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Comparing the Performance of Julia on CPUs versus GPUs and Julia-MPI versus Fortran-MPI: a case study with MPAS-Ocean (Version 7.1)

Abstract. Some programming languages are easy to develop at the cost of slow execution, while others are fast at runtime but much more difficult to write. Julia is a programming language that aims to be the best of both worlds – a development and production language at the same time. To test Julia's utility in scientific high-performance computing (HPC), we built an unstructured-mesh shallow water model in Julia and compared it against an established Fortran-MPI ocean model, the Model for Prediction Across Scales–Ocean (MPAS-Ocean), as well as a Python shallow water code. Three versions of the Julia shallow water code were created: for single-core CPU, graphics processing unit (GPU), and Message Passing Interface (MPI) CPU clusters. Comparing identical simulations revealed that our first version of the Julia model was 13 times faster than Python using NumPy, where both used an unthreaded single-core CPU. Further Julia optimizations, including static typing and removing implicit memory allocations, provided an additional 10–20× speed-up of the single-core CPU Julia model. The GPU-accelerated Julia code was almost identical in terms of performance to the MPI parallelized code on 64 processes, an unexpected result for such different architectures. Parallelized Julia-MPI performance was identical to Fortran-MPI MPAS-Ocean for low processor counts and ranges from 2× faster to 2× slower for higher processor counts. Our experience is that Julia development is fast and convenient for prototyping but that Julia requires further investment and expertise to be competitive with compiled codes. We provide advice on Julia code optimization for HPC systems.

54 ENVIRONMENTAL SCIENCES↗

Directed Incremental Symbolic Execution

The last few years have seen a resurgence of interest in the use of symbolic execution -- a program analysis technique developed more than three decades ago to analyze program execution paths. Scaling symbolic execution and other path-sensitive analysis techniques to large systems remains challenging despite recent algorithmic and technological advances. An alternative to solving the problem of scalability is to reduce the scope of the analysis. One approach that is widely studied in the context of regression analysis is to analyze the differences between two related program versions. While such an approach is intuitive in theory, finding efficient and precise ways to identify program differences, and characterize their effects on how the program executes has proved challenging in practice. In this paper, we present Directed Incremental Symbolic Execution (DiSE), a novel technique for detecting and characterizing the effects of program changes. The novelty of DiSE is to combine the efficiencies of static analysis techniques to compute program difference information with the precision of symbolic execution to explore program execution paths and generate path conditions affected by the differences. DiSE is a complementary technique to other reduction or bounding techniques developed to improve symbolic execution. Furthermore, DiSE does not require analysis results to be carried forward as the software evolves -- only the source code for two related program versions is required. A case-study of our implementation of DiSE illustrates its effectiveness at detecting and characterizing the effects of program changes.

Person, Suzette↗

Image Segmentation, Registration, Compression, and Matching

A novel computational framework was developed of a 2D affine invariant matching exploiting a parameter space. Named as affine invariant parameter space (AIPS), the technique can be applied to many image-processing and computer-vision problems, including image registration, template matching, and object tracking from image sequence. The AIPS is formed by the parameters in an affine combination of a set of feature points in the image plane. In cases where the entire image can be assumed to have undergone a single affine transformation, the new AIPS match metric and matching framework becomes very effective (compared with the state-of-the-art methods at the time of this reporting). No knowledge about scaling or any other transformation parameters need to be known a priori to apply the AIPS framework. An automated suite of software tools has been created to provide accurate image segmentation (for data cleaning) and high-quality 2D image and 3D surface registration (for fusing multi-resolution terrain, image, and map data). These tools are capable of supporting existing GIS toolkits already in the marketplace, and will also be usable in a stand-alone fashion. The toolkit applies novel algorithmic approaches for image segmentation, feature extraction, and registration of 2D imagery and 3D surface data, which supports first-pass, batched, fully automatic feature extraction (for segmentation), and registration. A hierarchical and adaptive approach is taken for achieving automatic feature extraction, segmentation, and registration. Surface registration is the process of aligning two (or more) data sets to a common coordinate system, during which the transformation between their different coordinate systems is determined. Also developed here are a novel, volumetric surface modeling and compression technique that provide both quality-guaranteed mesh surface approximations and compaction of the model sizes by efficiently coding the geometry and connectivity/topology components of the generated models. The highly efficient triangular mesh compression compacts the connectivity information at the rate of 1.5-4 bits per vertex (on average for triangle meshes), while reducing the 3D geometry by 40-50 percent. Finally, taking into consideration the characteristics of 3D terrain data, and using the innovative, regularized binary decomposition mesh modeling, a multistage, pattern-drive modeling, and compression technique has been developed to provide an effective framework for compressing digital elevation model (DEM) surfaces, high-resolution aerial imagery, and other types of NASA data.

Yadegar, Jacob↗

Data for: Patel et al. Carbon flux estimates are sensitive to data source: A comparison of field and lab temperature sensitivity data

This dataset contains data and code used for the paper "Carbon flux estimates are sensitive to data source: A comparison of field and lab temperature sensitivity data" [DOI COMING SOON]A large literature exists on mechanisms driving soil production of the greenhouse gases CO2 and CH4. Measurements of these gases’ fluxes are often performed using closed-chamber incubations in the laboratory or in situ, i.e., in the field. Although it is common knowledge that measurements obtained through field studies vs. laboratory incubations can diverge because of the vastly different conditions of these environments, few studies have systematically examined these patterns. It is crucial to understand the magnitude and reasons for any differences, as these data are used to parametrize and benchmark ecosystem- to global-scale models, which are then susceptible to the biases of the source data. Here, we specifically examine how greenhouse gas measurements may be influenced by whether the measurement/incubation was conducted in the field vs. laboratory, focusing on CO2 and CH4 measurements. We use Q10 of greenhouse gas flux (temperature sensitivity) for our analyses, because of the ubiquity of this metric in biological and Earth system sciences and its importance to many modeling frameworks. We predicted that laboratory measurements would be less variable, but also less representative of true field conditions. However, there was greater variability in the Q10 values calculated from lab-based measurements of CO2 fluxes, because lab experiments explore extremes rarely seen in situ, and reflect the physical and chemical disturbances occurring during sampling, transport, and incubation. Overall, respiration Q10 values were significantly greater in laboratory incubations (mean = 4.19) than field measurements (mean = 3.05), with strong influences of incubation temperature and climate region/biome. However, this was in part because field measurements typically represent total respiration (Rs), whereas lab incubations typically represent heterotrophic respiration (Rh), making direct comparisons difficult to interpret. Focusing only on Rh-derived Q10, these values showed almost identical distributions across laboratory (n = 1110) and field (n = 581) experiments, providing strong support for using the former as an experimental proxy for the latter, although we caution that geographic biases in the extant data make this conclusion tentative. Due to a smaller sample size of CH4 Q10 data, we were unable to perform a comparable robust analysis, but we expect similar interactions with soil temperature, moisture, and environmental/climatic variables. Our results here suggest the need for more concerted efforts to document and standardize these data, including sample and site metadata. This dataset contains a compressed (.zip) archive of the data and R scripts used for this manuscript. The dataset includes files in .csv format, which can be accessed and processed using MS Excel or R. This archive can also be accessed on GitHub at https://github.com/kaizadp/field_lab_q10 (DOI: 10.5281/zenodo.7106554).

54 ENVIRONMENTAL SCIENCES↗

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing. In order for large scale optimization to become routine, the benefits of parallel architectures should be exploited. Although the flow solver has been parallelized using compiler directives. The parallel efficiency is under 50 percent. Clearly, parallel versions of the codes will have an immediate impact on the ability to design realistic configurations on fine meshes, and this effort is currently underway.

Grossman, Bernard↗

Giant Molecular Cloud Structure and Evolution

Bodenheimer and Burkert extended earlier calculations of cloud core models to study collapse and fragmentation. The initial condition for an SPH collapse calculation is the density distribution of a Bonnor-Ebert sphere, with near balance between turbulent plus thermal energy and gravitational energy. The main parameter is the turbulent Mach number. For each Mach number several runs are made, each with a different random realization of the initial turbulent velocity field. The turbulence decays on a dynamical time scale, leading the cloud into collapse. The collapse proceeds isothermally until the density has increased to about 10(exp 13) g cm(exp -3). Then heating is included in the dense regions. The nature of the fragmentation is investigated. About 15 different runs have been performed with Mach numbers ranging from 0.3 to 3.5 (the typical value observed in molecular cloud cores is 0.7). The results show a definite trend of increasing multiplicity with increasing Mach number (M), with the number of fragments approximately proportional to (1 + M). In general, this result agrees with that of Fisher, Klein, and McKee who published three cases with an AMR grid code. However our results show that there is a large spread about this curve. For example, for M=0.3 one case resulted in no fragmentation while a second produced three fragments. Thus it is not only the value of M but also the details of the superposition of the various velocity modes that play a critical role in the formation of binaries. Also, the simulations produce a wide range of separations (10-1000 AU) for the multiple systems, in rough agreement with observations. These results are discussed in two conference proceedings.

Hollenbach, David↗

The InSAR Scientific Computing Environment 3.0: A Flexible Framework for NISAR Operational and User-Led Science Processing

The InSAR Scientific Computing Environment (ISCE) was first developed under the NASA Advanced Information Systems Technology as a flexible, extensible object-oriented framework for Interferometric Synthetic Aperture Radar (InSAR) processing. The ISCE framework uses Python 3 at the workflow level, controlling modules of compiled code for functional processing, and managing inputs, outputs, and other flow control services. The currently released version, called ISCE 2.1, is distributed to the research community through the Western North America InSAR Consortium under a research license. The ISCE team is working on the next generation of the code in order to prepare for the NASAISRO SAR (NISAR) mission operational processing. Innovations in this code include augmentation or conversion of the custom Python framework elements in ISCE with the Pyre framework, new workflows for interferometric and polarimetric stack processing, a more intuitive and graphically based user interface, and flow control for hybrid computing environments including CPU/GPU clusters, logging and error tracking facilities, and new more efficient computational modules that exploit graphical processor units (GPUs) when available. The ISCE 3.0 framework is designed to work in an operational environment as well as on a single user’s laptop or compute cluster, with services to discover capabilities and scale computations accordingly.

Buckley, Sean M.↗

CG-Kit: Code Generation Toolkit for performant and maintainable variants of source code applied to Flash-X hydrodynamics simulations

CG-Kit is a new Code Generation tool-Kit that we have developed as a part of the solution for portability and maintainability for multiphysics computing applications. The development of CG-Kit is rooted in the urgent need created by the shifting landscape of high-performance computing platforms and the algorithmic complexities of a particular large-scale multiphysics application: Flash-X. To efficiently use computing resources on a heterogeneous node, an application must have a map of computation to resources and a mechanism to move the data and computation to the resources according to the map. Most existing performance portability solutions are focussed on abstracting the expression of computations so that a unified source code can be specialized to run on different resources. However, such an approach is insufficient for a code like Flash-X, which has a multitude of code components that can be assembled in various permutations and combinations to form different instances of applications. Similar challenges apply to any code that has composability, where a single specified way of apportioning work among devices may not be optimal. Additionally, use cases arise where the optimal control flow of computation may differ for different devices while the underlying numerics remain identical. This combination leads to unique challenges including handling an existing large code base in Fortran and/or C/C++, subdivision of code into a great variety of units supporting a wide range of physics and numerical methods, different parallelization techniques for distributed and shared memory systems and accelerator devices, and heterogeneity of computing platforms requiring coexisting variants of parallel algorithms. All of these challenges demand that scientific software developers apply existing knowledge about domain applications, algorithms, and computing platforms to determine custom abstractions and granularity for code generation. There is a critical lack of tools to tackle those problems. CG-Kit is designed to fill this gap by providing a user with the ability to express their desired control flow and computation-to-resource map in the form a pseudocode-like recipe. It consists of standalone tools that can be combined into highly specific and, we argue, highly effective portability and maintainability toolchains. Here we present the design of our new tools: parametrized source trees, control flow graphs, and recipes. The tools are implemented in Python. They are agnostic to the programming language of the source code targeted for code generation. In conclusion, we demonstrate the capabilities of the toolkit with two examples, first, multithreaded variants of the basic AXPY operation, and second, variants of parallel algorithms within a hydrodynamics solver, called Spark, from Flash-X that operates on block-structured adaptive meshes.

Algorithmic portability↗

A comparative analysis of numerical approaches for the description of gas flow in clay-based repository systems: From a laboratory to a large-scale gas injection test

There is nowadays a consensus among many countries that geological disposal is a favourable solution for the long-term management. Although different host formations and different barrier systems are under consideration around the world, clay-based materials form an important component for waste isolation in most national programmes. Hence, a good comprehension of the effect of gas flow on the hydro-mechanical behaviour of clay-based soils is essential, both at laboratory and field scale. Task B under the international cooperative project DECOVALEX-2023 has recently shown that, after some enhancement, models can be employed to reproduce laboratory scale tests, even with different sample geometries 37 . However, further work is required to understand whether they can be applied to simulate a large-scale experiment. Up-scaling of models for the advective transport of gas through clay-based low permeable material presents a number of problems related to the difficulty in obtaining consistent hydrogeological parameters and constitutive relationships at both laboratory and field scale. Based on a unique dataset from a large-scale gas injection test (Lasgit) performed at the Äspö Hard Rock Laboratory (Sweden), Task B within DECOVALEX-2023 has explored the refinement of these numerical strategies applied to the simulation of gas flow. Work performed within the task reveals that codes do not need to be substantially modified from the laboratory models to reproduce full-scale tests: indeed, model parameters calibrated and validated at laboratory scale have been applied to predict field scale gas flow at Lasgit, including peak gas pressure and injected cumulative gas volume. By means of (1) the introduction of interfaces between blocks to reflect the experimental configuration and the (2) adjustment of some parameters (e.g., higher permeability), the updated models are able to represent most of the key features observed in the experimental data, even at a large scale.

Tamayo-Mas, E↗

Modelling CN Zeeman effect observations of the envelopes of a low-mass protostellar disc and a massive protostar

We use the POLARIS radiative transfer code to produce simulated circular polarization Zeeman emission maps of the cyanide (CN) J = 1–0 molecular line transition for two types of protostellar envelope magnetohydrodynamic simulations. Our first model is a low-mass disc envelope system (box length L = 200 au), and our second model is the envelope of a massive protostar (L = 104 au) with a protostellar wind and a CN-enhanced outflow shell. We compute the velocity-integrated Stokes I and V, as well as the implied V/I polarization percentage, for each detector pixel location in our simulated emission maps. Our results show that both types of protostellar environments are in principle accessible with current circular polarization instruments, with each containing swaths of envelope area that yield percentage polarizations that exceed the 1.8 percent nominal sensitivity limit for circular polarization experiments with the Atacama Large Millimeter/submillimeter Array. In both systems, high-polarization (≳1.8 percent) pixels tend to lie at an intermediate distance away from the central star and where the line-centre opacity of the CN emission is moderately optically thin (τLC ~ 0.1–1). Furthermore, our computed V/I values scale roughly with the density-weighted mean line-of-sight magnetic field strength, indicating that Zeeman observations can effectively diagnose the strength of envelope-scale magnetic fields. We also find that pixels with large V/I are preferentially co-located where the absolute value of the velocity-integrated V is also large, suggesting that locations with favourable percentage polarization are also favourable in terms of raw signal.

79 ASTRONOMY AND ASTROPHYSICS↗

Description of real-time Ada software implementation of a power system monitor for the Space Station Freedom PMAD DC testbed

The Ada language software development to perform the electrical system monitoring functions for the NASA Lewis Research Center's Power Management and Distribution (PMAD) DC testbed is described. The results of the effort to implement this monitor are presented. The PMAD DC testbed is a reduced-scale prototype of the electrical power system to be used in the Space Station Freedom. The power is controlled by smart switches known as power control components (or switchgear). The power control components are currently coordinated by five Compaq 382/20e computers connected through an 802.4 local area network. One of these computers is designated as the control node with the other four acting as subsidiary controllers. The subsidiary controllers are connected to the power control components with a Mil-Std-1553 network. An operator interface is supplied by adding a sixth computer. The power system monitor algorithm is comprised of several functions including: periodic data acquisition, data smoothing, system performance analysis, and status reporting. Data is collected from the switchgear sensors every 100 milliseconds, then passed through a 2 Hz digital filter. System performance analysis includes power interruption and overcurrent detection. The reporting mechanism notifies an operator of any abnormalities in the system. Once per second, the system monitor provides data to the control node for further processing, such as state estimation. The system monitor required a hardware time interrupt to activate the data acquisition function. The execution time of the code was optimized using an assembly language routine. The routine allows direct vectoring of the processor to Ada language procedures that perform periodic control activities. A summary of the advantages and side effects of this technique are discussed.

Ludwig, Kimberly↗

Wall Upgrades for Energy Retrofits: A Techno-Economic Study

Homes built before 1992, when the U.S. Department of Energy’s (DOE) Building Energy Codes Program was established, represent approximately 68% of the residential building stock in the country. Up to 43% of these homes have little to no insulation in the walls and have very high air leakage rates of 10 or more air changes per hour at 50 pascals of pressure (ACH50). These issues can represent a substantial portion of unnecessary money spent on utility bills for homeowners, especially in the colder climates. There is a significant need for cost-effective, reliable retrofit methods for these homes that include air, moisture, and vapor controls which are considered best practices for high-performance new home construction. Well-tested and documented wall retrofit systems can help to achieve substantial energy savings and also improve durability, comfort, health, and resilience. In 2018, DOE’s Building Technologies Office awarded Pacific Northwest National Laboratory, Oak Ridge National Laboratory, and the University of Minnesota funding to complete a 3-year project to compare a range of residential wall retrofit systems that prioritized affordability, durability and energy savings potential. In addition to these core criteria, the ease-of-construction and the wide-scale applicability of the solutions also were considered. In this project, the research team identified, constructed, tested, simulated, and analyzed the feasibility and economics of 16 wall retrofit assemblies (14 test configurations and two baseline configurations).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluation of Radiation Belt Space Weather Forecasts for Internal Charging Analyses

A variety of static electron radiation belt models, space weather prediction tools, and energetic electron datasets are used by spacecraft designers and operations support personnel as internal charging code inputs to evaluate electrostatic discharge risks in space systems due to exposure to relativistic electron environments. Evaluating the environment inputs is often accomplished by comparing whether the data set or forecast tool reliability predicts measured electron flux (or fluence over a given period) for some chosen period. While this technique is useful as a model metric, it does not provide the information necessary to evaluate whether short term deviances of the predicted flux is important in the charging evaluations. In this paper, we use a 1-D internal charging model to compute electric fields generated in insulating materials as a function of time when exposed to relativistic electrons in the Earth's magnetosphere. The resulting fields are assumed to represent the "true" electric fields and are compared with electric field values computed from relativistic electron environments derived from a variety of space environment and forecast tools. Deviances in predicted fields compared to the "true" fields which depend on insulator charging time constants will be evaluated as a potential metric for determining the importance of predicted and measured relativistic electron flux deviations over a range of time scales.

Minow, Joseph I.↗

Resiliency of Degraded Built Infrastructure

Infrastructure resiliency depends on the ability of infrastructure systems to withstand, adapt, and recover from chronic and extreme stresses. In this white paper, we address the resiliency of infrastructure assets and discuss improving infrastructure stability through development of our understanding of cement and concrete degradation. The resiliency of infrastructure during extreme events relies on the condition, adaptability, and recoverability of built infrastructure (roads, bridges, dams), which serves as the backbone of existing infrastructure systems. Much of the built infrastructure in the US has consistently been rated D+ by the American Society of Civil Engineers (ASCE). Aged infrastructure introduces risk to the system, since unreliable infrastructure increases the likelihood of failures under chronic and extreme stress and are particularly concerning when extreme events occur. To understand and account for this added risk from poor infrastructure quality, more research is needed on (i) how the changing environment alters the aging of new and existing built infrastructure and (ii) how degradation causes unique failure mechanisms. The aging of built infrastructure is based on degradation of the structural materials, such as concrete and steel supports, which causes failure. Current work in cement/concrete degradation is based on (i) the development of high strength and degradation resistance concrete mixtures, (ii) methods of assessing the age and reliability of existing structures, and (3) modeling of structural stability and the microstructural evolution of concrete/cement from degradation mechanisms (sulfide attack, carbonation, decalcification). Sandia National Laboratories (SNL) has made several investments in studying the durability and degradation of cement based materials, including using SNL-developed codes and methodologies (peridynamics, PFLOTRAN) to focus on chemo-mechanical fracture of cement for energy applications. Additionally, a recent collaboration with the University of Colorado Boulder has included fracture of concrete gravity dams, scaling the existing work to applications in full sized infrastructure problems. Ultimately, SNL has the experience in degradation of cementitious materials to extend the current research portfolio and answer concerns about the resilience of aging built infrastructure.

36 MATERIALS SCIENCE↗

Isotopic and Fuel Lattice Parameter Trends in Extended Enrichment and Higher Burnup LWR Fuel Vol I: PWR fuel

Commercial light water reactor (LWR) operators and fuel vendors in the United States are pursuing changes to nuclear fuel that include extended enrichment (EE) and accident-tolerant fuel (ATF) designs. The term EE (8% > 235 U > 5%) is used in this report to refer to a subset of high assay low-enriched uranium (HALEU) that is considered usable in commercial US LWRs in the near term. ATF features are designed to improve fuel system performance under accident conditions. One goal of EE is to improve fuel cycle economy by enabling fuel to be depleted to higher burnup than the typical current maximum pin burnup limits (62 gigawatt-days per metric ton of uranium [GWd/MTU]). Adoption of EE, ATF, and high burnup (HBU) fuels in the US commercial fleet requires a clear understanding of the effects on core physics parameters and used fuel isotopic content, as well as confidence in the accuracy of computer code predictions over an expanded range of materials, enrichment, and burnup. A thorough understanding of the applicability and adequacy of benchmark data (e.g., criticality, decay heat, isotopic content) for computer code validation is necessary to ensure that appropriate safety margins are maintained. To prepare for and support these potential changes, the effects of EE, ATF, and HBU are being assessed for selected representative LWR fuel designs. The project is divided into phases: this report summarizes the findings of Phase 1, which focuses on the lattice physics parameter and used fuel isotopic changes for a conventional Westinghouse 17×17 pressurized water reactor (PWR) design. The primary investigation tool is the SCALE Polaris code using the SCALE 56-group Evaluated Nuclear Data File (ENDF)/B-VII.1 cross sections. The goal of the current work is to (1) identify and explain important effects of EE and HBU (reactivity, lattice physics, and isotopic effects) assuming that PWR fuel design and usage remain similar to those for current enrichment fuel, (2) provide limited code-to-code comparisons with higher order cross section libraries and/or codes, and (3) identify any apparent anomalous trends in the results for further investigation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Godfrey, Andrew G.↗

Systematic and objective evaluation of Earth system models: PCMDI Metrics Package (PMP) version 3

Systematic, routine, and comprehensive evaluation of Earth system models (ESMs) facilitates benchmarking improvement across model generations and identifying the strengths and weaknesses of different model configurations. By gauging the consistency between models and observations, this endeavor is becoming increasingly necessary to objectively synthesize the thousands of simulations contributed to the Coupled Model Intercomparison Project (CMIP) to date. The Program for Climate Model Diagnosis and Intercomparison (PCMDI) Metrics Package (PMP) is an open-source Python software package that provides quick-look objective comparisons of ESMs with one another and with observations. The comparisons include metrics of large- to global-scale climatologies, tropical inter-annual and intra-seasonal variability modes such as the El Niño–Southern Oscillation (ENSO) and Madden–Julian Oscillation (MJO), extratropical modes of variability, regional monsoons, cloud radiative feedbacks, and high-frequency characteristics of simulated precipitation, including its extremes. The PMP comparison results are produced using all model simulations contributed to CMIP6 and earlier CMIP phases. An important objective of the PMP is to document the performance of ESMs participating in the recent phases of CMIP, together with providing version-controlled information for all datasets, software packages, and analysis codes being used in the evaluation process. Among other purposes, this also enables modeling groups to assess performance changes during the ESM development cycle in the context of the error distribution of the multi-model ensemble. Quantitative model evaluation provided by the PMP can assist modelers in their development priorities. In this paper, we provide an overview of the PMP, including its latest capabilities, and discuss its future direction.

54 ENVIRONMENTAL SCIENCES↗

A Digital Control Algorithm for Magnetic Suspension Systems

An ongoing program exists to investigate and develop magnetic suspension technologies and modelling techniques at NASA Langley Research Center. Presently, there is a laboratory-scale large air-gap suspension system capable of five degree-of-freedom (DOF) control that is operational and a six DOF system that is under development. Those systems levitate a cylindrical element containing a permanent magnet core above a planar array of electromagnets, which are used for levitation and control purposes. In order to evaluate various control approaches with those systems, the Generic Real-Time State-Space Controller (GRTSSC) software package was developed. That control software package allows the user to implement multiple control methods and allows for varied input/output commands. The development of the control algorithm is presented. The desired functionality of the software is discussed, including the ability to inject noise on sensor inputs and/or actuator outputs. Various limitations, common issues, and trade-offs are discussed including data format precision; the drawbacks of using either Direct Memory Access (DMA), interrupts, or program control techniques for data acquisition; and platform dependent concerns related to the portability of the software, such as memory addressing formats. Efforts to minimize overall controller loop-rate and a comparison of achievable controller sample rates are discussed. The implementation of a modular code structure is presented. The format for the controller input data file and the noise information file is presented. Controller input vector information is available for post-processing by mathematical analysis software such as MATLAB1.

Britton, Thomas C.↗