design optimization in this research is based on how these design variable affect the potential flow. The potential flow is computed as a function of the geometry and location of a series of panels describing the airframe, which are in turn a function of the design variables. Multipole accelerated panel methods improve the computational complexity of the problem and thus are an attractive approach. To utilize the methods in design optimization, it was necessary to define the appropriate sensitivity derivatives. The overhead incurred from finding the sensitivity derivatives in conjunction with the original computation should be small. This research developed the background for multipole-accelerated panel methods and the framework for finding sensitivity derivatives in the methods. Potential flow panel codes are commonly used for powered-lift aerodynamic predictions for three dimensional geometries. Given an airframe which has been discretized into a series of panels to define the airframe geometry, potential is computed as a function of the influence of all panels on all other panels. This is a computationally intensive problem for which efficient solutions are desired to improve the computational time and to allow greater resolution by use of more panels. One such solution is the use of hierarchical multipole methods which entail approximations of the effects of far-field terms. Hierarchical multipole methods have become prevalent in molecular dynamics and gravitational physics, and have been introduced into the fields of capacitance calculations, computational fluid dynamics, and electromagnetics. The methods utilize multipole expansions to describe the effect of bodies (i.e. particles, astrophysical bodies, panels, etc.) within a sphere on points distant from the sphere, where the influence diminishes as a function of distance. The expansions are exact with infinite series, however, for practical computations, the series are truncated and accuracy is selected based on the number of terms retained in the expansions. A hierarchical tree structure groups bodies together based on proximity to allow definition of multipole expansions for each group. The multipole expansions are then used to compute the effect of the bodies in a group on distant bodies.

Leathrum, James F., Jr.↗

The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves

Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.

Abarzhi, S. I.↗

Beyond Our Boundaries: Research and Technology

Topics considered include: Propulsion and Fluid Management; Structures and Dynamics; Materials and Manufacturing Processes; Sensor Technology; Software Technology; Optical Systems; Microgravity Science; Earth System Science; Astrophysics; Solar Physics; and Technology Transfer.

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Physics through the 1990s: Plasmas and fluids

The volume contains recommendations for programs in, and government support of, plasma and fluid physics. Four broad areas are covered: the physics of fluids, general plasma physics, fusion, and space and astrophysical plasmas. In the first section, the accomplishments of fluid physics and a detailed review of its sub-fields, such as combustion, non-Newtonian fluids, turbulence, aerodynamics, and geophysical fluid dynamics, are described. The general plasma physics section deals with the wide scope of the theoretical concepts involved in plasma research, and with the machines; intense beam systems, collective and laser-driven accelerators, and the associated diagnostics. The section on the fusion plasma research program examines confinement and heating systems, such as Tokamaks, magnetic mirrors, and inertial-confinement systems, and several others. Finally, theory and experiment in space and astrophysical plasma research is detailed, ranging from the laboratory to the solar system and beyond. A glossary is included.

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