Engineering topics

Schnetter, Erik

Publications and source records attributed to Schnetter, Erik.

10 records

DOE OSTI2019

Spectral methods in the presence of discontinuities

Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and L 2 -norm. However, for non-smooth problems, convergence is significantly worse—the L 2 -norm of the error for a discontinuous problem will converge at a sub-linear rate and the infinity norm will not converge at all. We explore and improve upon a post-processing technique—optimally convergent mollifiers—to recover exponential convergence from a poorly-converging spectral reconstruction of non-smooth data. Furthermore this is an important first step towards using these techniques for simulations of realistic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

r -process Nucleosynthesis from Three-dimensional Magnetorotational Core-collapse Supernovae

Here, we investigate r -process nucleosynthesis in 3D general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-temperature equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucleosynthetic signature. We find that production of r -process material beyond the second peak is reduced by a factor of 100 when the magnetorotational jets produced by the rapidly rotating core undergo a kink instability. Our results indicate that 3D magnetorotationally powered CCSNe are robust r -process sources only if they are obtained by the collapse of cores with unrealistically large precollapse magnetic fields of the order of 10 13 G. Additionally, a comparison simulation that we restrict to axisymmetry results in overly optimistic r -process production for lower magnetic field strengths.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

The Progenitor Dependence of Core-collapse Supernovae from Three-dimensional Simulations with Progenitor Models of 12–40 M ⊙

We present a first study of the progenitor star dependence of the three-dimensional (3D) neutrino mechanism of core-collapse supernovae. We employ full 3D general-relativistic multi-group neutrino radiation-hydrodynamics and simulate the postbounce evolutions of progenitors with zero-age main sequence masses of 12, 15, 20, 27, and 40 M ⊙ . All progenitors, with the exception of the 12 M ⊙ star, experience shock runaway by the end of their simulations. In most cases, a strongly asymmetric explosion will result. We demonstrate three qualitatively distinct evolutions that imply a complex dependence of explosion dynamics on progenitor density structure, neutrino heating, and 3D flow. (1) Progenitors with massive cores, shallow density profiles, and high post-core-bounce accretion rates experience very strong neutrino heating and neutrino-driven turbulent convection, leading to early shock runaway. Accretion continues at a high rate, likely leading to black hole formation. (2) Intermediate progenitors experience neutrino-driven, turbulence-aided explosions triggered by the arrival of density discontinuities at the shock. These occur typically at the silicon/silicon–oxygen shell boundary. (3) Progenitors with small cores and density profiles without strong discontinuities experience shock recession and develop the 3D standing-accretion shock instability (SASI). Shock runaway ensues late, once declining accretion rate, SASI, and neutrino-driven convection create favorable conditions. These differences in explosion times and dynamics conclude in a non-monotonic relationship between progenitor and compact remnant mass.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

General-relativistic three-dimensional multi-group neutrino radiation-hydrodynamics simulations of core-collapse supernovae

We report on a set of long-term general-relativistic three-dimensional (3D) multi-group (energy-dependent) neutrino radiation-hydrodynamics simulations of core-collapse supernovae. We employ a full 3D two-moment scheme with the local M1 closure, three neutrino species, and 12 energy groups per species. With this, we follow the post-core-bounce evolution of the core of a nonrotating 27-M{sub ⊙} progenitor in full unconstrained 3D and in octant symmetry for ≳380 ms. We find the development of an asymmetric runaway explosion in our unconstrained simulation. We test the resolution dependence of our results and, in agreement with previous work, find that low resolution artificially aids explosion and leads to an earlier runaway expansion of the shock. At low resolution, the octant and full 3D dynamics are qualitatively very similar, but at high resolution, only the full 3D simulation exhibits the onset of explosion.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

NEUTRINO-DRIVEN CONVECTION IN CORE-COLLAPSE SUPERNOVAE: HIGH-RESOLUTION SIMULATIONS

We present results from high-resolution semiglobal simulations of neutrino-driven convection in core-collapse supernovae. We employ an idealized setup with parameterized neutrino heating/cooling and nuclear dissociation at the shock front. We study the internal dynamics of neutrino-driven convection and its role in redistributing energy and momentum through the gain region. We find that even if buoyant plumes are able to locally transfer heat up to the shock, convection is not able to create a net positive energy flux and overcome the downward transport of energy from the accretion flow. Turbulent convection does, however, provide a significant effective pressure support to the accretion flow as it favors the accumulation of energy, mass, and momentum in the gain region. We derive an approximate equation that is able to explain and predict the shock evolution in terms of integrals of quantities such as the turbulent pressure in the gain region or the effects of nonradial motion of the fluid. We use this relation as a way to quantify the role of turbulence in the dynamics of the accretion shock. Finally, we investigate the effects of grid resolution, which we change by a factor of 20 between the lowest and highest resolution. Our results show that the shallow slopes of the turbulent kinetic energy spectra reported in previous studies are a numerical artifact. Kolmogorov scaling is progressively recovered as the resolution is increased.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

NEUTRINO-DRIVEN TURBULENT CONVECTION AND STANDING ACCRETION SHOCK INSTABILITY IN THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVAE

We conduct a series of numerical experiments into the nature of three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of core-collapse supernovae using 3D general-relativistic hydrodynamic simulations of a 27 M{sub ⊙} progenitor star with a neutrino leakage/heating scheme. We vary the strength of neutrino heating and find three cases of 3D dynamics: (1) neutrino-driven convection, (2) initially neutrino-driven convection and subsequent development of the standing accretion shock instability (SASI), and (3) SASI-dominated evolution. This confirms previous 3D results of Hanke et al. and Couch and Connor. We carry out simulations with resolutions differing by up to a factor of ∼4 and demonstrate that low resolution is artificially favorable for explosion in the 3D convection-dominated case since it decreases the efficiency of energy transport to small scales. Low resolution results in higher radial convective fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino heating. In the SASI-dominated case, lower resolution damps SASI oscillations. In the convection-dominated case, a quasi-stationary angular kinetic energy spectrum E(ℓ) develops in the heating layer. Like other 3D studies, we find E(ℓ) ∝ℓ{sup −1} in the “inertial range,” while theory and local simulations argue for E(ℓ) ∝ ℓ{sup −5/3}. We argue that current 3D simulations do not resolve the inertial range of turbulence and are affected by numerical viscosity up to the energy-containing scale, creating a “bottleneck” that prevents an efficient turbulent cascade.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

A survey of high level frameworks in block-structured adaptive mesh refinement packages

Over the last decade block-structured adaptive mesh refinement (SAMR) has found increasing use in large, publicly available codes and frameworks. SAMR frameworks have evolved along different paths. Some have stayed focused on specific domain areas, others have pursued a more general functionality, providing the building blocks for a larger variety of applications. In this survey paper we examine a representative set of SAMR packages and SAMR-based codes that have been in existence for half a decade or more, have a reasonably sized and active user base outside of their home institutions, and are publicly available. The set consists of a mix of SAMR packages and application codes that cover a broad range of scientific domains. We look at their high-level frameworks, their design trade-offs and their approach to dealing with the advent of radical changes in hardware architecture. Finally, the codes included in this survey are BoxLib, Cactus, Chombo, Enzo, FLASH, and Uintah.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

MAGNETOROTATIONAL CORE-COLLAPSE SUPERNOVAE IN THREE DIMENSIONS

We present results of new three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. These simulations are the first of their kind and include a microphysical finite-temperature equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae are fundamentally different from what was anticipated on the basis of previous simulations in axisymmetry (2D). A strong bipolar jet that develops in a simulation constrained to 2D is crippled by a spiral instability and fizzles in full 3D. While multiple (magneto-)hydrodynamic instabilities may be present, our analysis suggests that the jet is disrupted by an m = 1 kink instability of the ultra-strong toroidal field near the rotation axis. Instead of an axially symmetric jet, a completely new, previously unreported flow structure develops. Highly magnetized spiral plasma funnels expelled from the core push out the shock in polar regions, creating wide secularly expanding lobes. We observe no runaway explosion by the end of the full 3D simulation 185 ms after bounce. At this time, the lobes have reached maximum radii of ∼900 km.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

GENERAL-RELATIVISTIC SIMULATIONS OF THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVAE

We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 M{sub Sun} star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a three-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 M{sub Sun} progenitor was studied in 2D by Mueller et al., who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low-l-mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

From Physics Model to Results: An Optimizing Framework for Cross-Architecture Code Generation

Starting from a high-level problem description in terms of partial differential equations using abstract tensor notation, the Chemora framework discretizes, optimizes, and generates complete high performance codes for a wide range of compute architectures. Chemora extends the capabilities of Cactus, facilitating the usage of large-scale CPU/GPU systems in an efficient manner for complex applications, without low-level code tuning. Chemora achieves parallelism through MPI and multi-threading, combining OpenMP and CUDA. Optimizations include high-level code transformations, efficient loop traversal strategies, dynamically selected data and instruction cache usage strategies, and JIT compilation of GPU code tailored to the problem characteristics. The discretization is based on higher-order finite differences on multi-block domains. Chemora's capabilities are demonstrated by simulations of black hole collisions. This problem provides an acid test of the framework, as the Einstein equations contain hundreds of variables and thousands of terms.

Blazewicz, Marek↗