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DOE OSTI2022

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - II: Numerical results

This paper is the second part of a two-part paper that documents the numerical results for the partial derivatives model presented in part I. In this paper, we derive the error bounds for the analytical point-wise error expression and verify our bounds with numerical experiments. The point-wise error expressions make available, and bound, the sources that contribute to the total error of the interpolated cross section in terms of the Lagrange interpolation errors and the model form error. MPACT is used to generate two-group homogenized cross sections for Westinghouse's AP1000 Region 4 lattice to evaluate the accuracy of the bounds. Error bounds calculated over a grid are compared to numerical data for uni-variate and multi-variate interpolation. The point-wise error bounds of a typical case matrix - two branches in each state variable - are displayed for bi-variate interpolation in the state variables: moderator density, fuel temperature, and boron concentration. The error bounds are shown to be highly accurate compared to numerical results, and in accordance with the underlying physics. We then discuss and show how the sources of error contribute to the total error, and consider the improvement of each error source. Finally, we mention future work such as propagating our cross section error bounds through a reactivity calculation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

A New High-Order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed Elements

In the present study, a new spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third-order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. Studies have been performed for 2D wave equation and Euler equa- tions. Our present results demonstrated that the SDRT method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed- element meshes.

17 WIND ENERGY↗
DOE OSTI2016

TERRESTRIAL PLANET FORMATION FROM AN ANNULUS

It has been shown that some aspects of the terrestrial planets can be explained, particularly the Earth/Mars mass ratio, when they form from a truncated disk with an outer edge near 1.0 au. This has been previously modeled starting from an intermediate stage of growth utilizing pre-formed planetary embryos. We present simulations that were designed to test this idea by following the growth process from km-sized objects located between 0.7 and 1.0 au up to terrestrial planets. The simulations explore initial conditions where the solids in the disk are planetesimals with radii initially between 3 and 300 km, alternately including effects from a dissipating gaseous solar nebula and collisional fragmentation. We use a new Lagrangian code known as LIPAD, which is a particle-based code that models the fragmentation, accretion, and dynamical evolution of a large number of planetesimals, and can model the entire growth process from km-sizes up to planets. A suite of large (∼ Mars mass) planetary embryos is complete in only ∼1 Myr, containing most of the system mass. A quiescent period then persists for 10–20 Myr characterized by slow diffusion of the orbits and continued accretion of the remaining planetesimals. This is interrupted by an instability that leads to embryos crossing orbits and embryo–embryo impacts that eventually produce the final set of planets. While this evolution is different than that found in other works exploring an annulus, the final planetary systems are similar, with roughly the correct number of planets and good Mars-analogs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SANTA BARBARA CLUSTER COMPARISON TEST WITH DISPH

The Santa Barbara cluster comparison project revealed that there is a systematic difference between entropy profiles of clusters of galaxies obtained by Eulerian mesh and Lagrangian smoothed particle hydrodynamics (SPH) codes: mesh codes gave a core with a constant entropy, whereas SPH codes did not. One possible reason for this difference is that mesh codes are not Galilean invariant. Another possible reason is the problem of the SPH method, which might give too much “protection” to cold clumps because of the unphysical surface tension induced at contact discontinuities. In this paper, we apply the density-independent formulation of SPH (DISPH), which can handle contact discontinuities accurately, to simulations of a cluster of galaxies and compare the results with those with the standard SPH. We obtained the entropy core when we adopt DISPH. The size of the core is, however, significantly smaller than those obtained with mesh simulations and is comparable to those obtained with quasi-Lagrangian schemes such as “moving mesh” and “mesh free” schemes. We conclude that both the standard SPH without artificial conductivity and Eulerian mesh codes have serious problems even with such an idealized simulation, while DISPH, SPH with artificial conductivity, and quasi-Lagrangian schemes have sufficient capability to deal with it.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

EVOLUTION OF THE MAGNETIC FIELD LINE DIFFUSION COEFFICIENT AND NON-GAUSSIAN STATISTICS

The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with these underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

IMPROVED PERFORMANCES IN SUBSONIC FLOWS OF AN SPH SCHEME WITH GRADIENTS ESTIMATED USING AN INTEGRAL APPROACH

In this paper, we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically investigate the code behavior with subsonic flows, where it is well known that zeroth-order inconsistencies present in standard SPH make it particularly problematic to correctly model the fluid dynamics. In particular, we consider the Gresho–Chan vortex problem, the growth of Kelvin–Helmholtz instabilities, the statistics of driven subsonic turbulence and the cold Keplerian disk problem. We compare simulation results for the different tests with those obtained, for the same initial conditions, using standard SPH. We also compare the results with the corresponding ones obtained previously with other numerical methods, such as codes based on a moving-mesh scheme or Godunov-type Lagrangian meshless methods. We quantify code performances by introducing error norms and spectral properties of the particle distribution, in a way similar to what was done in other works. We find that the new SPH formulation exhibits strongly reduced gradient errors and outperforms standard SPH in all of the tests considered. In fact, in terms of accuracy, we find good agreement between the simulation results of the new scheme and those produced using other recently proposed numerical schemes. These findings suggest that the proposed method can be successfully applied for many astrophysical problems in which the presence of subsonic flows previously limited the use of SPH, with the new scheme now being competitive in these regimes with other numerical methods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SIMULATIONS OF VISCOUS ACCRETION FLOW AROUND BLACK HOLES IN A TWO-DIMENSIONAL CYLINDRICAL GEOMETRY

We simulate shock-free and shocked viscous accretion flows onto a black hole in a two-dimensional cylindrical geometry, where initial conditions were chosen from analytical solutions. The simulation code used the Lagrangian total variation diminishing plus remap routine, which enabled us to attain high accuracy in capturing shocks and to handle the angular momentum distribution correctly. The inviscid shock-free accretion disk solution produced a thick disk structure, while the viscous shock-free solution attained a Bondi-like structure, but in either case, no jet activity nor any quasi-periodic oscillation (QPO)-like activity developed. The steady-state shocked solution in the inviscid as well as in the viscous regime matched theoretical predictions well. However, increasing viscosity renders the accretion shock unstable. Large-amplitude shock oscillation is accompanied by intermittent, transient inner multiple shocks. This oscillation of the inner part of the disk is interpreted as the source of QPO in hard X-rays observed in micro-quasars. Strong shock oscillation induces strong episodic jet emission. The jets also show the existence of shocks, which are produced as one shell hits the preceding one. The periodicities of the jets and shock oscillation are similar; the jets for the higher viscosity parameter appear to be stronger and faster.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

THE FORMATION OF A MILKY WAY-SIZED DISK GALAXY. I. A COMPARISON OF NUMERICAL METHODS

The long-standing challenge of creating a Milky Way- (MW-) like disk galaxy from cosmological simulations has motivated significant developments in both numerical methods and physical models. We investigate these two fundamental aspects in a new comparison project using a set of cosmological hydrodynamic simulations of an MW-sized galaxy. In this study, we focus on the comparison of two particle-based hydrodynamics methods: an improved smoothed particle hydrodynamics (SPH) code Gadget, and a Lagrangian Meshless Finite-Mass (MFM) code Gizmo. All the simulations in this paper use the same initial conditions and physical models, which include star formation, “energy-driven” outflows, metal-dependent cooling, stellar evolution, and metal enrichment. We find that both numerical schemes produce a late-type galaxy with extended gaseous and stellar disks. However, notable differences are present in a wide range of galaxy properties and their evolution, including star-formation history, gas content, disk structure, and kinematics. Compared to Gizmo, the Gadget simulation produced a larger fraction of cold, dense gas at high redshift which fuels rapid star formation and results in a higher stellar mass by 20% and a lower gas fraction by 10% at z = 0, and the resulting gas disk is smoother and more coherent in rotation due to damping of turbulent motion by the numerical viscosity in SPH, in contrast to the Gizmo simulation, which shows a more prominent spiral structure. Given its better convergence properties and lower computational cost, we argue that the MFM method is a promising alternative to SPH in cosmological hydrodynamic simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

INTEGRATION OF PARTICLE-GAS SYSTEMS WITH STIFF MUTUAL DRAG INTERACTION

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff—particularly because of small particles and/or strong local solid concentration—that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct, we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A TRACER METHOD FOR COMPUTING TYPE IA SUPERNOVA YIELDS: BURNING MODEL CALIBRATION, RECONSTRUCTION OF THICKENED FLAMES, AND VERIFICATION FOR PLANAR DETONATIONS

We refine our previously introduced parameterized model for explosive carbon–oxygen fusion during thermonuclear Type Ia supernovae (SNe Ia) by adding corrections to post-processing of recorded Lagrangian fluid-element histories to obtain more accurate isotopic yields. Deflagration and detonation products are verified for propagation in a medium of uniform density. A new method is introduced for reconstructing the temperature–density history within the artificially thick model deflagration front. We obtain better than 5% consistency between the electron capture computed by the burning model and yields from post-processing. For detonations, we compare to a benchmark calculation of the structure of driven steady-state planar detonations performed with a large nuclear reaction network and error-controlled integration. We verify that, for steady-state planar detonations down to a density of 5 × 10{sup 6} g cm{sup −3}, our post-processing matches the major abundances in the benchmark solution typically to better than 10% for times greater than 0.01 s after the passage of the shock front. As a test case to demonstrate the method, presented here with post-processing for the first time, we perform a two-dimensional simulation of a SN Ia in the scenario of a Chandrasekhar-mass deflagration–detonation transition (DDT). We find that reconstruction of deflagration tracks leads to slightly more complete silicon burning than without reconstruction. The resulting abundance structure of the ejecta is consistent with inferences from spectroscopic studies of observed SNe Ia. We confirm the absence of a central region of stable Fe-group material for the multi-dimensional DDT scenario. Detailed isotopic yields are tabulated and change only modestly when using deflagration reconstruction.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

TEA: A CODE CALCULATING THERMOCHEMICAL EQUILIBRIUM ABUNDANCES

We present an open-source Thermochemical Equilibrium Abundances (TEA) code that calculates the abundances of gaseous molecular species. The code is based on the methodology of White et al. and Eriksson. It applies Gibbs free-energy minimization using an iterative, Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature–pressure pairs. We tested the code against the method of Burrows and Sharp, the free thermochemical equilibrium code Chemical Equilibrium with Applications (CEA), and the example given by Burrows and Sharp. Using their thermodynamic data, TEA reproduces their final abundances, but with higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a code document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

On the Detection of Habitable Trojan Planets in the Kepler Circumbinary Systems

We present the results of a study of the prospect of detecting habitable Trojan planets in the Kepler Habitable Zone circumbinary planetary systems (Kepler-16, -47, -453, -1647, and -1661). We integrated the orbits of 10,000 separate N-body systems (N = 4, 6), each with a one Earth-mass body in a randomly selected orbit near the L {sub 4} and L {sub 5} Lagrangian points of the host HZ circumbinary planet. We find that stable Trojan planets are restricted to a narrow range of semimajor axes in all five systems and limited to small eccentricities in Kepler-16, -47, and -1661. To assess the prospect of the detection of these habitable Trojan planets, we calculated the amplitudes of the variations they cause in the transit timing of their host bodies. Results show that the mean amplitudes of the transit timing variations (TTVs) correlate with the mass of the transiting planet and range from 70 minutes for Kepler-16b to 390 minutes for Kepler-47c. Our analysis indicates that the TTVs of the circumbinary planets caused by these Trojan bodies fall within the detectable range of timing precision obtained from the Kepler telescope’s long-cadence data. The latter points to Kepler data as a viable source to search for habitable Trojan planets.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

Neutrino astrophysics in slowly rotating spacetimes permeated by nonlinear electrodynamics fields

Many theoretical and astrophysical arguments involve consideration of the effects of super strong electromagnetic fields and the rotation during the late stages of core-collapse supernovae. In what follows, we solve Einstein field equations that are minimally coupled to an arbitrary (current-free) Born–Infeld nonlinear Lagrangian L(F,G) of electrodynamics (NLED) in the slow rotation regime a ≪ r{sub +} (outer horizon size), up to first order in a/r. We cross-check the physical properties of such NLED spacetime w.r.t. against the Maxwell one. A study case on both neutrino flavor (ν{sub e}→ν{sub μ},ν{sub τ}) oscillations and flavor+helicity (spin) flip (ν{sub e}→ ν-bar {sub μ,τ}) gyroscopic precession proves that in the spacetime of a slowly rotating nonlinear charged black hole (RNCBH), the neutrino dynamics translates into a positive enhancement of the r-process (reduction of the electron fraction Y{sub e} < 0.5). Consequently, it guarantees successful hyperluminous core-collapse supernova explosions due to the enlargement of the number and amount of decaying nuclide species. This posits that, as far as the whole luminosity is concerned, hypernovae will be a proof of the formation of astrophysical RNCBH.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

ELUCID—Exploring the Local Universe with the reConstructed Initial Density Field. II. Reconstruction Diagnostics, Applied to Numerical Halo Catalogs

The ELUCID project aims to build a series of realistic cosmological simulations that reproduce the spatial and mass distributions of the galaxies as observed in the Sloan Digital Sky Survey. This requires powerful reconstruction techniques to create constrained initial conditions (ICs). We test the reconstruction method by applying it to several N -body simulations. We use two medium-resolution simulations, which each produced three additional constrained N -body simulations. We compare the resulting friend-of-friend catalogs by using the particle indexes as tracers, and quantify the quality of the reconstruction by varying the main smoothing parameter. The cross-identification method we use proves to be efficient, and the results suggest that the most massive reconstructed halos are effectively traced from the same Lagrangian regions in the ICs. A preliminary time-dependence analysis indicates that high-mass-end halos converge only at a redshift close to the reconstruction redshift. This suggests that, for earlier snapshots, only collections of progenitors may be effectively cross-identified.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The Impact of Galactic Winds on the Angular Momentum of Disk Galaxies in the Illustris Simulation

Observed galactic disks have specific angular momenta similar to expectations for typical dark matter halos in ΛCDM. Cosmological hydrodynamical simulations have recently reproduced this similarity in large galaxy samples by including strong galactic winds, but the exact mechanism that achieves this is not yet clear. Here we present an analysis of key aspects contributing to this relation: angular momentum selection and evolution of Lagrangian mass elements as they accrete onto dark matter halos, condense into Milky-Way-scale galaxies, and join the z = 0 stellar phase. We contrast this evolution in the Illustris simulation with that in a simulation without galactic winds, where the z = 0 angular momentum is ≈0.6 dex lower. We find that winds induce differences between these simulations in several ways: increasing angular momentum, preventing angular momentum loss, and causing z = 0 stars to sample the accretion-time angular momentum distribution of baryons in a biased way. In both simulations, gas loses on average ≈0.4 dex between accreting onto halos and first accreting onto central galaxies. In Illustris, this is followed by ≈0.2 dex gains in the “galactic wind fountain” and no further net evolution past the final accretion onto the galaxy. Without feedback, further losses of ≈0.2 dex occur in the gas phase inside the galaxies. An additional ≈0.15 dex difference arises from feedback preferentially selecting higher angular momentum gas at accretion by expelling gas that is poorly aligned. These and additional effects of similar magnitude are discussed, suggesting a complex origin of the similarity between the specific angular momenta of galactic disks and typical halos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Implications for Post-processing Nucleosynthesis of Core-collapse Supernova Models with Lagrangian Particles

We investigate core-collapse supernova (CCSN) nucleosynthesis with self-consistent, axisymmetric (2D) simulations performed using the neutrino hydrodynamics code Chimera. Computational costs have traditionally constrained the evolution of the nuclear composition within multidimensional CCSN models to, at best, a 14-species α-network capable of tracking only (α,γ) reactions from {sup 4}He to {sup 60}Zn. Such a simplified network limits the ability to accurately evolve detailed composition and neutronization or calculate the nuclear energy generation rate. Lagrangian tracer particles are commonly used to extend the nuclear network evolution by incorporating more realistic networks into post-processing nucleosynthesis calculations. However, limitations such as poor spatial resolution of the tracer particles; inconsistent thermodynamic evolution, including misestimation of expansion timescales; and uncertain determination of the multidimensional mass cut at the end of the simulation impose uncertainties inherent to this approach. We present a detailed analysis of the impact of such uncertainties for four self-consistent axisymmetric CCSN models initiated from solar-metallicity, nonrotating progenitors of 12, 15, 20, and 25 M{sub ⊙} and evolved with the smaller α-network to more than 1 s after the launch of an explosion.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Light-curve Analysis of Ordinary Type IIP Supernovae Based on Neutrino-driven Explosion Simulations in Three Dimensions

Type II-plateau supernovae (SNe IIP) are the most numerous subclass of core-collapse SNe originating from massive stars. In the framework of the neutrino-driven explosion mechanism, we study the properties of the SN outburst for a red supergiant progenitor model and compare the corresponding light curves with observations of the ordinary Type IIP SN 1999em. Three-dimensional (3D) simulations of (parametrically triggered) neutrino-driven explosions are performed with the (explicit, finite-volume, Eulerian, multifluid hydrodynamics) code Prometheus, using a presupernova model of a 15 M {sub ⊙} star as initial data. On approaching homologous expansion, the hydrodynamic and composition variables of the 3D models are mapped to a spherically symmetric configuration, and the simulations are continued with the (implicit, Lagrangian, radiation hydrodynamics) code Crab to follow the evolution of the blast wave during the SN outburst. Our 3D neutrino-driven explosion model with an explosion energy of about 0.5×10{sup 51} erg produces {sup 56}Ni in rough agreement with the amount deduced from fitting the radioactively powered light-curve tail of SN 1999em. The considered presupernova model, 3D explosion simulations, and light-curve calculations can explain the basic observational features of SN 1999em, except for those connected to the presupernova structure of the outer stellar layers. Our 3D simulations show that the distribution of {sup 56}Ni-rich matter in velocity space is asymmetric with a strong dipole component that is consistent with the observations of SN 1999em. The monotonic decline in luminosity from the plateau to the radioactive tail in ordinary SNe IIP is a manifestation of the intense turbulent mixing at the He/H composition interface.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Convergence of the Critical Cooling Rate for Protoplanetary Disk Fragmentation Achieved: The Key Role of Numerical Dissipation of Angular Momentum

We carry out simulations of gravitationally unstable disks using smoothed particle hydrodynamics (SPH) and the novel Lagrangian meshless finite mass (MFM) scheme in the GIZMO code. Our aim is to understand the cause of the nonconvergence of the cooling boundary for fragmentation reported in the literature. We run SPH simulations with two different artificial viscosity implementations and compare them with MFM, which does not employ any artificial viscosity. With MFM we demonstrate convergence of the critical cooling timescale for fragmentation at β{sub crit}≈3. Nonconvergence persists in SPH codes. We show how the nonconvergence problem is caused by artificial fragmentation triggered by excessive dissipation of angular momentum in domains with large velocity derivatives. With increased resolution, such domains become more prominent. Vorticity lags behind density, due to numerical viscous dissipation in these regions, promoting collapse with longer cooling times. Such effect is shown to be dominant over the competing tendency of artificial viscosity to diminish with increasing resolution. When the initial conditions are first relaxed for several orbits, the flow is more regular, with lower shear and vorticity in nonaxisymmetric regions, aiding convergence. Yet MFM is the only method that converges exactly. Our findings are of general interest, as numerical dissipation via artificial viscosity or advection errors can also occur in grid-based codes. Indeed, for the FARGO code values of β{sub crit} significantly higher than our converged estimate have been reported in the literature. Finally, we discuss implications for giant planet formation via disk instability.

79 ASTRONOMY AND ASTROPHYSICS↗