Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical Methods”

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 1,765 records · Page 98

Design Optimization of a Criticality Experiment for the Molten Chloride Reactor Experiment Facility

Neutronics simulations of Molten Chloride Fast Reactors have quantifiable biases that arise from nuclear data, modeling choices, or numerical methods. The multiphysics nature of molten salt reactors makes it challenging to disentangle neutronics modeling biases from biases originating from other physical phenomena. In comparison to a mock-up reactor, criticality experiments can specifically assess the neutronics modeling bias while limiting multiphysics effects. The criticality experiment must be neutronically representative of the full-scale reactor to be valuable. Here, in this paper, we describe the design of a criticality experiment to validate only the neutronics of TerraPower’s Molten Chloride Reactor Experiment (MCRE) and its criticality safety upset scenarios. The proposed experiment uses different chlorine-containing materials to maximize its similarity to the MCRE. The design process uses a constrained Bayesian optimization algorithm to investigate different objective functions that use covariance information for 35 Cl nuclear data. The experiments could reduce the nuclear data–induced uncertainty in k eff of the MCRE from 2161 to 886 pcm. They would also increase the upper subcritical limit of the MCRE criticality safety upset scenario from 0.94101 to 0.94476 when using the WHISPER analysis framework.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

ON THE COAGULATION AND SIZE DISTRIBUTION OF PRESSURE CONFINED CORES

Observations of the Pipe Nebula have led to the discovery of dense starless cores. The mass of most cores is too small for their self-gravity to hold them together. Instead, they are thought to be pressure confined. The observed dense cores' mass function (CMF) matches well with the initial mass function of stars in young clusters. Similar CMFs are observed in other star forming regions such as the Aquila Nebula, albeit with some dispersion. The shape of these CMF provides important clues to the competing physical processes which lead to star formation and its feedback on the interstellar media. In this paper, we investigate the dynamical origin of the mass function of starless cores which are confined by a warm, less dense medium. In order to follow the evolution of the CMF, we construct a numerical method to consider the coagulation between the cold cores and their ablation due to Kelvin-Helmholtz instability induced by their relative motion through the warm medium. We are able to reproduce the observed CMF among the starless cores in the Pipe Nebula. Our results indicate that in environment similar to the Pipe Nebula: (1) before the onset of their gravitational collapse, the mass distribution of the progenitor cores is similar to that of the young stars, (2) the observed CMF is a robust consequence of dynamical equilibrium between the coagulation and ablation of cores, and (3) a break in the slope of the CMF is due to the enhancement of collisional cross section and suppression of ablation for cores with masses larger than the cores' Bonnor-Ebert mass.

79 ASTRONOMY AND ASTROPHYSICS↗

Differential rotation in solar-like stars from global simulations

To explore the physics of large-scale flows in solar-like stars, we perform three-dimensional anelastic simulations of rotating convection for global models with stratification resembling the solar interior. The numerical method is based on an implicit large-eddy simulation approach designed to capture effects from non-resolved small scales. We obtain two regimes of differential rotation, with equatorial zonal flows accelerated either in the direction of rotation (solar-like) or in the opposite direction (anti-solar). While the models with the solar-like differential rotation tend to produce multiple cells of meridional circulation, the models with anti-solar differential rotation result in only one or two meridional cells. Our simulations indicate that the rotation and large-scale flow patterns critically depend on the ratio between buoyancy and Coriolis forces. By including a sub-adiabatic layer at the bottom of the domain, corresponding to the stratification of a radiative zone, we reproduce a layer of strong radial shear similar to the solar tachocline. Similarly, enhanced super-adiabaticity at the top results in a near-surface shear layer located mainly at lower latitudes. The models reveal a latitudinal entropy gradient localized at the base of the convection zone and in the stable region, which, however, does not propagate across the convection zone. In consequence, baroclinicity effects remain small, and the rotation isocontours align in cylinders along the rotation axis. Our results confirm the alignment of large convective cells along the rotation axis in the deep convection zone and suggest that such 'banana-cell' pattern can be hidden beneath the supergranulation layer.

79 ASTRONOMY AND ASTROPHYSICS↗

Non-coherent continuum scattering as a line polarization mechanism

Line scattering polarization can be strongly affected by Rayleigh scattering at neutral hydrogen and Thomson scattering at free electrons. Often a depolarization of the continuum results, but the Doppler redistribution produced by the continuum scatterers, which are light (hence, fast), induces more complex interactions between the polarization in spectral lines and in the continuum. Here we formulate and solve the radiative transfer problem of scattering line polarization with non-coherent continuum scattering consistently. The problem is formulated within the spherical tensor representation of atomic and light polarization. The numerical method of solution is a generalization of the Accelerated Lambda Iteration that is applied to both the atomic system and the radiation field. We show that the redistribution of the spectral line radiation due to the non-coherence of the continuum scattering may modify the shape of the emergent fractional linear polarization patterns significantly, even yielding polarization signals above the continuum level in intrinsically unpolarizable lines.

79 ASTRONOMY AND ASTROPHYSICS↗

Characterizing the convective velocity fields in massive stars

We apply the mathematical formalism of vector spherical harmonics decomposition to convective stellar velocity fields from multidimensional hydrodynamics simulations and show that the resulting power spectra furnish a robust and stable statistical description of stellar convective turbulence. Analysis of the power spectra helps identify key physical parameters of the convective process such as the dominant scale of the turbulent motions that influence the structure of massive evolved pre-supernova stars. We introduce the numerical method that can be used to calculate vector spherical harmonics power spectra from two-dimensional (2D) and three-dimensional (3D) convective shell simulation data. Using this method we study the properties of oxygen shell burning and convection for a 15 M {sub ☉} star simulated by the hydrodynamics code FLASH in 2D and 3D. We discuss the importance of realistic initial conditions to achieving successful core-collapse supernova explosions in multidimensional simulations. We show that the calculated power spectra can be used to generate realizations of the velocity fields of presupernova convective shells. We find that the slope of the solenoidal mode power spectrum remains mostly constant throughout the evolution of convection in the oxygen shell in both 2D and 3D simulations. We also find that the characteristic radial scales of the convective elements are smaller in 3D than in 2D, while the angular scales are larger in 3D.

79 ASTRONOMY AND ASTROPHYSICS↗

Modeling the Transfer Function for the Dark Energy Survey

We present a forward-modeling simulation framework designed to model the data products from the Dark Energy Survey (DES). This forward-model process can be thought of as a transfer function—a mapping from cosmological/astronomical signals to the final data products used by the scientists. Using output from the cosmological simulations (the Blind Cosmology Challenge), we generate simulated images (the Ultra Fast Image Simulator) and catalogs representative of the DES data. In this work we demonstrate the framework by simulating the 244 deg 2 coadd images and catalogs in five bands for the DES Science Verification data. The simulation output is compared with the corresponding data to show that major characteristics of the images and catalogs can be captured. We also point out several directions of future improvements. Two practical examples—star-galaxy classification and proximity effects on object detection—are then used to illustrate how one can use the simulations to address systematics issues in data analysis. With clear understanding of the simplifications in our model, we show that one can use the simulations side-by-side with data products to interpret the measurements. This forward modeling approach is generally applicable for other upcoming and future surveys. It provides a powerful tool for systematics studies that is sufficiently realistic and highly controllable.

79 ASTRONOMY AND ASTROPHYSICS↗

PARTICLE ACCELERATION IN SUPERLUMINAL STRONG WAVES

We calculate the electron acceleration in random superluminal strong waves (SLSWs) and radiation from them using numerical methods in the context of the termination shocks of pulsar wind nebulae. We pursue the orbit of electrons by solving the equation of motion in the analytically expressed electromagnetic turbulences. These consist of a primary SLS and isotropically distributed secondary electromagnetic waves. Under the dominance of the secondary waves, all electrons gain nearly equal energy. On the other hand, when the primary wave is dominant, selective acceleration occurs. The phase of the primary wave for electrons moving nearly along the wavevector changes very slowly compared with the oscillation of the wave, which is “phase-locked,” and such electrons are continuously accelerated. This acceleration by SLSWs may play a crucial role in pre-shock acceleration. In general, the radiation from the phase-locked population is different from the synchro-Compton radiation. However, when the amplitude of the secondary waves is not extremely weaker than that of the primary wave, the typical frequency can be estimated from synchro-Compton theory using the secondary waves. The primary wave does not contribute to the radiation because the SLSW accelerates electrons almost linearly. This radiation can be observed as a radio knot at the upstream of the termination shocks of the pulsar wind nebulae without counterparts in higher frequency ranges.

79 ASTRONOMY AND ASTROPHYSICS↗

CRITICAL CURVES AND CAUSTICS OF TRIPLE-LENS MODELS

Among the 25 planetary systems detected up to now by gravitational microlensing, there are two cases of a star with two planets, and two cases of a binary star with a planet. Other, yet undetected types of triple lenses include triple stars or stars with a planet with a moon. The analysis and interpretation of such events is hindered by the lack of understanding of essential characteristics of triple lenses, such as their critical curves and caustics. We present here analytical and numerical methods for mapping the critical-curve topology and caustic cusp number in the parameter space of n-point-mass lenses. We apply the methods to the analysis of four symmetric triple-lens models, and obtain altogether 9 different critical-curve topologies and 32 caustic structures. While these results include various generic types, they represent just a subset of all possible triple-lens critical curves and caustics. Using the analyzed models, we demonstrate interesting features of triple lenses that do not occur in two-point-mass lenses. We show an example of a lens that cannot be described by the Chang–Refsdal model in the wide limit. In the close limit we demonstrate unusual structures of primary and secondary caustic loops, and explain the conditions for their occurrence. In the planetary limit we find that the presence of a planet may lead to a whole sequence of additional caustic metamorphoses. We show that a pair of planets may change the structure of the primary caustic even when placed far from their resonant position at the Einstein radius.

79 ASTRONOMY AND ASTROPHYSICS↗

COMPARISONS OF TWO- AND THREE-DIMENSIONAL CONVECTION IN TYPE I X-RAY BURSTS

We perform the first detailed three-dimensional simulation of low Mach number convection preceding runaway thermonuclear ignition in a mixed H/He X-ray burst. Our simulations include a moderate-sized, approximate network that captures hydrogen and helium burning up through rp-process breakout. We look at the difference between two- and three-dimensional convective fields, including the details of the turbulent convection.

79 ASTRONOMY AND ASTROPHYSICS↗

A HYDROCHEMICAL HYBRID CODE FOR ASTROPHYSICAL PROBLEMS. I. CODE VERIFICATION AND BENCHMARKS FOR A PHOTON-DOMINATED REGION (PDR)

A two-dimensional hydrochemical hybrid code, KM2, is constructed to deal with astrophysical problems that would require coupled hydrodynamical and chemical evolution. The code assumes axisymmetry in a cylindrical coordinate system and consists of two modules: a hydrodynamics module and a chemistry module. The hydrodynamics module solves hydrodynamics using a Godunov-type finite volume scheme and treats included chemical species as passively advected scalars. The chemistry module implicitly solves nonequilibrium chemistry and change of energy due to thermal processes with transfer of external ultraviolet radiation. Self-shielding effects on photodissociation of CO and H{sub 2} are included. In this introductory paper, the adopted numerical method is presented, along with code verifications using the hydrodynamics module and a benchmark on the chemistry module with reactions specific to a photon-dominated region (PDR). Finally, as an example of the expected capability, the hydrochemical evolution of a PDR is presented based on the PDR benchmark.

79 ASTRONOMY AND ASTROPHYSICS↗

CONNECTING ANGULAR MOMENTUM AND GALACTIC DYNAMICS: THE COMPLEX INTERPLAY BETWEEN SPIN, MASS, AND MORPHOLOGY

The evolution and distribution of the angular momentum of dark matter (DM) halos have been discussed in several studies over the past decades. In particular, the idea arose that angular momentum conservation should allow us to infer the total angular momentum of the entire DM halo from measuring the angular momentum of the baryonic component, which is populating the center of the halo, especially for disk galaxies. To test this idea and to understand the connection between the angular momentum of the DM halo and its galaxy, we use a state-of-the-art, hydrodynamical cosmological simulation taken from the set of Magneticum Pathfinder simulations. Thanks to the inclusion of the relevant physical processes, the improved underlying numerical methods, and high spatial resolution, we successfully produce populations of spheroidal and disk galaxies self-consistently. Thus, we are able to study the dependence of galactic properties on their morphology. We find that (1) the specific angular momentum of stars in disk and spheroidal galaxies as a function of their stellar mass compares well with observational results; (2) the specific angular momentum of the stars in disk galaxies is slightly smaller compared to the specific angular momentum of the cold gas, in good agreement with observations; (3) simulations including the baryonic component show a dichotomy in the specific stellar angular momentum distribution when splitting the galaxies according to their morphological type (this dichotomy can also be seen in the spin parameter, where disk galaxies populate halos with slightly larger spin compared to spheroidal galaxies); (4) disk galaxies preferentially populate halos in which the angular momentum vector of the DM component in the central part shows a better alignment to the angular momentum vector of the entire halo; and (5) the specific angular momentum of the cold gas in disk galaxies is approximately 40% smaller than the specific angular momentum of the total DM halo and shows a significant scatter.

79 ASTRONOMY AND ASTROPHYSICS↗

THE HYDRODYNAMICAL MODELS OF THE COMETARY COMPACT H ii REGION

We have developed a full numerical method to study the gas dynamics of cometary ultracompact H ii regions, and associated photodissociation regions (PDRs). The bow-shock and champagne-flow models with a 40.9/21.9 M{sub ⊙} star are simulated. In the bow-shock models, the massive star is assumed to move through dense (n = 8000 cm{sup −3}) molecular material with a stellar velocity of 15 km s{sup −1}. In the champagne-flow models, an exponential distribution of density with a scale height of 0.2 pc is assumed. The profiles of the [Ne ii] 12.81 μm and H{sub 2} S(2) lines from the ionized regions and PDRs are compared for two sets of models. In champagne-flow models, emission lines from the ionized gas clearly show the effect of acceleration along the direction toward the tail due to the density gradient. The kinematics of the molecular gas inside the dense shell are mainly due to the expansion of the H ii region. However, in bow-shock models the ionized gas mainly moves in the same direction as the stellar motion. The kinematics of the molecular gas inside the dense shell simply reflects the motion of the dense shell with respect to the star. These differences can be used to distinguish two sets of models.

79 ASTRONOMY AND ASTROPHYSICS↗

THE ORBITAL PERIOD EVOLUTION OF THE SUPERSOFT X-RAY SOURCE CAL 87

CAL 87 is one of the best known supersoft X-ray sources (SSSs). However, the measured masses, orbital period, and orbital period evolution of CAL 87 cannot be addressed by the standard thermal-timescale mass-transfer model for SSSs. In this work we explore the orbital evolution of CAL 87 with both analytic and numerical methods. We demonstrate that the characteristics mentioned above can be naturally accounted for by the excited-wind-driven mass-transfer model.

79 ASTRONOMY AND ASTROPHYSICS↗

GPUPEGAS: A NEW GPU-ACCELERATED HYDRODYNAMIC CODE FOR NUMERICAL SIMULATIONS OF INTERACTING GALAXIES

In this paper, a new scalable hydrodynamic code, GPUPEGAS (GPU-accelerated Performance Gas Astrophysical Simulation), for the simulation of interacting galaxies is proposed. The details of a parallel numerical method co-design are described. A speed-up of 55 times was obtained within a single GPU accelerator. The use of 60 GPU accelerators resulted in 96% parallel efficiency. A collisionless hydrodynamic approach has been used for modeling of stars and dark matter. The scalability of the GPUPEGAS code is shown.

79 ASTRONOMY AND ASTROPHYSICS↗

THREE-DIMENSIONAL BOLTZMANN HYDRO CODE FOR CORE COLLAPSE IN MASSIVE STARS. I. SPECIAL RELATIVISTIC TREATMENTS

We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled with hydrodynamics equations. This method is meant to be applied to simulations of core-collapse supernovae. We handle special relativity in a non-conventional way, taking account of all orders of v/c. Consistent treatment of the advection and collision terms in the Boltzmann equations has been a challenge, which we overcome by employing two different energy grids: Lagrangian remapped and laboratory fixed grids. We conduct a series of basic tests and perform a one-dimensional simulation of core-collapse, bounce, and shock-stall for a 15 M {sub ☉} progenitor model with a minimum but essential set of microphysics. We demonstrate in the latter simulation that our new code is capable of handling all phases in core-collapse supernova. For comparison, a non-relativistic simulation is also conducted with the same code, and we show that they produce qualitatively wrong results in neutrino transfer. Finally, we discuss a possible incorporation of general relativistic effects into our method.

79 ASTRONOMY AND ASTROPHYSICS↗

AN OPEN-SOURCE NEUTRINO RADIATION HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE

We present an open-source update to the spherically symmetric, general-relativistic hydrodynamics, core-collapse supernova (CCSN) code GR1D. The source code is available at http://www.GR1Dcode.org. We extend its capabilities to include a general-relativistic treatment of neutrino transport based on the moment formalisms of Shibata et al. and Cardall et al. We pay special attention to implementing and testing numerical methods and approximations that lessen the computational demand of the transport scheme by removing the need to invert large matrices. This is especially important for the implementation and development of moment-like transport methods in two and three dimensions. A critical component of neutrino transport calculations is the neutrino–matter interaction coefficients that describe the production, absorption, scattering, and annihilation of neutrinos. In this article we also describe our open-source neutrino interaction library NuLib (available at http://www.nulib.org). We believe that an open-source approach to describing these interactions is one of the major steps needed to progress toward robust models of CCSNe and robust predictions of the neutrino signal. We show, via comparisons to full Boltzmann neutrino-transport simulations of CCSNe, that our neutrino transport code performs remarkably well. Furthermore, we show that the methods and approximations we employ to increase efficiency do not decrease the fidelity of our results. We also test the ability of our general-relativistic transport code to model failed CCSNe by evolving a 40-solar-mass progenitor to the onset of collapse to a black hole.

79 ASTRONOMY AND ASTROPHYSICS↗

An implementation of the phase-field model based on coupled thermomechanical finite element solvers for large-strain twinning, explicit dynamic fracture and the classical Stefan problem

The implementation of a phase-field model in finite elements usually requires significant expertise and involves the development of a user element with additional degrees of freedom. An alternative implementation of the phase-field model within a thermo-mechanical finite element simulation package was presented in (Cho et al 2012 Int. J. Solids Struct. 49 1973–1992), where the phase-field variable is treated as the temperature degree of freedom. However, this approach has only been used for small strain phase-field modelling of martensitic transformations and quasistatic phase-field modelling of fracture. Here, we present a phase-field finite element implementation via the temperature degree of freedom for several additional cases from the literature: (i) the large-strain phase-field description of deformation twinning presented in (Clayton and Knap 2011 Physica D 240 841–858), (ii) phase-field description of brittle fracture with inertial effects based on the theory from (Molnár and Gravouil 2017, Finite Elem. Anal. Des. 130 27–38) and (Miehe et al 2010 Int. J. Numer. Methods Eng. 83 1273–1311) and (iii) the classical Stefan problem of solidification presented in (Mackenzie and Robertson 2002 J. Comput. Phys. 181 526–544). The last problem involves the temperature and phase-field variables as unknowns.

36 MATERIALS SCIENCE↗

Linearised Fokker–Planck collision model for gyrokinetic simulations

We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids 19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys. 391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗