SEARCH · Engineering Papers

Results for “high-order features”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

94 records · Page 6

All sources NASA NTRS DOE OSTI

NASA NTRS1994

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Bey, Kim S.↗

NASA NTRS2004

Simultaneous FUSE, HST, and Chandra Observations or Intrinsic Absorbers in NGC 7469 and MRK 279

We obtained FUSE observations of NGC 7469 on 2002 Dec 13 & 14. The two exposures totaled only 7 ks. The observations only have good data in one channel, LiF1, due to channel alignment problems. These observations were obtained simultaneously with high-quality HST/STIS and Chandra HETG spectra. The previously known O VI absorption lines in the FUSE spectrum are detected at good signal to noise ratio, and a wide array of other intrinsic absorption lines are visible in the X-ray spectrum and in the STIS spectrum. Compared to prior FUSE observations, the continuum flux for this observation was 50% lower. We see the effects of this in the lowest-velocity O VI absorber, which we associate with the X-ray absorbing gas also detected in this object. This O VI absorber has only a 50% covering fraction, consistent with its covering only the continuum in this source, and its strength and inferred column density increased as the continuum flux of NGC 7469 decreased. This is consistent with the recombination expected from photoionization models of the highly ionized gas. We obtained FUSE observations of Mrk 279 on 2002 May 18. As for NGC 7469, channel alignment problems led to good data being present only in LiFl. While we obtained a much longer integration on the target than planned (47.4 ks vs. 31 ks requested), the UV flux was down a factor of 10 or more from previous HST and FUSE observations, and our wavelength coverage was restricted due to the channel alignment problems. These data still cover the important O VI emission line and absorption lines in Mrk 279. The FUSE flux also agrees well with the simultaneous HST STIS data, which have good signal to noise. We have also analyzed FUSE observations made at three earlier epochs. We detect the Fe K-alpha emission line in the Chandra spectrum, and its flux is consistent with the low X-ray continuum flux level of Mrk 279 at the time of the observation. Because of low signal-to-noise ratios (S/N) in the Chandra spectrum, no O VII or O VIII absorption features are observable in the Chandra data, but the UV spectra reveal strong and complex absorption from H I and high-ionization species such as O VI, N V, and C IV, as well as from low-ionization species such as C III, N III, C II, and N II in some velocity components. The far-UV spectral coverage of the FUSE data provides information on high-order Lyman series absorption, which we use to calculate the optical depths and line and continuum covering fractions in the intrinsic H I absorbing gas in a self-consistent fashion. Based on the velocities, profile shapes, covering fractions and variability of the UV absorption, we conclude that some of the absorption components, particularly those showing prominent low-ionization lines, are likely associated with the host galaxy of Mrk 279, and possibly with its interaction with a close companion galaxy, while the remainder arises in a nuclear outflow.

Sonneborn, George↗

NASA NTRS2013

Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes

With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.

Chang, Chau-Lyan↗

DOE OSTI2024

Hybridized Discontinuous Galerkin Methods for Computational Fluid Dynamics

Hybridizable Discontinuous Galerkin (HDG) methods hold promise for any applications with significant advection character, including thermal hydraulics in light water reactors and advanced reactor concepts and fluid models of plasmas in magnetic confinement fusion. Its features include natural upwinding, local element conservation, and extensibility to arbitrarily high order accuracy. In the last fiscal year we have implemented HDG in the Multiphysics Object-Oriented Simulation Environment (MOOSE). We developed a first-of-its-kind automatic static condensation system in MOOSE’s underlying finite element library libMesh which can condense out arbitrarily many internal variables. Finally, we developed the first preconditioner for HDG discretizations of the Navier-Stokes equations which shows robust performance across a wide range of problem sizes and Reynolds numbers. This preconditioner yields solution times that are equivalent to the fastest developed for industry standard finite volume methods. Moreover, the arbitrarily high-order nature of HDG makes it a prime candidate for acceleration via graphical processing units (GPUs). We believe these developments will hold significant importance for future DOE Nuclear Energy (NE) and Fusion Energy Science (FES) programs.

97 MATHEMATICS AND COMPUTING↗