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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

ON THE ROLE OF INVOLUTIONS IN THE DISCONTINUOUS GALERKIN DISCRETIZATION OF MAXWELL AND MAGNETOHYDRODYNAMIC SYSTEMS

The role of involutions in energy stability of the discontinuous Galerkin (DG) discretization of Maxwell and magnetohydrodynamic (MHD) systems is examined. Important differences are identified in the symmetrization of the Maxwell and MHD systems that impact the construction of energy stable discretizations using the DG method. Specifically, general sufficient conditions to be imposed on the DG numerical flux and approximation space are given so that energy stability is retained These sufficient conditions reveal the favorable energy consequence of imposing continuity in the normal component of the magnetic induction field at interelement boundaries for MHD discretizations. Counterintuitively, this condition is not required for stability of Maxwell discretizations using the discontinuous Galerkin method.

Barth, Timothy↗
NASA NTRS2006

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Helenbrook, B. T.↗
NASA NTRS2022

The Discontinuous Galerkin Finite Element Method

The purpose of this report is to present details of the Discontinuous Galerkin (DG) Finite Element Method (DG FEM). First the weighted-residual (WR) form is introduced and then the Galerkin Finite Element (FE) (GFE) and the Petrov-Galerkin FE (PG FE) methods are discussed. The details of the implementation of the DG FEM are presented along with two examples, 2nd order and 4th order differential equations, and the performance of the method is discussed.

Finite element↗
NASA NTRS2015

A Survey of the Isentropic Euler Vortex Problem Using High-Order Methods

The flux reconstruction (FR) method offers a simple, efficient, and easy to implement method, and it has been shown to equate to a differential approach to discontinuous Galerkin (DG) methods. The FR method is also accurate to an arbitrary order and the isentropic Euler vortex problem is used here to empirically verify this claim. This problem is widely used in computational fluid dynamics (CFD) to verify the accuracy of a given numerical method due to its simplicity and known exact solution at any given time. While verifying our FR solver, multiple obstacles emerged that prevented us from achieving the expected order of accuracy over short and long amounts of simulation time. It was found that these complications stemmed from a few overlooked details in the original problem definition combined with the FR and DG methods achieving high-accuracy with minimal dissipation. This paper is intended to consolidate the many versions of the vortex problem found in literature and to highlight some of the consequences if these overlooked details remain neglected.

High-Order↗
DOE OSTI2024

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. Here we use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov–Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1976

Far-ultraviolet rocket astronomy program

The launch of sounding rocket 26.056 DG on 29 October 1976 is described and quick-look results from that mission are given. Also further work on data obtained by 13.118 DG, launched 5 December 1975 is reported.

Carruthers, G. R.↗
NASA NTRS1995

Coronagraphic imaging of pre-main-sequence stars: Remnant evvelopes of star formation seen in reflection

We have obtained R- and I-band coronagraphic images of the vicinities of 11 pre-main sequence (PMS) stars to search for faint, small-scale reflection nebulae. The inner radius of the search and the field of view are 1.9 arcsec and 1x1 arcmin, respectively. Reflection nebulae were imaged around RY Tau, T Tau,DG Tau, SU Aur, AB Aur, FU Ori, and Z CMa. No nebulae were detected around HBC 347, GG Tau, V773 Tau, and V830 Tau. Categorically speaking, most of the classical T Tauri program stars and all the FU Orionis-type program stars are associated with the reflection nebulae, while none of the weak-line T Tauri program stars are associated with nebulae. The detected nebulae range in size from 250 to 37 000 AU. From the brightness ratios of the stars and nebulae, we obtain a lower limit to the visual extinction of PMS star light through the nebulae of (A(sub V))(sub neb) = 0.1. The lower limits of masses and volume densities of the nebulae associated with the classical T Tauri stars are 10(exp-6) Solar mass and N(sub H) = 10(exp 5)/cu cm, respectively. Lower limits for the nebulae around FU Orionis stars are 10(exp -5) Solar mass and n(sub H) = 10 (exp 5)/cu cm, respectively. Some reflection nebulae may trace the illuminated surfaces of the optically thick dust nebulae, so these mass estimates are not stringent. All the PMS stars with associated nebulae are strong far-infrared emitters. Both the far-infrared emission and the reflection nebulae appear to originate from the remnant envelopes of star formation. The 100 micrometers emitting regions of SU Aur and FU Ori are likely to be cospatial with the reflection nebulae. A spatial discontinuity between FU Ori and its reflection nebula may explain the dip in the far-infrared spectral energy distribution at 60 micrometers. The warped, disk-like nebulae around T Tau and Z CMa are aligned with and embrace the inner star/circumstellar disk systems. The arc-shaped nebula around DG Tau may be in contact with the coaligned inner star/disk system. These three-reflection nebulae may trace the surfaces of pseudodisks from which matter accretes onto the stars or the inner circumstellar disks. 19 stellar objects brighter than I = 19 were detected around 9 program stars. Using a color-magnitude diagram, we have identified three new PMS candidates aroun Z CMa and one previously known PMS candidate, GG Tau/c.

Nakajima, Tadashi↗
NASA NTRS2000

Efficient Multi-Dimensional Simulation of Quantum Confinement Effects in Advanced MOS Devices

We investigate the density-gradient (DG) transport model for efficient multi-dimensional simulation of quantum confinement effects in advanced MOS devices. The formulation of the DG model is described as a quantum correction to the classical drift-diffusion model. Quantum confinement effects are shown to be significant in sub-100nm MOSFETs. In thin-oxide MOS capacitors, quantum effects may reduce gate capacitance by 25% or more. As a result, the inclusion or quantum effects in simulations dramatically improves the match between C-V simulations and measurements for oxide thickness down to 2 nm. Significant quantum corrections also occur in the I-V characteristics of short-channel (30 to 100 nm) n-MOSFETs, with current drive reduced by up to 70%. This effect is shown to result from reduced inversion charge due to quantum confinement of electrons in the channel. Also, subthreshold slope is degraded by 15 to 20 mV/decade with the inclusion of quantum effects via the density-gradient model, and short channel effects (in particular, drain-induced barrier lowering) are noticeably increased.

Biegel, Bryan A.↗
NASA NTRS1997

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

Barth, Timothy↗
NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.

Barth, Timothy J.↗
NASA NTRS2002

Unsteady Pressures in a Transonic Fan Cascade Due to a Single Oscillating Airfoil

An extensive set of unsteady pressure data was acquired along the midspan of a modern transonic fan blade for simulated flutter conditions. The data set was acquired in a nine-blade linear cascade with an oscillating middle blade to provide a database for the influence coefficient method to calculate instantaneous blade loadings. The cascade was set for an incidence of 10 dg. The data were acquired on three stationary blades on each side of the middle blade that was oscillated at an amplitude of 0.6 dg. The matrix of test conditions covered inlet Mach numbers of 0.5, 0.8, and 1.1 and the oscillation frequencies of 200, 300, 400, and 500 Hz. A simple quasiunsteady two-dimensional computer simulation was developed to aid in the running of the experimental program. For high Mach number subsonic inlet flows the blade pressures exhibit very strong, low-frequency, self-induced oscillations even without forced blade oscillations, while for low subsonic and supersonic inlet Mach numbers the blade pressure unsteadiness is quite low. The amplitude of forced pressure fluctuations on neighboring stationary blades strongly depends on the inlet Mach number and forcing frequency. The flowfield behavior is believed to be governed by strong nonlinear effects due to a combination of viscosity, compressibility, and unsteadiness. Therefore, the validity of the quasi-unsteady simplified computer simulation is limited to conditions when the flowfield is behaving in a linear, steady manner. Finally, an extensive set of unsteady pressure data was acquired to help development and verification of computer codes for blade flutter effects.

Lepicovsky, J.↗
NASA NTRS2002

Discontinuous Galerkin Methods for Turbulence Simulation

A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to turbulent channel flow at low Reynolds number, where it is found to successfully predict low-order statistics with fewer degrees of freedom than traditional numerical methods. This reduction is achieved by utilizing local hp-refinement such that the computational grid is refined simultaneously in all three spatial coordinates with decreasing distance from the wall. Another advantage of DG is that Dirichlet boundary conditions can be enforced weakly through integrals of the numerical fluxes. Both for a model advection-diffusion problem and for turbulent channel flow, weak enforcement of wall boundaries is found to improve results at low resolution. Such weak boundary conditions may play a pivotal role in wall modeling for large-eddy simulation.

Collis, S. Scott↗
NASA NTRS2003

Detection of Strand Cleavage And Oxidation Damage Using Model DNA Molecules Captured in a Nanoscale Pore

We use a biological nano-scale pore to distinguish among individual DNA hairpins that differ by a single site of oxidation or a nick in the sugar-phosphate backbone. In earlier work we showed that the protein ion channel alpha-hemolysin can be used as a detector to distinguish single-stranded from double-stranded DNA, single base pair and single nucleotide differences. This resolution is in part a result of sensitivity to structural changes that influence the molecular dynamics of nucleotides within DNA. The strand cleavage products we examined here included a 5-base-pair (5-bp) hairpin with a 5-prime five-nucleotide overhang, and a complementary five-nucleotide oligomer. These produced predictable shoulder-spike and rapid near-full blockade signatures, respectively. When combined, strand annealing was monitored in real time. The residual current level dropped to a lower discrete level in the shoulder-spike blockade signatures, and the duration lengthened. However, these blockade signatures had a shorter duration than the unmodified l0bp hairpin. To test the pore sensitivity to nucleotide oxidation, we examined a 9-bp hairpin with a terminal 8-oxo-deoxyguanosine (8-oxo-dG), or a penultimate 8-oxo-dG. Each produced blockade signatures that differed from the otherwise identical control 9bp hairpins. This study showed that DNA structure is modified sufficiently by strand cleavage or oxidation damage at a single site to alter in a predictable manner the ionic current blockade signatures produced. This technique improves the ability to assess damage to DNA, and can provide a simple means to help characterize the risks of radiation exposure. It may also provide a method to test radiation protection.

Vercoutere, W.↗
NASA NTRS2004

An Investigation of Wave Propagations in Discontinuous Galerkin Method

Analysis of the discontinuous Galerkin method has been carried out for one- and two-dimensional system of hyperbolic equations. Analytical, as well as numerical, properties of wave propagation in a DGM scheme are derived and verified with direct numerical simulations. In addition to a systematic examination of the dissipation and dispersion errors, behaviours of a DG scheme at an interface of two different grid topologies are also studied. Under the same framework, a quantitative discrete analysis of various artificial boundary conditions is also conducted. Progress has been made in numerical boundary condition treatment that is closely related to the application of DGM in aeroacoustics problems. Finally, Fourier analysis of DGM for the Convective diffusion equation has also be studied in connection with the application of DG schemes for the Navier-Stokes equations. This research has resulted in five(5) publications, plus one additional manuscript in preparation, four(4) conference presentations, and three(3) departmental seminars, as summarized in part II. Abstracts of papers are given in part 111 of this report.

Hu, Fang Q.↗
NASA NTRS1994

Complex polar lipids of a hot spring cyanobacterial mat and its cultivated inhabitants

The complex polar lipids of the hot spring cyanobacterial mat in the 50 to 55 degrees C region of Octopus Spring, Yellowstone National Park, and of thermophilic bacteria cultivated from this or similar habitats, were compared in an attempt to understand the microbial sources of the major lipid biomarkers in this community. Intact complex lipids were analyzed directly by fast atom bombardment mass spectrometry (FAB-MS), two-dimensional thin-layer chromatography (TLC), and combined TLC-FAB-MS. FAB-MS and TLC gave qualitatively similar results, suggesting that the mat contains major lipids most like those of the cyanobacterial isolate we studied, Synechococcus sp. strain Y-7c-s. These include monoglycosyl, diglycosyl, and sulfoquinosovyl diglycerides (MG, DG, and SQ, respectively) and phosphatidyl glycerol (PG). Though Chloroflexus aurantiacus also contains MG, DG, and PG, the fatty acid chain lengths of mat MGs, DGs, and PGs resemble more those of cyanobacterial than green nonsulfur bacterial lipids. FAB-MS spectra of the lipids of nonphototrophic bacterial isolates were distinctively different from those of the mat and phototrophic isolates. The lipids of these nonphototrophic isolates were not detected in the mat, but most could be detected when added to mat samples. The mat also contains major glycolipids and aminophospholipids of unknown structure and origin. FAB-MS and TLC did not always give quantitatively similar results. In particular, PG and SQ may give disproportionately high FAB-MS responses.

Non-NASA Center↗
NASA NTRS2000

Efficient Multi-Dimensional Simulation of Quantum Confinement Effects in Advanced MOS Devices

We investigate the density-gradient (DG) transport model for efficient multi-dimensional simulation of quantum confinement effects in advanced MOS devices. The formulation of the DG model is described as a quantum correction ot the classical drift-diffusion model. Quantum confinement effects are shown to be significant in sub-100nm MOSFETs. In thin-oxide MOS capacitors, quantum effects may reduce gate capacitance by 25% or more. As a result, the inclusion of quantum effects may reduce gate capacitance by 25% or more. As a result, the inclusion of quantum effects in simulations dramatically improves the match between C-V simulations and measurements for oxide thickness down to 2 nm. Significant quantum corrections also occur in the I-V characteristics of short-channel (30 to 100 nm) n-MOSFETs, with current drive reduced by up to 70%. This effect is shown to result from reduced inversion charge due to quantum confinement of electrons in the channel. Also, subthreshold slope is degraded by 15 to 20 mV/decade with the inclusion of quantum effects via the density-gradient model, and short channel effects (in particular, drain-induced barrier lowering) are noticeably increased.

Biegel, Bryan A.↗
NASA NTRS2000

Preliminary Estimates of the Possibilities for Developing a Deployable Greenhouse for a Planetary Surface (Mars)

Two of the main conditions for plant growth and development on the Martian surface are irradiation (optimal range from 80 W/sq m to 180 W/sq m of photosynthetically active radiation) and temperature (optimal range from 20 C to 27 C). The only known natural source of energy on Mars is sunlight, with a general intensity of 589 +/- 142 W/sq m (Martian Solar Constant). Comparisons of plant growth requirements with conditions on the Martian surface are presented in Table 1, while some basic considerations for implementing plant growth in a Martian DG are presented in Table 2. The general scenario and approximate schedule of startup and development of operations in DG are shown in Table 3.

Rygalov, V. Y.↗