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At least 649 records · Page 36

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Yan, Jue↗

Test Method Designed to Evaluate Cylinder Liner-Piston Ring Coatings for Advanced Heat Engines

Research on advanced heat engine concepts, such as the low-heat-rejection engine, have shown the potential for increased thermal efficiency, reduced emissions, lighter weight, simpler design, and longer life in comparison to current diesel engine designs. A major obstacle in the development of a functional advanced heat engine is overcoming the problems caused by the high combustion temperatures at the piston ring/cylinder liner interface, specifically at top ring reversal (TRR). Therefore, advanced cylinder liner and piston ring materials are needed that can survive under these extreme conditions. To address this need, researchers at the NASA Lewis Research Center have designed a tribological test method to help evaluate candidate piston ring and cylinder liner materials for advanced diesel engines.

Radil, Kevin C.↗

The Building Blocks for JWST I and T (Integrations and Test) to Operations - From Simulator to Flight Units

The James Webb Space Telescope (JWST) Project has an extended integration and test (I&T) phase due to long procurement and development times of various components as well as recent launch delays. The JWST Ground Segment and Operations group has developed a roadmap of the various ground and flight elements and their use in the various JWST I&T test programs. The JWST Project s building block approach to the eventual operational systems, while not new, is complex and challenging; a large-scale mission like JWST involves international partners, many vendors across the United States, and competing needs for the same systems. One of the challenges is resource balancing so simulators and flight products for various elements congeal into integrated systems used for I&T and flight operations activities. This building block approach to an incremental buildup provides for early problem identification with simulators and exercises the flight operations systems, products, and interfaces during the JWST I&T test programs. The JWST Project has completed some early I&T with the simulators, engineering models and some components of the operational ground system. The JWST Project is testing the various flight units as they are delivered and will continue to do so for the entire flight and operational system. The JWST Project has already and will continue to reap the value of the building block approach on the road to launch and flight operations.

Fatig, Curtis↗

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems

In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

97 MATHEMATICS AND COMPUTING↗

Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere

This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.

97 - MATHEMATICS AND COMPUTING↗

Computation of Acoustic Waves Through Sliding-Zone Interfaces Using an Euler/Navier-Stokes Code

The effect of a patched sliding-zone interface on the transmission of acoustic waves is examined for two- and three-dimensional model problems. A simple but general interpolation scheme at the patched boundary passes acoustic waves without distortion, provided that a sufficiently small time step is taken. A guideline is provided for the maximum permissible time step or zone speed that gives an acceptable error introduced by the sliding-zone interface.

Rumsey, Christopher L.↗

A method of testing attitude control systems during the development phase

A technique, utilized on the Space Telescope Program, and used for testing satellite attitude pointing and control systems during the engineering and development phases is presented. The technique verifies the hardware models used in design phase computer simulations, verifies the interface between the flight hardware and flight software, and uncovers hardware/software switching or mode logic problems. The testing is accomplished in two phases: a dynamic hardware simulator phase using hardware electronic simulators and an electronic vehicle motion simulator; and a second real hardware phase utilizing engineering model gyros and reaction wheels on an airbearing table. Both phases use an engineering model of the flight computer, flight algorithms and software, and a breadboard data management and computer hardware interface for timing simulations. The purpose of each test and the test phases are described, and examples of closed loop test results for both attitude hold and maneuvering models are given.

Besonis, A.↗

Mixing across stable density interfaces in forced stratified turbulence

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyse spatial correlations between the vertical density gradient $\partial \rho /\partial z$ and the dissipation rates of kinetic energy $\epsilon$ and scalar variance $\chi$ , the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $\epsilon$ alone. While the majority of the domain is characterized by the canonical flux coefficient $\varGamma \equiv \chi /\epsilon =0.2$ , often assumed in ocean mixing parametrizations, extreme values of $\chi$ within the statically stable interfaces, associated with elevated $\varGamma$ , strongly skew the bulk statistics. Our findings suggest that current parametrizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.

Couchman, Miles M. P. (ORCID:0000000246676829)↗

Mental workload dynamics in adaptive interface design

In examining the role of time in mental workload, the authors present a different perspective from which to view the problem of assessment. Mental workload is plotted in three dimensions, whose axes represent effective time for action, perceived distance from desired goal state, level of effort required to achieve the time-constrained goal. This representation allows the generation of isodynamic workload contours that incorporate the factors of operator skill and equifinality of effort. An adaptive interface for dynamic task reallocation is described that uses this form of assessment to reconcile the joint aims of stable operator loading and acceptable primary task performance by the total system.

Hancock, Peter A.↗

Acute Radiation Risk and BRYNTRN Organ Dose Projection Graphical User Interface

The integration of human space applications risk projection models of organ dose and acute radiation risk has been a key problem. NASA has developed an organ dose projection model using the BRYNTRN with SUM DOSE computer codes, and a probabilistic model of Acute Radiation Risk (ARR). The codes BRYNTRN and SUM DOSE are a Baryon transport code and an output data processing code, respectively. The risk projection models of organ doses and ARR take the output from BRYNTRN as an input to their calculations. With a graphical user interface (GUI) to handle input and output for BRYNTRN, the response models can be connected easily and correctly to BRYNTRN. A GUI for the ARR and BRYNTRN Organ Dose (ARRBOD) projection code provides seamless integration of input and output manipulations, which are required for operations of the ARRBOD modules. The ARRBOD GUI is intended for mission planners, radiation shield designers, space operations in the mission operations directorate (MOD), and space biophysics researchers. BRYNTRN code operation requires extensive input preparation. Only a graphical user interface (GUI) can handle input and output for BRYNTRN to the response models easily and correctly. The purpose of the GUI development for ARRBOD is to provide seamless integration of input and output manipulations for the operations of projection modules (BRYNTRN, SLMDOSE, and the ARR probabilistic response model) in assessing the acute risk and the organ doses of significant Solar Particle Events (SPEs). The assessment of astronauts radiation risk from SPE is in support of mission design and operational planning to manage radiation risks in future space missions. The ARRBOD GUI can identify the proper shielding solutions using the gender-specific organ dose assessments in order to avoid ARR symptoms, and to stay within the current NASA short-term dose limits. The quantified evaluation of ARR severities based on any given shielding configuration and a specified EVA or other mission scenario can be made to guide alternative solutions for attaining determined objectives set by mission planners. The ARRBOD GUI estimates the whole-body effective dose, organ doses, and acute radiation sickness symptoms for astronauts, by which operational strategies and capabilities can be made for the protection of astronauts from SPEs in the planning of future lunar surface scenarios, exploration of near-Earth objects, and missions to Mars.

Cucinotta, Francis A.↗

A Transient Response Method for Linear Coupled Substructures

A method is presented for determining the transient response of a discrete coordinate model of a linear structural system composed of substructures. The method is applicable to systems consisting of any number of substructures, both determinate and indeterminate interface boundaries, and any topological arrangement of the substructures. The method is simple to implement from a computational point of view because the equations of motion of each of the substructures are solved independently, and the interface boundary compatibility conditions are enforced at each integration time step by a matrix multiplication. The method is demonstrated for a structural system consisting of two beam segments and acted upon by a time dependent force. The numerical results from the demonstration problem validates the accuracy of the method. The application of this method to structural systems with changing interface boundary conditions between substructures is discussed.

Admire, J. R.↗

Virtual Reality Simulation of the International Space Welding Experiment

Virtual Reality (VR) is a set of breakthrough technologies that allow a human being to enter and fully experience a 3-dimensional, computer simulated environment. A true virtual reality experience meets three criteria: (1) It involves 3-dimensional computer graphics; (2) It includes real-time feedback and response to user actions; and (3) It must provide a sense of immersion. Good examples of a virtual reality simulator are the flight simulators used by all branches of the military to train pilots for combat in high performance jet fighters. The fidelity of such simulators is extremely high -- but so is the price tag, typically millions of dollars. Virtual reality teaching and training methods are manifestly effective, and we have therefore implemented a VR trainer for the International Space Welding Experiment. My role in the development of the ISWE trainer consisted of the following: (1) created texture-mapped models of the ISWE's rotating sample drum, technology block, tool stowage assembly, sliding foot restraint, and control panel; (2) developed C code for control panel button selection and rotation of the sample drum; (3) In collaboration with Tim Clark (Antares Virtual Reality Systems), developed a serial interface box for the PC and the SGI Indigo so that external control devices, similar to ones actually used on the ISWE, could be used to control virtual objects in the ISWE simulation; (4) In collaboration with Peter Wang (SFFP) and Mark Blasingame (Boeing), established the interference characteristics of the VIM 1000 head-mounted-display and tested software filters to correct the problem; (5) In collaboration with Peter Wang and Mark Blasingame, established software and procedures for interfacing the VPL DataGlove and the Polhemus 6DOF position sensors to the SGI Indigo serial ports. The majority of the ISWE modeling effort was conducted on a PC-based VR Workstation, described below.

Phillips, James A.↗

Finite-element methods for steady solidification problems

Four Galerkin finite-element methods are tested for solving the free-boundary problem that describes steady solidification. The formulations differ in the solution method used to account for the unknown shape of the melt/solid interface, in the interphase condition (either balance of heat flux or equilibrium of temperature) distinguished for locating the interface, and in the technique used for solving the systems of algebraic equations that result from the finite-element approximations. Methods that use the melting point isotherm to locate the melt/solid interface are found more accurate and efficient than formulations based on the interfacial energy balance. Solution by a Galerkin-Newton algorithm of the free-boundary problem transformed to a fixed domain is most efficient when the field problem in each phase is made nonlinear by including radiation from the melt and solid to the surroundings.

Ettouney, H. M.↗

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .

Mechanics↗

Model-Invariant Hybrid RANS-LES Computations on Unstructured Meshes

Hybrid RANS-LES computations combine the bene ts of RANS and LES so that LES is used in regions where the accuracy of RANS deteriorates. The numerous hybrid approaches are limited by the speci cation of the LES-RANS interface, which can cause nonphysical results such as log-layer mismatch and low shear stress. The hybrid RANS-LES approach based on the concept of model invariance, mitigates these problems, enabling seamless blending of the RANS and LES regions while forming the basis for interpreting the results in the interface region. This hybrid formulation was implemented in the NASA FUN3D unstructured code and computations for ow in a channel at Reynolds number of 3300 (based on the channel half width h and the bulk in ow velocity u(infinity) were carried out. An isotropic stochastic turbulence generator was implemented to generate in ow turbulence. The present approach was able to eliminate the log-layer mismatch and predict the shear stress fairly well. Thus, the model-invariant hybrid formulation coupled with the isotropic turbulence in ow generation serves as a physically meaningful way of performing hybrid RANS-LES computations.

Sreekanth, R.↗

Orbiter LH2 Feedline Flowliner Cracking Problem

In May of 2002, three cracks were found in the downstream flowliner at the gimbal joint in the LH2 feedline at the interface with the Low Pressure Fuel Turbopump (LPFP) of Space Shuttle Main Engine (SSME) #1 of Orbiter OV-104. Subsequent inspections of the feedline flowliners in the other orbiters revealed the existence of 8 additional cracks. No cracks were found in the LO2 feedline flowliners. A solution to the cracking problem was developed and implemented on all orbiters. The solution included weld repair of all detectable cracks and the polishing of all slot edges to remove manufacturing discrepancies that could initiate new cracks. Using the results of a fracture mechanics analysis with a scatter factor of 4 on the predicted fatigue life, the orbiters were cleared for return to flight with a one-flight rationale requiring inspections after each flight. OV-104 flew mission STS-112 and OV-105 flew mission STS-113. The post-flight inspections did not find any cracks in the repaired flowliners. At the request of the Orbiter Program, the NESC conducted an assessment of the Orbiter LH2 Feedline Flowliner cracking problem with a team of subject matter experts from throughout NASA.

Harris, Charles E.↗

A general framework for substructuring‐based domain decomposition methods for models having nonlocal interactions

Abstract A mathematical framework is provided for a substructuring‐based domain decomposition (DD) approach for nonlocal problems that features interactions between points separated by a finite distance. Here, by substructuring it is meant that a traditional geometric configuration for local partial differential equation (PDE) problems is used in which a computational domain is subdivided into non‐overlapping subdomains. In the nonlocal setting, this approach is substructuring‐based in the sense that those subdomains interact with neighboring domains over interface regions having finite volume, in contrast to the local PDE setting in which interfaces are lower dimensional manifolds separating abutting subdomains. Key results include the equivalence between the global, single‐domain nonlocal problem and its multi‐domain reformulation, both at the continuous and discrete levels. These results provide the rigorous foundation necessary for the development of efficient solution strategies for nonlocal DD methods.

Capodaglio, Giacomo↗

Efficiency, Power Loss, and Power Factor Measurement of Quadrupole Magnet Power Supplies at the Spallation Neutron Source

The linear accelerator (LINAC) quadrupole magnets are powered by 42 silicon-controlled rectifier (SCR) based power supplies at the Spallation Neutron Source (SNS) facility of Oak Ridge National Laboratory. These 35V, 525A power supplies are bulky, inefficient and require both air and water cooling. The reliability of the SNS facility is impacted due to water leaks internal to power supplies and current readback issues associated with their unique control system interface, resulting in multiple downtime events. Hence, an alternate solution is necessary for the continued reliable operation of the SNS. To mitigate the above-mentioned problems, this paper proposes the use of off-the-shelf Switch Mode Power Supplies (SMPS) rated for 20V, 500A with serial control interface. These SMPS are air-cooled, more efficient and more compact owing to their switching speeds of approximately 160 kHz. The performance enhancements of the SMPS in comparison with the existing SCR power supply are discussed in detail in this paper. The features of the SMPS, along with experimental results for both power supplies, like efficiency, power losses and stability, are presented. Ongoing work is also discussed.

Harave, Sudarshan↗