Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations

A new strategy for finite element computations involving moving boundaries and interfaces-The deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders

New finite element computational strategies for free-surface flows, two-liquid flows, and flows with drifting cylinders are presented. These strategies are based on the deforming spatial-domain/spacetime (DSD/ST) procedure. In the DSD/ST approach, the stabilized variational formulations for these types of flow problem are written over their space-time domains. One of the important features of the approach is that it enables one to circumvent the difficulty involved in remeshing every time step and thus reduces the projection errors introduced by such frequent remeshings. Computations are performed for various test problems mainly for the purpose of demonstrating the computational capability developed for this class of problems. In some of the test cases, such as the liquid drop problem, surface tension is taken into account. For flows involving drifting cylinders, the mesh moving and remeshing schemes proposed are convenient and reduce the frequency of remeshing

Investigation and Comparison between New Satellite Impact Test Results and NASA Standard Breakup Model

This paper summarizes two new satellite impact tests conducted in order to investigate on the outcome of low- and hyper-velocity impacts on two identical target satellites. The first experiment was performed at a low velocity of 1.5 km/s using a 40-gram aluminum alloy sphere, whereas the second experiment was performed at a hyper-velocity of 4.4 km/s using a 4-gram aluminum alloy sphere by two-stage light gas gun in Kyushu Institute of Technology. To date, approximately 1,500 fragments from each impact test have been collected for detailed analysis. Each piece was analyzed based on the method used in the NASA Standard Breakup Model 2000 revision. The detailed analysis will conclude: 1) the similarity in mass distribution of fragments between low and hyper-velocity impacts encourages the development of a general-purpose distribution model applicable for a wide impact velocity range, and 2) the difference in area-to-mass ratio distribution between the impact experiments and the NASA standard breakup model suggests to describe the area-to-mass ratio by a bi-normal distribution

Effect of Au spacer layer on \u3ci\u3eL\u3c/i\u3e1\u3csub\u3e0\u3c/sub\u3e phase ordering temperature of CoPt thin films

We have studied the effect of Au on the ordering temperature of CoPt films. The coercivity of the CoPt multilayer with 2 nm Au inserted is around 5 kOe after annealing at 400 °C. This ordering temperature is about 200 °C lower than that of a pure CoPt film. Crystallographical analysis using x-ray diffraction has also revealed that the lattice constant is drastically changed around the same temperature, which is related to the formation of the L10-ordered structure. Thus, the Au plays an important role in reducing the ordering temperature

Effect of Au spacer layer on \u3ci\u3eL\u3c/i\u3e1\u3csub\u3e0\u3c/sub\u3e phase ordering temperature of CoPt thin films

We have studied the effect of Au on the ordering temperature of CoPt films. The coercivity of the CoPt multilayer with 2 nm Au inserted is around 5 kOe after annealing at 400 °C. This ordering temperature is about 200 °C lower than that of a pure CoPt film. Crystallographical analysis using x-ray diffraction has also revealed that the lattice constant is drastically changed around the same temperature, which is related to the formation of the L10-ordered structure. Thus, the Au plays an important role in reducing the ordering temperature

Anatomy of the Soft-Photon Approximation in Hadron-Hadron Bremsstrahlung

A modified Low procedure for constructing soft-photon amplitudes has been used to derive two general soft-photon amplitudes, a two-s-two-t special amplitude $M^{TsTts}_{\mu}$ and a two-u-two-t special amplitude $M^{TuTts}_{\mu}$, where s, t and u are the Mandelstam variables. $M^{TsTts}_{\mu}$ depends only on the elastic T-matrix evaluated at four sets of (s,t) fixed by the requirement that the amplitude be free of derivatives ($\partial$T/$\partial$s and /or $\partial$T/$\partial t$). Likewise $M^{TuTts}_{\mu}$ depends only on the elastic T-matrix evaluated at four sets of (u,t). In deriving these amplitudes, we impose the condition that $M^{TsTts}_{\mu}$ and $M^{TuTts}_{\mu}$ reduce to $\bar{M}^{TsTts}_{\mu}$ and $\bar{M}^{TuTts}_{\mu}$, respectively, their tree level approximations. The amplitude $\bar{M}^{TsTts}_{\mu}$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle s-channel exchange diagrams, while the amplitude $\bar{M}^{TuTts} _{\mu}$ represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle u-channel exchange diagrams. The precise expressions for $\bar{M}^{TsTts}_{\mu}$ and $\bar{M}^{TuTts}_{\mu}$ are determined by using the radiation decomposition identities of Brodsky and Brown. We point out that it is theoretically impossible to describe all bremsstrahlung processes by using only a single class of soft-photon amplitudes. At least two different classes are required: the amplitudes which depend on s and t or the amplitudes which depend on u and t. When resonance effects are important, the amplitude $M^{TsTts}_{\mu}$, not $M^{Low(st)}_{\mu}$, should be used. For processes with strong u-channel exchange effects, the amplitude $M^{TuTts}_{\mu}$ should be the first choice.Comment: 49 pages report # LA-UR-92-270

DebriSat - A Planned Laboratory-Based Satellite Impact Experiment for Breakup Fragment Characterization

DebriSat is a planned laboratory ]based satellite hypervelocity impact experiment. The goal of the project is to characterize the orbital debris that would be generated by a hypervelocity collision involving a modern satellite in low Earth orbit (LEO). The DebriSat project will update and expand upon the information obtained in the 1992 Satellite Orbital Debris Characterization Impact Test (SOCIT), which characterized the breakup of a 1960 's US Navy Transit satellite. There are three phases to this project: the design and fabrication of an engineering model representing a modern, 50-cm/50-kg class LEO satellite known as DebriSat; conduction of a laboratory-based hypervelocity impact to catastrophically break up the satellite; and characterization of the properties of breakup fragments down to 2 mm in size. The data obtained, including fragment size, area ]to ]mass ratio, density, shape, material composition, optical properties, and radar cross ]section distributions, will be used to supplement the DoD fs and NASA fs satellite breakup models to better describe the breakup outcome of a modern satellite. Updated breakup models will improve mission planning, environmental models, and event response. The DebriSat project is sponsored by the Air Force fs Space and Missile Systems Center and the NASA Orbital Debris Program Office. The design and fabrication of DebriSat is led by University of Florida with subject matter experts f support from The Aerospace Corporation. The major milestones of the project include the complete fabrication of DebriSat by September 2013, the hypervelocity impact of DebriSat at the Air Force fs Arnold Engineering Development Complex in early 2014, and fragment characterization and data analyses in late 2014

A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation

A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model

Average Cross-Sectional Area of DebriSat Fragments Using Volumetrically Constructed 3D Representations

Debris fragments from the hypervelocity impact testing of DebriSat are being collected and characterized for use in updating existing satellite breakup models. One of the key parameters utilized in these models is the ballistic coefficient of the fragment which is directly related to its areatomass ratio. However, since the attitude of fragments varies during their orbital lifetime, it is customary to use the average crosssectional area in the calculation of the areatomass ratio. The average crosssectional area is defined as the average of the projected surface areas perpendicular to the direction of motion and has been shown to be equal to onefourth of the total surface area of a convex object. Unfortunately, numerous fragments obtained from the DebriSat experiment show significant concavity (i.e., shadowing) and thus we have explored alternate methods for computing the average crosssectional area of the fragments. An imaging system based on the volumetric reconstruction of a 3D object from multiple 2D photographs of the object was developed for use in determining the size characteristic (i.e., characteristics length) of the DebriSat fragments. For each fragment, the imaging system generates N number of images from varied azimuth and elevation angles and processes them using a spacecarving algorithm to construct a 3D point cloud of the fragment. This paper describes two approaches for calculating the average crosssectional area of debris fragments based on the 3D imager. Approach A utilizes the constructed 3D object to generate equally distributed crosssectional area projections and then averages them to determine the average crosssectional area. Approach B utilizes a weighted average of the area of the 2D photographs to directly compute the average crosssectional area. A comparison of the accuracy and computational needs of each approach is described as well as preliminary results of an analysis to determine the "optimal" number of images needed for the 3D imager to accurately measure the average cross sectional area of objects with known dimensions