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NASA NTRSDate not supplied

Explicit Discontinuous Galerkin Methods for Conservation Laws

The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz (2007, 2008) called space–time expansion discontinuous Galerkin or STE-DG scheme, and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky (CK) procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction of the data among neighboring cells takes place; the difference, however, is in how the resulting space-time volume integral is estimated. As a consequence of the different estimates, for the case of advection in one spatial dimension (1D), the moment scheme has a CFL (Courant-Friedrichs-Lewy) condition of 1 for all p and is accurate to order 2p+1, i.e., it possesses the super accuracy property, whereas the STE-DG method has a more restrictive CFL condition and is accurate to the expected order of p+1. For 1D advection, compared with the CFL conditions of 1/(2p+1) of standard RK-DG (Runge-Kutta) scheme where space and time discretization are of the same order, the moment scheme allows a significantly larger time step size. It also turns out that the scheme yields a result identical to Van Leer’s scheme III (1977), which amounts to shifting the data a distance of advection corresponding to the time step and projecting the result onto the space of polynomial solutions. Contrary to Van Leer’s approach, however, the space-time ‘predictor-corrector’ formulation facilitates extensions to the case of systems of equations. Concerning 2D extensions, in the case of advection, when the flow is along the diagonal direction, the CFL conditions for the moment schemes become restrictive as will be shown by Fourier (Von Neumann) stability and accuracy analyses. Since the moment scheme employs the right Radau points as collocation points in time, the method is closely related to the implicit Radau IIA scheme, which is stable for any time step size. The role of Radau IIA in relieving stability restriction for these explicit DG schemes remains to be explored

Discontinuous Galerkin↗
NASA NTRS1999

Multi-Dimensional Quantum Tunneling and Transport Using the Density-Gradient Model

We show that quantum effects are likely to significantly degrade the performance of MOSFETs (metal oxide semiconductor field effect transistor) as these devices are scaled below 100 nm channel length and 2 nm oxide thickness over the next decade. A general and computationally efficient electronic device model including quantum effects would allow us to monitor and mitigate these effects. Full quantum models are too expensive in multi-dimensions. Using a general but efficient PDE solver called PROPHET, we implemented the density-gradient (DG) quantum correction to the industry-dominant classical drift-diffusion (DD) model. The DG model efficiently includes quantum carrier profile smoothing and tunneling in multi-dimensions and for any electronic device structure. We show that the DG model reduces DD model error from as much as 50% down to a few percent in comparison to thin oxide MOS capacitance measurements. We also show the first DG simulations of gate oxide tunneling and transverse current flow in ultra-scaled MOSFETs. The advantages of rapid model implementation using the PDE solver approach will be demonstrated, as well as the applicability of the DG model to any electronic device structure.

Biegel, Bryan A.↗
NASA NTRS2016

Improving Fidelity of Launch Vehicle Liftoff Acoustic Simulations

Launch vehicles experience high acoustic loads during ignition and liftoff affected by the interaction of rocket plume generated acoustic waves with launch pad structures. Application of highly parallelized Computational Fluid Dynamics (CFD) analysis tools optimized for application on the NAS computer systems such as the Loci/CHEM program now enable simulation of time-accurate, turbulent, multi-species plume formation and interaction with launch pad geometry and capture the generation of acoustic noise at the source regions in the plume shear layers and impingement regions. These CFD solvers are robust in capturing the acoustic fluctuations, but they are too dissipative to accurately resolve the propagation of the acoustic waves throughout the launch environment domain along the vehicle. A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed to improve such liftoff acoustic environment predictions. The framework combines the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin (DG) solver, Loci/THRUST, developed in the same computational framework. Loci/THRUST employs a low dissipation, high-order, unstructured DG method to accurately propagate acoustic waves away from the source regions across large distances. The DG solver is currently capable of solving up to 4th order solutions for non-linear, conservative acoustic field propagation. Higher order boundary conditions are implemented to accurately model the reflection and refraction of acoustic waves on launch pad components. The DG solver accepts generalized unstructured meshes, enabling efficient application of common mesh generation tools for CHEM and THRUST simulations. The DG solution is coupled with the CFD solution at interface boundaries placed near the CFD acoustic source regions. Both simulations are executed simultaneously with coordinated boundary condition data exchange.

Liever, Peter↗
NASA NTRS2015

De-Aliasing Through Over-Integration Applied to the Flux Reconstruction and Discontinuous Galerkin Methods

High-order methods are quickly becoming popular for turbulent flows as the amount of computer processing power increases. The flux reconstruction (FR) method presents a unifying framework for a wide class of high-order methods including discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV). It offers a simple, efficient, and easy way to implement nodal-based methods that are derived via the differential form of the governing equations. Whereas high-order methods have enjoyed recent success, they have been known to introduce numerical instabilities due to polynomial aliasing when applied to under-resolved nonlinear problems. Aliasing errors have been extensively studied in reference to DG methods; however, their study regarding FR methods has mostly been limited to the selection of the nodal points used within each cell. Here, we extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the FR framework. Our results show that over-integration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution (for FR as well as DG).

High-Order↗
NASA NTRS1983

Androgens enhance in vivo 2-deoxyglucose uptake by rat striated muscle

It is shown that testosterone propionate (TP) causes a striking increase in the in vivo uptake of 2-deoxyglucose (2-DG) by the levator ani muscle of immature male rats, which was found to be uniformly distributed over the entire muscle. After a single subcutaneous injection of TP, no enhancement of 2-DG was observed before 3.5 hr, at which time uptake was increased 2-fold; maximum enhancement (4-fold) was attained at 12 hr. At 72 hr, 2-DG uptake remained elevated at twice the control value. It was determined that the effect of TP probably is mediated by specific androgen receptors. In addition, it was found that the effect of TP was blocked by the simultaneous administration of an androgen antagonist, cyproterone acetate. TP also was found to enhance the uptake of 2-DG in the bulbocavernosus (253 percent over control) and extensor digitorum longus muscles (150 percent over control), but not in the biceps brachii or soleus. It is suggested that the increased uptake of glucose may be an important early step in the anabolic response of muscle to androgens.

Max, S. R.↗
NASA NTRS1994

Emission-line studies of young stars. 4: The optical forbidden lines

Optical forbidden line strengths and profiles are discussed for a sample of 30 T Tauri stars and 12 Herbig Ae-Be stars. Transitions of (C I), (N II), (O I), (O II), (S II), (Ca II), (Cr II), (Fe II), and (Ni II) are detected. Profile variability occurred in DG Tau and probably other sources. The ensemble profiles can be divided into four generic components that may represent distinct emitting regions; (1) narrow rest-velocity lines, (2) 'low'-velocity lines (peaking at less than or approximately +/- 50 km s(exp -1)), (3) 'high'-velocity (usually greater than or approximately +/- 100 km s(exp -1)) blueshifted peaks or wings, and (4) high-velocity redshifted peaks. Among T Tauri stars, the rest-velocity lines appear most often in sources with weak and narrow permitted lines, such as the Ca II triplet. The low- and high-velocity blueshifted components usually appear together in sources with strong and broad Ca II triplet lines. If the velocity-shifted lines form in jets, the smallest (full) opening angles required by the profiles are less than or approximately 20 deg for the narrow, blueshifted (Ca II) lines of DG Tau and HL Tau. Other lines in DG Tau are much broader, implying larger opening angles or greater velocity dispersions. The variability in DG Tau also implies significant changes in the collimation or velocity coherence on timescales of a few years. RW Aur and AS 353A have blue- and redshifted line peaks that could form in oppositely directed jets. The strong (S II) lambda 6716 and lambda 6731 lines in RW Aur are exclusively redshifted and require opening angles less than or approximately 60 deg. Measurements of different profiles in the same spectrum show that the physical conditions change with the line-of-sight velocities. The most persistent trends are for more (N II) and (O II) and less (O I) lambda 5577 flux at high velocities. Constraints on the physical conditions are derived by modeling the emission lines via multilevel ions in 'coronal ionization equilibrium.' A single temperature and density cannot fully describe the line spectra in any velocity interval. Temperatures in the (O I) region are 9000 less than or approximately T(sub e) less than 14,000 K, and the ionization fraction (of H) is less than 35%. The densities derived from (O I) include n(sub e) less than or approximately 5 x 10(exp 5) to approximately 10(exp 7) cm(exp -3), but n(sub e) greater than or approximately 10(exp 6) cm(exp -3) obtains only at low velocities. In the (S II) regions the densities are lower, 10(exp 3) less than or approximately n(sub e) less than or approximately 7 x 10(exp 4) cm(exp -3), and the temperatures are probably higher, T(sub e) greater than or approximately 13,000 K. At high velocities (only) there is additional hot gas that produces (N II) and (O II), possibly most of the (S II), and little (O I). This region is characterized by T(sub e) greater than or approximately 15,000 K, n(sub e) less than or approximately 10(exp 5) cm(exp -3), and an ionization fraction greater than or approximately 50%. When combined with the spatially segregated emitting regions observed by others by spectral imaging, these results suggest decreasing n(sub e) and increasing T(sub e) away from the star in at least the high velocity gas.

Hamann, Fred↗
NASA NTRS1995

Immune Alterations in Male and Female Mice after 2-Deoxy-D-Glucose Administration

Administration of 2-deoxy-D-glucose (2-DG), an analog of glucose which inhibits glycolysis by competitive antagonism for phosphohexose isomerase, results in acute periods of intracellular glucoprivation and hyperglycemia resulting in hyperphagia. In addition to these changes in the carbohydrate metabolism, injection of 2-DG results in alterations of both the endocrine and neurological systems as suggested by modifications in oxytocin and glucocorticoid levels and norepinephrine production. Moreover, alterations of the immune response, such as a decrease in the in vitro proliferation of splenocytes after mitogen-stimulation, were observed in mice injected with 2-DG. Sex, genotype and environment are among the factors that may modulate effects of catecholamines and hypothalamo-pituitary-adrenal axis on these immune changes. Sexual dimorphism in immune function resulting from the effects of sex hormones on immune effector cells has been shown in both animals and humans. These observations have important implications, especially with regard to higher incidence of many autoimmune diseases in females. Evidence exists that reproductive hormones influence the immune system and increase the risk of immunologically related disorders in both animals and humans. Indeed, immunological responses in stressful situations may also be confounded by fluctuations of sex hormones especially in females. Lymphocyte distribution, cytoldne production, and the ability of lymphocyte to proliferate in vitro were analyzed in male and female mice to determine if sex influenced 2-DG immunomodulation. In addition, the influence of hormones, especially sex hormones, on these changes were evaluated.

Dreau, Didier↗
NASA NTRS1999

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Barth, Timothy↗
NASA NTRS2000

Oxidant damage during and after spaceflight

The objectives of this study were to assess oxidant damage during and after spaceflight and to compare the results against bed rest with 6 degrees head-down tilt. We measured the urinary excretion of the F(2) isoprostane, 8-iso-prostaglandin (PG) F(2alpha), and 8-oxo-7,8-dihydro-2 deoxyguanosine (8-OH DG) before, during, and after long-duration spaceflight (4-9 mo) on the Russian space station MIR, short-duration spaceflight on the shuttle, and 17 days of bed rest. Sample collections on MIR were obtained between 88 and 186 days in orbit. 8-iso-PGF(2alpha) and 8-OH DG are markers for oxidative damage to membrane lipids and DNA, respectively. Data are mean +/- SE. On MIR, isoprostane levels were decreased inflight (96. 9 +/- 11.6 vs. 76.7 +/- 14.9 ng. kg(-1). day(-1), P < 0.05, n = 6) due to decreased dietary intake secondary to impaired thermoregulation. Isoprostane excretion was increased postflight (245.7 +/- 55.8 ng. kg(-1). day(-1), P < 0.01). 8-OH DG excretion was unchanged with spaceflight and increased postflight (269 +/- 84 vs 442 +/- 180 ng. kg(-1). day(-1), P < 0.05). On the shuttle, 8-OH DG excretion was unchanged in- and postflight, but 8-iso-PGF(2alpha) excretion was decreased inflight (15.6 +/- 4.3 vs 8.0 +/- 2.7 ng. kg(-1). day(-1), P < 0.05). No changes were found with bed rest, but 8-iso-PGF(2alpha) was increased during the recovery phase (48.9 +/- 23.0 vs 65.4 +/- 28.3 ng. kg(-1). day(-1), P < 0.05). The changes in isoprostane production were attributed to decreased production of oxygen radicals from the electron transport chain due to the reduced energy intake inflight. The postflight increases in the excretion of the products of oxidative damage were attributed to a combination of an increase in metabolic activity and the loss of some host antioxidant defenses inflight. We conclude that 1) oxidative damage was decreased inflight, and 2) oxidative damage was increased postflight.

Mir Project↗
NASA NTRS2011

Collocation and Galerkin Time-Stepping Methods

We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.

Huynh, H. T.↗
NASA NTRS1975

Steering law for parallel mounted double-gimbaled control moment gyros

Parallel mounting of double-gimbaled control moment gyros (DG CMG) is discussed in terms of simplification of the steering law. The steering law/parallel mounted DG CMG is considered to be a 'CMG kit' applicable to any space vehicle where the need for DG CMG's has been established.

Kennel, H. F.↗
NASA NTRS1986

Radio variability and structure of T Tauri stars

Observations of radio variability in V410 Tau and in HP Tau/G2 and /G3, and striking variations in the radio structure of DG Tau, are reported. The position of the radio peak of DG Tau has shown apparent motion between 1982 and 1985 along the flow axis from this star, while its morphology has varied from point-like to bipolar. These changes and the spectral index of 0.6 at high frequencies are interpreted as indicative of a variable, freely expanding radio jet in DG Tau.

Cohen, Martin↗
NASA NTRS1977

Research on Graphite Reinforced Glass Matrix Composites

This report contains the results obtained in the first twelve months of research under NASA Langley Contract NAS1-14346 for the origination of graphite-fiber reinforced glass matrix composites. Included in the report is a summary of the research by other investigators in this area. The method selected to form the composites consisted of pulling the graphite fiber through a slurry containing powdered glass, winding up the graphite fiber and the glass it picks up on a drum, drying, cutting into segments, loading the tape segment into a graphite die, and hot pressing. During the course of the work, composites were made with a variety of graphite fibers in a C.G.W. 7740 (Pyrex) glass matrix. The graphite fibers used included Hercules HMS, Hercules HTS, Thornel 300S, and Celanese DG-102 and, of these, the Hercules HMS and Celanese DG-102 graphite fibers in C.G.W. 7740 gave the most interesting but widely different results. Hercules HMS fiber in C.G.W. 7740 glass (Pyrex) showed an average four-point flexural strength of 848 MPa or 127,300 psi. As the test temperature was raised from room temperature to 560 C in argon or vacuum, the strength was higher by 50 percent. However, in air, similar tests at 560 C gave a severe loss in strength. These composites also have good thermal cycle properties in argon or vacuum, greatly increased toughness compared to glass, and no loss in strength in a 100 cycle fatigue test. Celanese DG-102 fiber in C.G.W. 7740 glass (Pyrex) had a much lower flexural strength but did not suffer any loss in this strength when samples were heated to 560 C in air for 4 hrs.

Bacon, J. F.↗
NASA NTRS2001

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Barth, Timothy↗
NASA NTRS2001

Discontinuous Galerkin Methods for NonLinear Differential Systems

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

Barth, Timothy↗
NASA NTRS1998

Multi-Dimensional Quantum Effect Simulation Using a Density-Gradient Model and Script-Level Programming Techniques

A density-gradient (DG) model is used to calculate quantum-mechanical corrections to classical carrier transport in MOS (Metal Oxide Semiconductor) inversion/accumulation layers. The model is compared to measured data and to a fully self-consistent coupled Schrodinger and Poisson equation (SCSP) solver. Good agreement is demonstrated for MOS capacitors with gate oxide as thin as 21 A. It is then applied to study carrier distribution in ultra short MOSFETs (Metal Oxide Semiconductor Field Effect Transistor) with surface roughness. This work represents the first implementation of the DG formulation on multidimensional unstructured meshes. It was enabled by a powerful scripting approach which provides an easy-to-use and flexible framework for solving the fourth-order PDEs (Partial Differential Equation) of the DG model.

Rafferty, Connor S.↗
NASA NTRS1998

Simulation of Ultra-Small MOSFETs Using a 2-D Quantum-Corrected Drift-Diffusion Model

We describe an electronic transport model and an implementation approach that respond to the challenges of device modeling for gigascale integration. We use the density-gradient (DG) transport model, which adds tunneling and quantum smoothing of carrier density profiles to the drift-diffusion model. We present the current implementation of the DG model in PROPHET, a partial differential equation solver developed by Lucent Technologies. This implementation approach permits rapid development and enhancement of models, as well as run-time modifications and model switching. We show that even in typical bulk transport devices such as P-N diodes and BJTs, DG quantum effects can significantly modify the I-V characteristics. Quantum effects are shown to be even more significant in small, surface transport devices, such as sub-0.1 micron MOSFETs. In thin-oxide MOS capacitors, we find that quantum effects may reduce gate capacitance by 25% or more. The inclusion of quantum effects in simulations dramatically improves the match between C-V simulations and measurements. Significant quantum corrections also occur in the I-V characteristics of short-channel MOSFETs due to the gate capacitance correction.

Biegel, Bryan A.↗
NASA NTRS2004

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Liu, Yen↗