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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A Survey: Handling Irregularities in Neural Network Acceleration with FPGAs

In the last decade, Artificial Intelligence (AI) through Deep Neural Networks (DNNs) has penetrated virtually every aspect of science, technology, and business. Many types of DNNs have been and continue to be developed, including Convolutional Neural Networks (CNNs), Recurrent Neural Net- works (RNNs), and Graph Neural Networks (GNNs). The overall problem for all of these Neural Networks (NNs) is that their target applications generally pose stringent constraints on latency and throughput, while also having strict accuracy requirements. There have been many previous efforts in creating hardware to accelerate NNs. The problem designers face is that optimal NN models typically have significant irregularities, making them hardware-unfriendly. In this paper, we first define the problems in NN acceleration by characterizing common irregularities in NN processing into 4 types; then we summarize the existing works that handle the four types of irregularities efficiently using hardware, especially FPGAs; finally, we provide a new vision of next-generation FPGA-based NN acceleration: that the emerging heterogeneity in the next-generation FPGAs is the key to achieving higher performance.

Geng, Tong↗
DOE OSTI2021

Observation of Polarization-Dependent Changes in Higher-Order Mode Responses as a Function of Transverse Beam Position in Tesla-Type Cavities at FAST

Higher-order modes (HOMs) in superconducting rf cavities present problems for an electron bunch traversing the cavity in the form of long-range wakefields from previous bunches. These may dilute the emittance of the macropulse average, especially with low emittance beams at facilities such as the European X-ray Free-electron Laser (XFEL) and the upgraded Linac Coherent Light Source (LCLS-II). Here we present observations of HOMs driven by the beam at the Fermilab Accelerator Science and Technology (FAST) facility. The FAST facility features two independent TESLA-type cavities (CC1 and CC2) after a photocathode rf gun followed by an 8-cavity cryomodule. The HOM signals were acquired from cavities using bandpass filters of 1.75 ± 0.15 GHz, 2.5 ± 0.2 GHz, and 3.25 ± 0.2 GHz and recorded using an 8-GHz, 20 GSa/s oscilloscope. The frequency resolution obtained is sufficient to separate polarization components of many of the HOMs. These HOM signals were captured from CC1 and cavities 1 and 8 of the cryomodule for various initial trajectories through the cavities, and we observe correlations between trajectory, HOM signals, and which polarization component of a mode is affected.

Thurman-Keup, Randy Michael↗
DOE OSTI2024

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Matérn-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory to characterize the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and MAP estimators for nonlinear inverse problems. Furthermore, our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.

Bayesian inverse problem↗
DOE OSTI2023

High-fidelity simulations of the run-in process for a pebble-bed reactor

Pebble-bed reactors (PBRs) rely on a continual feed of fuel pebbles being cycled through the core. As a result, they require a “run-in” period in order to reach an equilibrium state. The run-in period for a PBR is a complex, time-dependent problem that requires the injection of new fuel, different types of fuel, and power increases. This complexity in the run-in makes it important to capture the physical processes in order to generate an accurate representation. The present work details the creation of a high-fidelity Monte Carlo methodology for analyzing the run-in and subsequent approach to equilibrium for PBRs. The methodology entails a Python module wrapped around Serpent so as to perform neutronics calculations, move pebbles, refuel the core, and discharge pebbles, thereby modeling the explicit behavior of the PBR run-in. Further, three run-in simulations (a constant temperature profile, a linear temperature profile, and a constant temperature profile using control rods) were examined in order to identify the key physical phenomena present in the run-in process. Utilizing kugelpy, we found the inclusion of a temperature profile to be important for accurately capturing a discharge burnup (around 141 MWd/kg), a consistent k-eff (around 1.005), and an average pebble power (around 2.5 kW/pebble) that all fall within acceptable limits.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A classical, non-singular, bouncing universe

We present a model for a classical, non-singular bouncing cosmology without violation of the null energy condition (NEC). The field content is General Relativity plus a real scalar field with a canonical kinetic term and only renormalizable, polynomial-type self-interactions for the scalar field in the Jordan frame. The universe begins vacuum-energy dominated and is contracting at t=-∞. We consider a closed universe with a positive spatial curvature, which is responsible for the universe bouncing without any NEC violation. An Rφ 2 coupling between the Ricci scalar and the scalar field drives the scalar field from the initial false vacuum to the true vacuum during the bounce. The model is sub-Planckian throughout its evolution and every dimensionful parameter is below the effective-field-theory scale M P , so we expect no ghost-type or tachyonic instabilities. This model solves the horizon problem and extends co-moving particle geodesics to past infinity, resulting in a geodesically complete universe without singularities. We solve the Friedman equations and the scalar-field equation of motion numerically, and analytically under certain approximations.

Astronomy & Astrophysics↗
DOE OSTI2021

Decision-Making Under Uncertainty for a Digital Thread-Enabled Design Process

Abstract Digital thread is a data-driven architecture that links together information from all stages of the product lifecycle. Despite increasing application in manufacturing, maintenance/operations, and design related tasks, a principled formulation of analyzing the decision-making problem under uncertainty for the digital thread remains absent. The contribution of this article is to present a formulation using Bayesian statistics and decision theory. First, we address how uncertainty propagates in the product lifecycle and how the digital thread evolves based on the decisions we make and the data we collect. By using these mechanics, we explore designing over multiple product generations or iterations and provide an algorithm to solve the underlying multistage decision problem. We illustrate our method on an example structural design problem where our method can quantify and optimize different types and sequences of decisions, ranging from experimentation, manufacturing, and sensor placement/selection, to minimize total accrued costs.

Engineering↗
DOE OSTI2021

Test Points for Online Monitoring of Quantum Circuits

Noisy Intermediate-Scale Quantum (NISQ) computers consisting of tens of inherently noisy quantum bits (qubits) suffer from reliability problems. Qubits and their gates are susceptible to various types of errors. Due to limited numbers of qubits and high error rates, quantum error correction cannot be applied. Physical constraints of quantum hardware including the error rates are used to guide the design and the layout of quantum circuits. The error rates determine the selection of qubits and their operations. The resulting circuit is executed on the quantum computer. This study explores the risk of unexpected changes in the error rates of NISQ computers post-calibration. We show that unexpected changes in error rates can alter the output state of a quantum circuit. To detect these changes, we propose the insertion of test points into the quantum circuit to enable online monitoring of the physical qubit behavior. We utilize classical, superposition, and uncompute test points. Furthermore, we use a gate error coverage metric to assess the quality of the tests. We verify the effectiveness of the proposed scheme on different IBM quantum computers (IBM Q), in addition to a noisy simulation that shows the scalability of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

People are like plutonium

An analogy is drawn between the study of human behavior and the study of plutonium to demonstrate that soft and hard sciences are more similar than different, making the distinction moot and unproductive. The studies of human behavior and plutonium follow a common scientific research cycle that aligns with Thomas Kuhn’s views of scientific change. This common research cycle provides evidence that the thought processes and methodologies required for success are congruent in the soft and hard sciences. The primary implication from this analogy is that scientists in all disciplines should eradicate the distinction between soft and hard sciences. Focusing on similarities rather than differences among researchers from different disciplines is necessary to enhance collective intelligence and the type of transdisciplinary collaboration required to tackle difficult sociotechnical problems. CCS Concepts: • Social and professional topics • User characteristics • Cultural characteristics.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2022

Computational Imaging for Intelligence in Highly Scattering Aerosols (Final Report)

Natural and man-made degraded visual environments pose major threats to national security. The random scattering and absorption of light by tiny particles suspended in the air reduces situational awareness and causes unacceptable down-time for critical systems and operations. To improve the situation, we have developed several approaches to interpret the information contained within scattered light to enhance sensing and imaging in scattering media. These approaches were tested at the Sandia National Laboratory Fog Chamber facility and with tabletop fog chambers. Computationally efficient light transport models were developed and leveraged for computational sensing. The models are based on a weak angular dependence approximation to the Boltzmann or radiative transfer equation that appears to be applicable in both the moderate and highly scattering regimes. After the new model was experimentally validated, statistical approaches for detection, localization, and imaging of objects hidden in fog were developed and demonstrated. A binary hypothesis test and the Neyman-Pearson lemma provided the highest theoretically possible probability of detection for a specified false alarm rate and signal-to-noise ratio. Maximum likelihood estimation allowed estimation of the fog optical properties as well as the position, size, and reflection coefficient of an object in fog. A computational dehazing approach was implemented to reduce the effects of scatter on images, making object features more readily discernible. We have developed, characterized, and deployed a new Tabletop Fog Chamber capable of repeatably generating multiple unique fog-analogues for optical testing in degraded visual environments. We characterized this chamber using both optical and microphysical techniques. In doing so we have explored the ability of droplet nucleation theory to describe the aerosols generated within the chamber, as well as Mie scattering theory to describe the attenuation of light by said aerosols, and correlated the aerosol microphysics to optical properties such as transmission and meteorological optical range (MOR). This chamber has proved highly valuable and has supported multiple efforts inclusive to and exclusive of this LDRD project to test optics in degraded visual environments. Circularly polarized light has been found to maintain its polarization state better than linearly polarized light when propagating through fog. This was demonstrated experimentally in both the visible and short-wave infrared (SWIR) by imaging targets made of different commercially available retroreflective films. It was found that active circularly polarized imaging can increase contrast and range compared to linearly polarized imaging. We have completed an initial investigation of the capability for machine learning methods to reduce the effects of light scattering when imaging through fog. Previously acquired experimental long-wave images were used to train an autoencoder denoising architecture. Overfitting was found to be a problem because of lack of variability in the object type in this data set. The lessons learned were used to collect a well labeled dataset with much more variability using the Tabletop Fog Chamber that will be available for future studies. We have developed several new sensing methods using speckle intensity correlations. First, the ability to image moving objects in fog was shown, establishing that our unique speckle imaging method can be implemented in dynamic scattering media. Second, the speckle decorrelation over time was found to be sensitive to fog composition, implying extensions to fog characterization. Third, the ability to distinguish macroscopically identical objects on a far-subwavelength scale was demonstrated, suggesting numerous applications ranging from nanoscale defect detection to security. Fourth, we have shown the capability to simultaneously image and localize hidden objects, allowing the speckle imaging method to be effective without prior object positional information. Finally, an interferometric effect was presented that illustrates a new approach for analyzing speckle intensity correlations that may lead to more effective ways to localize and image moving objects. All of these results represent significant developments that challenge the limits of the application of speckle imaging and open important application spaces. A theory was developed and simulations were performed to assess the potential transverse resolution benefit of relative motion in structured illumination for radar systems. Results for a simplified radar system model indicate that significant resolution benefits are possible using data from scanning a structured beam over the target, with the use of appropriate signal processing.

58 GEOSCIENCES↗
DOE OSTI2021

Development and Performance Simulations of the MPACT-AGREE Code Coupling Interface for MAGNOX Reactors

MPACT is a whole-core 3D neutron transport code jointly developed by Oak Ridge National Laboratory and the University of Michigan to perform high-fidelity light water reactor (LWR) analysis. Its capability was recently extended for gas-cooled reactor analysis by coupling to the thermo-fluids code AGREE for thermal feedback. This paper presents the MPACT-AGREE code coupling for the simulation of MAGNOX-type gas-cooled graphite-moderated reactors. A coupling interface has been developed, along with methods to accurately simulate MAGNOX type reactors. The coupling mechanics were tested using two problems derived from the Calder Hall reactor. Simulations of these models demonstrated that the codes have been successfully coupled and can provide reasonable results in a tractable simulation time.

Gentry, Cole↗
DOE OSTI2020

Choosing the Best Modeling Platform for Radiological Risk Assessment Models - 20468

Radiological risk assessments, in the form of performance or safety assessments, are often required under regulations or guidance for remediation of contaminated land, decommissioning of contaminated buildings or structures, and radioactive waste disposal. These risk assessments are usually supported by fate and transport models that address decay and ingrowth of radionuclides, as well as their movement through engineered systems and the natural environment. These models are often projected thousands, or more, years into the future, largely because the radioactive species change through decay and ingrowth, and hence the magnitude of the radioactive effect changes with time. There are many computer codes that are available to address this type of modeling. They range from addressing specific pathways or processes such as infiltration of water, groundwater, surface water, air, biota, diffusion and advection of water and gases, to those that try to couple all processes together to evaluate the impact of fate and transport through the entire system to places in space and time to which access is assumed. These different types of codes are sometimes separated with the monikers process-level and systems-level codes, although it is often not clear that this separation does justice to the capabilities of the many codes that are available to evaluate fate and transport of radionuclides. The focus of this paper is the latter group of modeling codes. Several systems level modeling codes exist and are used. There are differences between these codes in terms of utility, flexibility, complexity and cost. The purpose of this paper is to compare a few of these codes in the context of work currently being performed by the International Atomic Energy Agency (IAEA) Modeling and Data for Radiological Impact Assessments (MODARIA) II Working Group 1 (WG1). The MODARIA II WG1's main focus is how stakeholder engaged decision analysis can, or should, be applied to radiological contamination problems so that better, longstanding, sustainable, solutions are reached. However, the WG1 also recognizes the potential impact of the modeling tools that are chosen to address radiological risk, which is often a primary objective of decision making for radiological problems. Other objectives might also be important, such as constraining costs, obtaining financing, minimizing impact on ecosystems, saving cultural resources, saving jobs, farmland, environmental justice, etc., in a full decision analysis for a given radiological contamination problem, but none of these other objectives have the same types of complex modeling needs as minimize radiological dose. Consequently, a further focus of WG1 is to evaluate the potential impacts on decision making of the choice of fate and transport, and risk assessment, modeling codes that are used to support decision making. The WG1 will produce a report at the end of 2020 that will focus on an approach to effective decision making and stakeholder engagement. The report will also consider the role that performance assessment modeling should play in the decision-making process, including the impact of the choice of modeling tools or computer codes on risk-informed decision making. Several sites around the World have been made available by Member States for these model comparisons, and several modeling tools have been considered. However, the focus of this paper is on two of the sites, one in Belgium and one in Ukraine, and on three of the tools: NORMALYSA (NORM And Legacy Site Assessment); GoldSim{sup C}, and AMBER{sup C}. The final report from this working group will also cover other modeling tools, including RESRAD, and PC-Cream{sup R}. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Node Monitoring as a Fault Detection Countermeasure against Information Leakage within a RISC-V Microprocessor

Advanced, superscalar microprocessors (μP) are highly susceptible to wear-out failures because of their highly complex, densely packed circuit structure and extreme operational frequencies. Although many types of fault detection and mitigation strategies have been proposed, none have addressed the specific problem of detecting faults that lead to information leakage events on I/O channels of the μP. Information leakage can be defined very generally as any type of output that the executing program did not intend to produce. In this work, we restrict this definition to output that represents a security concern, and in particular, to the leakage of plaintext or encryption keys, and propose a counter-based countermeasure to detect faults that cause this type of leakage event. Fault injection (FI) experiments are carried out on two RISC-V microprocessors emulated as soft cores on a Xilinx multi-processor System-on-chip (MPSoC) FPGA. The μP designs are instrumented with a set of counters that records the number of transitions that occur on internal nodes. The transition counts are collected from all internal nodes under both fault-free and faulty conditions, and are analyzed to determine which counters provide the highest fault coverage and lowest latency for detecting leakage faults. We show that complete coverage of all leakage faults is possible using only a single counter strategically placed within the branch compare logic of the μPs.

42 ENGINEERING↗
DOE OSTI2024

Optical and photoelectric properties of surface barrier diodes based on n- Hg3In2Te6 crystals

The high radiation resistance of Hg3In2Te6 (MIT) single crystals to large doses of ionizing radiation makes devices quite attractive. Such a feature of the crystal structure has not only important advantages, but also causes serious technological difficulties in doping and controlling the specific resistance within the required limits and type of conductivity of single crystals. These technological difficulties create serious problems when creating structures with a potential barrier, especially with a p-n junction. At the moment, there are no publications on the creation of a p-n junction based on MIT. The only alternative is to create a potential barrier such as a Schottky diode or a metal-dielectric-semiconductor structure. This limits the use of MIT to produce, for example, rectifier diodes that can operate at relatively high reverse bias voltages. The typical resistivity of single crystals of MIT of n-type conductivity, which are used for the manufacture of diodes and photodiodes, is approximately equal to ρ≈103-104 Ω×cm. Such a specific resistance leads to a relatively large resistance of the neutral part of the single crystal, which in turn limits the direct currents of the rectifier diodes and significantly limits an important parameter of photodiodes - the dynamic range of the watt-ampere characteristic. This problem arises from the relatively high series resistance of the substrate. For rectifier diodes, this relatively large series resistance leads to a significant forward bias voltage drop, which reduces both the rectification factor and the amount of rectified current. We have already created diodes and photodiodes on Cr/MIT/Cr single crystals with a specific resistance of ρ≈103-104 Ω×cm. The diodes had relatively small dark currents but had the disadvantage of a relatively large specific resistance of the substrate, which we have already discussed above [1,2,3].

Sklyarchuk, V.↗
DOE OSTI2023

CHARM-SYCL: New Unified Programming Environment for Multiple Accelerator Types

Addressing performance portability across diverse accelerator architectures has emerged as a major challenge in the development of application and programming systems for high-performance computing environments. Although recent programming systems that focus on performance portability have significantly improved productivity in an effort to meet this challenge, the problem becomes notably more complex when compute nodes are equipped with multiple accelerator types—each with unique performance attributes, optimal data layout, and binary formats. To navigate the intricacies of multi-accelerator programming, we propose CHARM-SYCL as an extension of our CHARM multi-accelerator execution environment [27]. This environment will combine our SYCL-based performance-portability programming front end with a back end for extremely heterogeneous architectures as implemented with the IRIS runtime from Oak Ridge National Laboratory. Our preliminary evaluation indicates potential productivity boost and reasonable performance compared to vendor-specific programming system and runtimes.

Fujita, Norihisa↗
DOE OSTI2026

Extreme-scale EV charging infrastructure planning for last-mile delivery using high-performance parallel computing

Here, this paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Capacity allocation↗
DOE OSTI2022

Kinetic and equilibrium reactions on natural and laboratory generation of thermogenic gases from Type II marine shale

The phenomenon that laboratory pyrolysis experiments produce much wetter gases than those in natural reservoirs is a long-recognized and debated problem in the investigation of natural gases in sedimentary basins. In this study, we explore the discrepancy by pyrolyzing a type II kerogen from the Woodford Shale in Oklahoma, compared with the previous results on the produced natural gases from the Arkoma Basin generated from the same source rock (Liu et al., 2019) with the discussion of gas and isotopic compositions at bulk and position-specific (PS) levels. An improved GC-pyrolysis-GC IRMS method is applied for the determination of PS δ 13 C of propane produced in the pyrolysis of the Woodford Shale at Easy %R o from 0.76 to 3.27. Kinetic and thermodynamic considerations of the chemical and isotopic compositions of the natural and laboratory pyrolysis gases suggest that the generation of light hydrocarbons involves uni-directional cracking reactions, exchange reactions with water, and likely reversible reactions among light hydrocarbons and other H-containing volatiles. After the gas generation in the unconventional Woodford Shale reservoirs, the C 1 -C 4 gases might have approached close to chemical equilibrium of C 1 -C 3 and isotope equilibrium of C 2 -C 1 and C 3 -C 1 pairs at their peak temperatures. The capping H for the generation of C 1 -C 4 in the Woodford Shale gases appears to have experienced at least partial exchange with the water, while that in the pyrolysis gases is only originated from organic-bound compounds with large kinetic isotope effects (KIE). Our findings indicate that elevated compound-specific and PS δ 13 C values of propane in the wet-gas cracking stage are significantly influenced by the breakdown of the thermally stable compounds (e.g., remaining kerogen, residues). A first synthesis of PS δ 13 C and δ 2 H isotopic compositions of propane from this study and the literature data suggests relatively similar isotopic structures of propane precursors in kerogens. Finally, this study demonstrates that PS isotope analysis of propane can contribute to identifying various geological (e.g., maturation, wet-gas cracking, H exchange, diffusion) and biodegradation processes.

58 GEOSCIENCES↗
DOE OSTI2021

Discrete Green’s functions and spectral graph theory for computationally efficient thermal modeling

Here, this work concerns solutions of the heat equation with the spectral graph method, for which the temperature is defined at discrete points in the domain and the spatial relationship among the points is described by a graph. The heat equation on the graph is solved using matrix techniques involving the eigenvectors and eigenvalues of the Laplacian matrix. The spectral graph approach precludes the computationally intensive meshing and numerous time-integration steps of the finite element method. In the present work, the spectral graph method is extended to include heat loss at the boundaries with a generalized boundary condition, and physics-based edge weights are introduced which simplify the calibration process. From this approach a discrete Green’s function is defined which allows for solutions under a variety of heating conditions including: space-varying initial conditions; time-and-space varying internal heating; and, time-and-space-varying heating at boundaries of type 1 (Dirichlet), type 2 (Neumann) and type 3 (Robin). Results are provided for benchmark heat transfer problems in one spatial dimension and in three spatial dimensions, and verification is provided by comparison with exact analytical solutions and finite difference solutions. The spectral graph method converges within 0.4% error of the analytical solution. The practical utility of the approach is demonstrated by thermal simulation of a multilayer additive manufacturing process. The spectral graph results are compared to experimentally-obtained temperature data for two metal parts, with error less than 5% of the experimental measurements, with computation time less than one minute on a desktop computer.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗