Search NASA⌕ Search

SEARCH · Search NASA

Results for “Numerical Relativity”

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.

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

At least 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Development of efficient time-evolution method based on three-term recurrence relation

The advantage of the real-time (RT) propagation method is a direct solution of the time-dependent Schrödinger equation which describes frequency properties as well as all dynamics of a molecular system composed of electrons and nuclei in quantum physics and chemistry. Its applications have been limited by computational feasibility, as the evaluation of the time-evolution operator is computationally demanding. In this article, a new efficient time-evolution method based on the three-term recurrence relation (3TRR) was proposed to reduce the time-consuming numerical procedure. The basic formula of this approach was derived by introducing a transformation of the operator using the arcsine function. Since this operator transformation causes transformation of time, we derived the relation between original and transformed time. The formula was adapted to assess the performance of the RT time-dependent Hartree-Fock (RT-TDHF) method and the time-dependent density functional theory. Compared to the commonly used fourth-order Runge-Kutta method, our new approach decreased computational time of the RT-TDHF calculation by about factor of four, showing the 3TRR formula to be an efficient time-evolution method for reducing computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗
NASA NTRS1989

Assessment of numerical techniques for unsteady flow calculations

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

Hsieh, Kwang-Chung↗
NASA NTRS1999

Climatological Structures of the GRIPS Models: Mean States and Forcing

The GCM-Reality Intercomparison Project for SPARC (GRIPS) is assessing and monitoring the performance of state-of-the-art general circulation models (GCMs). A wide variety of tasks have been initiated. These are designed to: (1) assess the ability of the GCMs to represent the current climatological structure of the troposphere and middle atmosphere,(2) to compare their response to imposed forcing anomalies, and (3) to estimate the certainty with which future climate perturbations can be predicted. This paper is concerned with assessments of the climatological states in the GCM simulations. Comparing the simulations with observational datasets reveals considerable discrepancies in the modelled fields. While it might be anticipated that certain types of biases in the model simulations might be related to the formulation of different aspects of the numerical package (dynamical schemes, cloud schemes, radiation transfer, inclusion of gravity wave drag), there is no clear relationship between these features. This paper attempts to draw a more comprehensive picture of the GCMs'performance than has previously been shown, by comparing the dominant forcing mechanisms in the models with observational estimates, and relating model deficiencies to the differences in the physical mechanisms in the GCMS.

Pawson, Steven↗
DOE OSTI2022

Experiments and numerical modeling of surrogate droplet combustion for a 93 octane gasoline calibration fuel

Gasoline is the world’s most prolific liquid transportation fuel for ground transportation vehicles. Yet, a fundamental understanding of its burning characteristics is still lacking. Complicating this matter is the highly multicomponent nature of gasoline (comprised of hundreds of chemical species) and the seasonable variability of its composition due to variations in the crude oil feedstocks used in refining. The need to bring order to this complex problem has led to development of calibration fuels (Tier II in presented study) which on average will provide repeatable metrics that replicate performance of refined gasoline for various engine designs. This study presents results of experiments using the configuration of an isolated droplet to study the combustion dynamics of calibration fuel and three different surrogates (S4, S5, S6) for the calibration fuel. Droplet burning is under microgravity conditions, where gas transport is determined entirely by fuel evaporation in order to promote spherical symmetry in the burning process. The initial droplet diameters ranged between 0.55 mm and 0.60 mm. The droplets were spark-ignited and their burning histories were recorded by digital video cameras to obtain quantitative data. For each fuel, the evolutions of droplet, flame, and soot-shell diameters were measured to calculate the burn rates, flame-droplet diameter ratios (FSR) and soot-droplet diameter ratios. Additionally, a detailed numerical modeling is presented. This simulation includes multicomponent phase equilibrium, unsteady gas and liquid transport, radiative heat transfer, internal liquid diffusion and detailed combustion chemistry of different fuels during their burning process. Experiment results show that the calibration fuel and surrogates have a close burn rates and FSR, and S5 presents a relatively similar results with calibration fuel. Predictions from the numerical simulation using the surrogate are compared with experiment measurements, which showed a good agreement with the experiment results, including the droplet burning rate and FSR.

Guo, Songtao↗
DOE OSTI2015

Relativistic MHD simulations of collision-induced magnetic dissipation in Poynting-flux-dominated jets/outflows

The question of the energy composition of the jets/outflows in high-energy astrophysical systems, e.g. GRBs, AGNs, is taken up first: Matter-flux-dominated (MFD), σ < 1, and/or Poynting-flux-dominated (PFD), σ >1? The standard fireball IS model and dissipative photosphere model are MFD, while the ICMART (Internal-Collision-induced MAgnetic Reconnection and Turbulence) model is PFD. Motivated by ICMART model and other relevant problems, such as “jets in a jet” model of AGNs, the author investigates the models from the EMF energy dissipation efficiency, relativistic outflow generation, and σ evolution points of view, and simulates collisions between high-σ blobs to mimic the situation of the interactions inside the PFD jets/outflows by using a 3D SRMHD code which solves the conservative form of the ideal MHD equations. σ b,f is calculated from the simulation results (threshold = 1). The efficiency obtained from this hybrid method is similar to the efficiency got from the energy evolution of the simulations (35.2%). Efficiency is nearly σ independent, which is also confirmed by the hybrid method. σ b,i - σ b,f provides an interesting linear relationship. Results of several parameter studies of EMF energy dissipation efficiency are shown.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Reactive Transport Modeling of Anthropogenic Carbon Mineralization in Stacked Columbia River Basalt Reservoirs

Numerical simulation of CO2 storage in basalts and related reactive lithologies requires modeling complex, coupled hydrologic and chemical processes, including multi-phase flow and transport, partitioning of CO2 into the aqueous phase, and chemical interactions with aqueous fluids and rock minerals. We conducted reactive transport simulations of the Wallula pilot-scale CO2 injection into the flow tops of the Grande Ronde Basalt using our PNNL STOMP-CO2 simulator with the ECKEChem reactive module. Our mineralization simulation of the ~1,000 tons of injected CO2 into the interflow zones was based on the hydrologic transport model we previously developed. For this work, the simulations considered geochemical reactions involving the basalt components, precipitates, formation brine, and injected CO2. In our benchmark case, carbonate minerals precipitated, resulting in ~20% of the CO2 being mineralized in 10 years. Increasing the reaction rate of a single primary mineral phase (clinopyroxene) by an order of magnitude resulted in a carbon mineralization reaction extent of ~90% over the same time interval. Based on these initial sensitivity analysis results, it is clear that a thorough understanding of primary mineral dissolution rates is required for accurately predicting long-term fate and transport of injected CO2 into basalt formations. Our reactive transport numerical simulations will be key components of commercial-scale CO2 storage operation permitting, de-risking, and optimization in mafic and ultramafic reservoirs.

Cao, Ruoshi↗
DOE OSTI2015

THERMAL-GRAVITATIONAL WIND EQUATION FOR THE WIND-INDUCED GRAVITATIONAL SIGNATURE OF GIANT GASEOUS PLANETS: MATHEMATICAL DERIVATION, NUMERICAL METHOD, AND ILLUSTRATIVE SOLUTIONS

The standard thermal wind equation (TWE) relating the vertical shear of a flow to the horizontal density gradient in an atmosphere has been used to calculate the external gravitational signature produced by zonal winds in the interiors of giant gaseous planets. We show, however, that in this application the TWE needs to be generalized to account for an associated gravitational perturbation. We refer to the generalized equation as the thermal-gravitational wind equation (TGWE). The generalized equation represents a two-dimensional kernel integral equation with the Green’s function in its integrand and is hence much more difficult to solve than the standard TWE. We develop an extended spectral method for solving the TGWE in spherical geometry. We then apply the method to a generic gaseous Jupiter-like object with idealized zonal winds. We demonstrate that solutions of the TGWE are substantially different from those of the standard TWE. We conclude that the TGWE must be used to estimate the gravitational signature of zonal winds in giant gaseous planets.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

Computing unsteady shock waves for aeroacoustic applications

The computation of unsteady shock waves, which contribute significantly to noise generation in supersonic jet flows, is investigated. The paper focuses on the difficulties of computing slowly moving shock waves. Numerical error is found to manifest itself principally as a spurious entropy wave. Calculations presented are performed using a third-order essentially nonoscillatory scheme. The effect of stencil biasing parameters and of two versions of numerical flux formulas on the magnitude of spurious entropy are investigated. The level of numerical error introduced in the calculation is quantified as a function of shock pressure ratio, shock speed, Courant number, and mesh density. The spurious entropy relative to the entropy jump across a static shock decreases with increasing shock strength and shock velocity relative to the grid, but is insensitive to Courant number. The structure of the spurious entropy wave is affected by the choice of flux formulas and algorithm biasing parameters. The effect of the spurious numerical waves on the calculation of sound amplification by a shock wave is investigated. For this class of problem, the acoustic pressure waves are relatively unaffected by the spurious numerical phenomena.

Meadows, Kristine R.↗
NASA NTRS1994

Computing unsteady shock waves for aeroacoustic applications

The computation of unsteady shock waves, which contribute significantly to noise generation in supersonic jet flows, is investigated. This paper focuses on the difficulties of computing slowly moving shock waves. Numerical error is found to manifest itself principally as a spurious entropy wave. Calculations presented are performed using a third order essentially nonoscillatory scheme. The effect of stencil biasing parameters and of two versions of numerical flux formulas on the magnitude of spurious entropy are investigated. The level of numerical error introduced in the calculation in quantified as a function of shock pressure ratio, shock speed, Courant number, and mesh density. The spurious entropy relative to the entropy jump across a static shock decreases with increasing shock strength and shock velocity relative to the grid, but is insensitive to Courant number. The structure of the spurious entropy wave is affected by the choice of flux formulas and algorithm biasing parameters. The effect of the spurious numerical waves on the calculation of sound amplification by a shock wave is investigated. For this class of problem, the acoustic pressure waves are relatively unaffected by the spurious numerical phenomena.

Meadows,, Kristine r.↗
NASA NTRS2007

Modeling the Observed Solar Cycle Variations of the Quasi-biennial Oscillation (QBO): Amplification by Wave Forcing

In several papers, the solar cycle (SC) effect in the lower atmosphere has been linked observationally to the Quasi-biennial Oscillation (QBO) of the zonal circulation, which is generated primarily by small-scale gravity waves (GW). Salby and Callaghan (2000) in particular analyzed the QBO, covering more than 40 years, and discovered that it contains a large SC signature at 20 km. With our Numerical Spectral Model (NSM), we conducted a 3D study to describe the QBO under the influence of the SC, and some results have been published (Mayr et al., GRL, 2005,2006). For a SC period of 10 years, the relative amplitude of radiative forcing is taken to vary exponentially with height, i.e., 0.2% at the surface, 2% at 50 km, 20% at 100 km and above. Applying spectral analysis to filter out and identify the SC signature, the model generates a relatively large modulation of the QBO, which reproduces the observations qualitatively. Our numerical results demonstrate that the modulation of the QBO, with constant phase relative to the SC, persist at least for 60 years. The same model run generates in the seasonal variations a hemispherically symmetric Equatorial Annual Oscillation (EAO, with 12-month period), which is confined to low latitudes like the QBO and is also modulated by the SC. Although the amplitude of the EAO is relatively small, its SC modulation is large, and it is in phase with that of the QBO. The SC modulated EAO is evidently the pathway and pacemaker for the solar influence on the QBO. To shed light on the dynamical processes involved, we present model results that show how the seasonal cycle induces the SC modulations of the EAO and QBO. Our analysis further demonstrates that the SC modulations of the QBO and EAO are amplified by the GW interaction with the flow. The GW momentum source clearly shows a SC modulation that is in phase with the corresponding modulations of the QBO and EAO. By tapping the momentum from the upward propagating GWs, the QBO and EAO apparently serve as conduits to amplify and transfer to lower altitudes the larger SC variations in the UV absorbed in the mesosphere. Our model also produces in the temperature variations of the QBO and EAO measurable SC modulations at polar latitudes near the tropopause, and such signatures have been reported in the literature. Contrary to conventional interpretation, however, we suggest that the effects are generated at least in part by the meridional circulation, and planetary waves presumably, which redistribute the energy from the equatorial region where wave forcing is very efficient and thereby amplifies the SC influence.

Mayr, Hans G.↗
NASA NTRS1972

Relative motion of orbiting satellites

The relative motion problem is analyzed, as a linearized case, and as a numerically determined solution to provide a time history of the geometries representing the motion state. The displacement history and the hodographs for families of solutions are provided, analytically and graphically, to serve as an aid to understanding this problem area. Linearized solutions to relative motion problems of orbiting particles are presented for the impulsive and fixed thrust cases. Second order solutions are described to enhance the accuracy of prediction. A method was developed to obtain accurate, numerical solutions to the intercept and rendezvous problem; and, special situations are examined. A particular problem related to relative motions, where the motion traces develop a cusp, is examined in detail. This phenomenon is found to be dependent on a particular relationship between orbital eccentricity and the inclination between orbital planes. These conditions are determined, and, example situations are presented and discussed.

Eades, J. B., Jr.↗
NASA NTRS1993

The acoustic and instability waves of jets confined inside an acoustically lined rectangular duct

An analysis of linear wave modes associated with supersonic jets confined inside an acoustically lined rectangular duct is presented. Mathematical formulations are given for the vortex-sheet model and continuous mean flow model of the jet flow profiles. Detailed dispersion relations of these waves in a two-dimensional confined jet as well as an unconfined free jet are computed. Effects of the confining duct and the liners on the jet instability and acoustic waves are studied numerically. It is found that the effect of the liners is to attenuate waves that have supersonic phase velocities relative to the ambient flow. Numerical results also show that the growth rates of the instability waves could be reduced significantly by the use of liners. In addition, it is found that the upstream propagating neutral waves of an unconfined jet could become attenuated when the jet is confined.

Hu, Fang Q.↗
DOE OSTI2020

Analysis of muntjac deer genome and chromatin architecture reveals rapid karyotype evolution

Abstract Closely related muntjac deer show striking karyotype differences. Here we describe chromosome-scale genome assemblies for Chinese and Indian muntjacs, Muntiacus reevesi (2 n = 46) and Muntiacus muntjak vaginalis (2 n = 6/7), and analyze their evolution and architecture. The genomes show extensive collinearity with each other and with other deer and cattle. We identified numerous fusion events unique to and shared by muntjacs relative to the cervid ancestor, confirming many cytogenetic observations with genome sequence. One of these M. muntjak fusions reversed an earlier fission in the cervid lineage. Comparative Hi-C analysis showed that the chromosome fusions on the M. muntjak lineage altered long-range, three-dimensional chromosome organization relative to M. reevesi in interphase nuclei including A/B compartment structure. This reshaping of multi-megabase contacts occurred without notable change in local chromatin compaction, even near fusion sites. A few genes involved in chromosome maintenance show evidence for rapid evolution, possibly associated with the dramatic changes in karyotype.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1992

Vorticity generation by contoured wall injectors

A class of contoured wall fuel injectors was designed to enable shock-enhancement of hypervelocity mixing for supersonic combustion ramjet applications. Previous studies of these geometries left unresolved questions concerning the relative importance of various axial vorticity sources in mixing the injectant with the freestream. The present study is a numerical simulation of two generic fuel injectors which is aimed at elucidating the relative roles of axial vorticity sources including: baroclinic torque through shock-impingement, cross-stream shear, turning of boundary layer vorticity, shock curvature, and diffusive flux. Both the magnitude of the circulation, and the location of vorticity with respect to the mixing interface were considered. Baroclinic torque and cross-stream shear were found to be most important in convectively mixing the injectant with the freestream, with the former providing for deposition of vorticity directly on the fuel/air interface.

Waitz, Ian A.↗
NASA NTRS1993

Parametric instabilities of circularly polarized Alfven waves in high-beta plasmas

CGL relations including the effect of finite ion Larmor radius are used to consider a class of parametric instabilities of finite-amplitude, circularly polarized Alfven waves in high-beta plasmas. The disperison relation governing the instabilities is a sixth-order polynomial which is solved numerically. There are two types of instabilities: a modulational instability at k is less than k(0) and a relatively weak and narrow bandwidth instability at k is less than approximately k(0), where k and k(0) are the wavenumbers of the unstable density fluctuation and the 'pump' wave, respectively. It is shown that these instabilities can occur for left-handed pump waves and that the modulational instability is unstable over a very broad band in k with a maximum growth rate at finite k is not equal to 0.

Hamabata, Hiromitsu↗
DOE OSTI2019

Self-focusing of cosh-Gaussian laser beam and its effect on the excitation of ion-acoustic wave and stimulated Brillouin backscattering in collisionless plasma

An analytical and numerical study has been carried out for self-focusing of an intense cosh-Gaussian laser beam in collisionless plasma and its impact on the excitation of ion-acoustic wave and stimulated Brillouin backscattering process. The analytical model has been developed under Wentzel–Kramers–Brillouin and paraxial ray approximations. The nonlinearities of ponderomotive force on electron and the relativistic oscillation of the electron mass have been used in this study. The nonlinear differential equations have been set up for the beam width parameters of the main beam, ion-acoustic wave, backscattered wave and back reflectivity of stimulated Brillouin scattering (SBS). These equations have been solved numerically for different values of decentred parameter (b), relative plasma density (ω{sub p0}/ω{sub 0}) and incident laser intensity (a). The results have been compared with only relativistic nonlinearity and Gaussian profile of laser beam. The focusing of laser beam, ion-acoustic wave and scattered wave are found to be strong under relativistic-ponderomotive regime compared to only relativistic regime. Further, it is observed that focusing/intensity of main laser beam, ion acoustic wave and SBS back reflectivity increases with increasing the values of b and ω{sub p0}/ω{sub 0}. Itis also found that back reflectivity of SBS process gets suppressed with the increase in the value of a. This study may be useful in laser induced fusion scheme where back scattering of SBS plays very important role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Impacts of Multidimensional Progenitor Perturbations on Core-collapse Supernova Explosions

Numerical studies of core-collapse supernovae have demonstrated the importance of nonradial motions in precollapse progenitors on the explosion outcome. We use the Chimera neutrino radiation hydrodynamics code running seven two-dimensional simulations of 15 M⊙ progenitors with different progenitor structures introduced by different one- and two-dimensional precollapse stellar evolution environments to examine the impacts of stellar structure and nonspherical motion in the precollapse progenitor on the development of explosions. We compare the explosion evolution of these models in terms of shock dynamics, diagnostic energy, neutrino heating, accretion, explosion geometry, nuclear abundances, and turbulent convection. We also analyze how stochastic variation impacts our simulations. Contrary to results reported in prior studies examining the impacts of multidimensional progenitors, we observe similar shock revival times and explosion development in our simulations despite differences in initial compositions and structures. We find no discernible impact from the accretion of nonradial perturbations from a multi-D progenitor onto the stalled shock in the revival and strength of explosion, as fully developed neutrino-driven convection behind the stalled shock is similar for all our models. For models with physically sourced noise in the iron core, a strong oscillation of the shock occurs after bounce and deflects infall laterally, and accelerates the saturation of the lateral turbulent kinetic energy. An examination of model stochasticity shows that any prior expected impacts on explosive outcome due to convection-related perturbations lie below the detectable threshold of numerical variation.

Chen, Chien-Hui [North Carolina State University]↗