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Recovery Act: Advanced Interaction, Computation, and Visualization Tools for Sustainable Building Design

Current building energy simulation technology requires excessive labor, time and expertise to create building energy models, excessive computational time for accurate simulations and difficulties with the interpretation of the results. These deficiencies can be ameliorated using modern graphical user interfaces and algorithms which take advantage of modern computer architectures and display capabilities. To prove this hypothesis, we developed an experimental test bed for building energy simulation. This novel test bed environment offers an easy-to-use interactive graphical interface, provides access to innovative simulation modules that run at accelerated computational speeds, and presents new graphics visualization methods to interpret simulation results. Our system offers the promise of dramatic ease of use in comparison with currently available building energy simulation tools. Its modular structure makes it suitable for early stage building design, as a research platform for the investigation of new simulation methods, and as a tool for teaching concepts of sustainable design. Improvements in the accuracy and execution speed of many of the simulation modules are based on the modification of advanced computer graphics rendering algorithms. Significant performance improvements are demonstrated in several computationally expensive energy simulation modules. The incorporation of these modern graphical techniques should advance the state of the art in the domain of whole building energy analysis and building performance simulation, particularly at the conceptual design stage when decisions have the greatest impact. More importantly, these better simulation tools will enable the transition from prescriptive to performative energy codes, resulting in better, more efficient designs for our future built environment.

99 GENERAL AND MISCELLANEOUS↗

High Energy Physics Forum for Computational Excellence: Working Group Reports (I. Applications Software II. Software Libraries and Tools III. Systems)

Computing plays an essential role in all aspects of high energy physics. As computational technology evolves rapidly in new directions, and data throughput and volume continue to follow a steep trend-line, it is important for the HEP community to develop an effective response to a series of expected challenges. In order to help shape the desired response, the HEP Forum for Computational Excellence (HEP-FCE) initiated a roadmap planning activity with two key overlapping drivers -- 1) software effectiveness, and 2) infrastructure and expertise advancement. The HEP-FCE formed three working groups, 1) Applications Software, 2) Software Libraries and Tools, and 3) Systems (including systems software), to provide an overview of the current status of HEP computing and to present findings and opportunities for the desired HEP computational roadmap. The final versions of the reports are combined in this document, and are presented along with introductory material.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fusion Energy Sciences Exascale Requirements Review. An Office of Science review sponsored jointly by Advanced Scientific Computing Research and Fusion Energy Sciences, January 27-29, 2016, Gaithersburg, Maryland

The additional computing power offered by the planned exascale facilities could be transformational across the spectrum of plasma and fusion research — provided that the new architectures can be efficiently applied to our problem space. The collaboration that will be required to succeed should be viewed as an opportunity to identify and exploit cross-disciplinary synergies. To assess the opportunities and requirements as part of the development of an overall strategy for computing in the exascale era, the Exascale Requirements Review meeting of the Fusion Energy Sciences (FES) community was convened January 27–29, 2016, with participation from a broad range of fusion and plasma scientists, specialists in applied mathematics and computer science, and representatives from the U.S. Department of Energy (DOE) and its major computing facilities. This report is a summary of that meeting and the preparatory activities for it and includes a wealth of detail to support the findings. Technical opportunities, requirements, and challenges are detailed in this report (and in the recent report on the Workshop on Integrated Simulation). Science applications are described, along with mathematical and computational enabling technologies. Also see http://exascaleage.org/fes/ for more information.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Biological and Environmental Research Exascale Requirements Review. An Office of Science review sponsored jointly by Advanced Scientific Computing Research and Biological and Environmental Research, March 28-31, 2016, Rockville, Maryland

Understanding the fundamentals of genomic systems or the processes governing impactful weather patterns are examples of the types of simulation and modeling performed on the most advanced computing resources in America. High-performance computing and computational science together provide a necessary platform for the mission science conducted by the Biological and Environmental Research (BER) office at the U.S. Department of Energy (DOE). This report reviews BER’s computing needs and their importance for solving some of the toughest problems in BER’s portfolio. BER’s impact on science has been transformative. Mapping the human genome, including the U.S.-supported international Human Genome Project that DOE began in 1987, initiated the era of modern biotechnology and genomics-based systems biology. And since the 1950s, BER has been a core contributor to atmospheric, environmental, and climate science research, beginning with atmospheric circulation studies that were the forerunners of modern Earth system models (ESMs) and by pioneering the implementation of climate codes onto high-performance computers. See http://exascaleage.org/ber/ for more information.

54 ENVIRONMENTAL SCIENCES↗

DUNE Offline Computing Conceptual Design Report

This document describes Offline Software and Computing for the Deep Underground Neutrino Experiment (DUNE) experiment, in particular, the conceptual design of the offline computing needed to accomplish its physics goals. Our emphasis in this document is the development of the computing infrastructure needed to acquire, catalog, reconstruct, simulate and analyze the data from the DUNE experiment and its prototypes. In this effort, we concentrate on developing the tools and systems that facilitate the development and deployment of advanced algorithms. Rather than prescribing particular algorithms, our goal is to provide resources that are flexible and accessible enough to support creative software solutions as HEP computing evolves and to provide computing that achieves the physics goals of the DUNE experiment.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Computationally Guided Design of Multiple Impurities Tolerant Electrode (Final Report)

The current project was based on a combined experimental and computational approach, which can help recommend better cathode materials under multiple impurities conditions. The PI will mainly take in charge of experimental and computational thermodynamics of the selected cathode materials for the SOFC applications under multiple impurities. While the co-PI will run the electrochemical tests of the cathodes recommended and eventually the long-term degradation tests. At the end of the project, a multiple tolerant cathode material based on the combined experimental and computational approach will be recommended and the reliability of the commonly used accelerated testing will be evaluated. It will address multiple impurities poisoning effect of SO2, CO2, Cr and H2O on the LSM, LSCF and LNO cathodes by identifying the formation of the detrimental secondary phases by XRD, SEM and TEM techniques. And further recommended cathode material will be subjected to electrochemical testing and the most promising ones will be applied to long-term tests. The hybrid approach the PI proposed will not only be applied to the design of multiple impurities tolerant cathodes but will also be considered in the future oxygen electrode applications in SOECs or reversible SOCs. This hybrid computational and experimental approach includes four sections: 1) Investigation of single impurity poisoning on LSM, LSCF and LNO cathodes in the presence of SO2, CO2, Cr. In this section, LSM, LSCF cathodes from FuelCellMaterials and LNO cathodes from Sol-Gel synthesis will be heat-treated in the above single impurity. And the formation of the secondary phases as well as the corresponding simulations will be cross compared, which shows good agreement between each other. Meanwhile, the accelerated testing approach will be evaluated in these systems compared with the previous published work to understand the reliability of the approach. 2) Investigation of multiple impurities poisoning on LSM, LSCF and LNO cathodes in the presence of Cr+H2O, SO2+Cr and SO2+Cr+H2O conditions. We have also applied these 3 candidate cathodes under these multiple impurities’ conditions and the long-term degradation mechanism of the multiple impurities will be understood with the help of the combined experimental and computational approach. Meanwhile, the synergistic effect of those impurities will be compared with the individual ones in the same cathode system to further reveal the actual operating conditions. 3) Electrochemical testing and polarization of the recommended cathode. We have demonstrated very low polarization resistance in LSCF (core)-LSM (shell) electrodes using MSD process and analyzed impedance spectra using DRT analysis and confirming that the low polarization resistance in LSM infiltrated MSD cells is due to reduction in polarization resistance associated with O2-adsorption process. 4). Long-term degradation testing. We have developed a versatile MSD-based process to deposit various continuous coatings onto porous scaffolds and established baseline for longer term Cr-impurity testing in future projects.

36 MATERIALS SCIENCE↗

Building a Computational and Experimental Rapid Response Pipeline to Counter the Coronavirus Disease 2019 Outbreak and Emerging Biothreats

The COVID-19 pandemic underscored the promise of monoclonal antibody-based prophylactic and therapeutic drugs, especially where protective candidates can be rapidly identified or developed for emerging biothreats and escape variants. Current cutting-edge technologies for this purpose still rely on pathogen-exposed convalescent volunteers and a large screening effort to find a proverbial needle in a haystack. Computational design of protective antibodies based on pre-existing templates skips those requirements and allows for greater control over the breadth and target epitope, while also co-optimizing for potency and developability or other biophysical characteristics. We approached this problem by building and expanding an in vitro experimental rapid antibody production and characterization pipeline to support development of an autonomous, closed loop, active learning software system based on structural simulation and ground truth experimental data to design and evaluate antibody antigen interactions. Starting from early in the pandemic, we targeted SARS-CoV-2, the causative agent of COVID-19, by re-purposing neutralizing antibodies against SARS-CoV-1 that had been identified in the wake of that outbreak in the early 2000’s. We successfully re-targeted three different anti-SARS-CoV-1 antibodies to neutralize SARS-CoV-2 in vitro, where the antibodies were generated externally and tested through conventional binding and neutralization assays internally or with collaborators. As antibodies were identified from the blood of humans infected with SARS-CoV-2, we shifted to collaborate with academic partners to develop improved versions of their human-derived antibodies. This work reached its most important stage in rapid response to the emergence of the Omicron variant of concern (VOC) in late 2021. In a matter of weeks, enabled by on demand innovation to our screening pipeline, we computationally designed and experimentally characterized derivative antibodies of COV2-2130, one of two antibodies from Vanderbilt that form the basis of the AstraZeneca Evusheld prophylactic drug product. This drug product suffers a serious loss of efficacy against Omicron BA.1 and BA.1.1, the first Omicron strains. Due to tight integration of computational design and experimental evaluation, we were able to identify a pair of designs with potent neutralization of the main targets Omicron BA.1 and BA.1.1; but also the earlier Delta variant, and subsequent Omicron strains including BA.2, BA.4, BA.5, and BA.2.75, demonstrating that our multi-target design process can, by its nature, produce robust antibody designs that strictly improve over the parental antibody. These results, recognized by a 2022 Director’s Science and Technology award, have enabled the follow-on GUIDE program, to commence in FY23. While earlier design campaigns were substantially outsourced, we have engineered better and faster processes internally to better compliment, calibrate, and speed computational designs. As part of the follow-on GUIDE program, we will stand up a rapid and high-throughput antibody production and characterization facility staffed with the expertise and capabilities to foster our current collaboration across PLS and ENG as well as other partnerships toward computational design of biologics.

59 BASIC BIOLOGICAL SCIENCES↗

A cloud computing approach to massively-parallel distributed stochastic optimization with application to geomechanical reservoir characterization

Many search strategies used to optimize parameters during hydrologic model calibration are inherently limited in that simulations must be performed sequentially in order for the algorithm to converge. As a result, the overall time required to reach a solution increases linearly with the number of steps necessary. In contrast, sampling strategies that attempt to approximate the posterior distribution of the parameters do not require the model simulations to be run in sequence and therefore invite the use of a massively parallel approach across heterogeneous computing environments. We apply a cloud computing methodology to this problem where a head node running on Amazon Web Services continuously produces candidate models that are distributed to arbitrary compute environments to run the simulation, in our case Clemson’s Palmetto cluster computer. Thus the time required to obtain a sufficient number of samples to produce an adequate approximation of the posterior distribution of the parameters is limited by the number of available compute sites. Monte Carlo sampling of the posterior space would be duplicative and inefficient, thus we combine Latin hypercube methods with genetic algorithms to ensure that no large regions of the parameter space are left unexplored, and that high probability regions are investigated thoroughly. We independently assess the fit to different types of data sets without the need to construct a single objective function. Sets of Pareto optimal models are particularly valuable when the quality and information content of data is poorly known or conceptual model errors exist in our simulation. We illustrate our approach for a problem where in situ strain data are used to calibrate the parameters of an oil reservoir in the Avant oil field in Oklahoma. We use well injection and shut-in to stress a deep (500m) confined formation, and observe the geomechanical response using borehole strainmeters installed in the shallow subsurface (30m). These data were then used to calibrate the poroelastic properties of the reservoir and caprock along with the geometry of an elliptic channel associated with the formation. Using our approach we are able to identify issues with model error as well as substantial tradeoffs that occur within the parameters.

inversion, stochastic, geomechanics, poroelastic, ↗

EJFAT: Towards Intelligent Compute Destination Load Balancing

To handle increased data flow, Jefferson Lab (JLab) is partnering with ESnet for development of an AI/ML directed compute work Load Balancer (LB) of UDP streamed data. The LB is FPGA based featuring dynamically configurable, low latency and high throughput destination address switching. The LB provides integration of edge and core computing to support JLab experimental programs, the Electron-Ion Collider, as well as data centers of the future. In the ESnet/JLab FPGA Accelerated Transport (EJFAT) initiative, the function of the LB Data Plane (DP) is to redirect data streams to selectable (but unknown to sender) destination hosts based on current worload and within that host to destination ports as a function of sub- stream id. This effects hierarchical scaling, first across compute machines for processing over a series of events and second, across ports so different data source sub-streams may be assigned to different processors for further parallelization. The LB Control Plane (CP) programs the DP using compute farm telemetry to direct and balance workloads across a compute cluster as the operating conditions require. While Proportional/Integrative/Derivative (PID) controllers are often seen in similar applications, here we investigate the feasibility of a Reinforcement Learning (RL) based schedule manager running in the CP to provide dynamic updates to the DP scheduling policy.

Lawrence, David↗

Computationally Accelerated Discovery and Experimental Demonstration of High-Performance Materials for Advanced Solar Thermochemical Hydrogen Production

This project achieved its overarching goal of accelerating the discovery and validation of solar thermochemical hydrogen (STCH) materials through a tightly integrated approach that combined high-throughput computational screening, advanced machine learning (ML), and experimental testing. Guided by the objectives outlined in the Statement of Project Objectives (SOPO), our work fulfilled all major milestones across four technical tasks and delivered scientific breakthroughs and practical tools that significantly exceeded the original scope of the project. We began by addressing the challenge of predicting material phase stability through machine learning. A novel Python module was developed to generate thousands of meaningful features from composition, structure, and electronic properties, enabling rapid and reproducible ML model development. Using these tools, we trained a model to predict temperature-dependent Gibbs energies (G(T)) for inorganic crystalline materials with near-chemical accuracy—roughly 40 meV/atom—marking the first such descriptor of its kind. We also introduced a new machine-learned tolerance factor, τ, that accurately predicted perovskite formability with over 90% success, outperforming traditional heuristic models, such as the Goldschmidt tolerance factor. These capabilities allowed for rapid and accurate predictions of phase stability across a vast oxide composition space, setting the stage for high-throughput thermodynamic screening. Building on this foundation, we conducted an extensive computational screening of candidate STCH oxide materials. Over 1.1 million perovskite compositions were evaluated using the τ descriptor, leading to the identification of more than 27,000 predicted stable structures. Using density functional theory (DFT), we refined over 68,000 multinary perovskite structures and computed oxygen vacancy formation energies for over 1,300 ternary and double perovskites. These calculations enabled us to isolate compounds with redox behavior consistent with STCH requirements and resulted in a public dataset now hosted on the Materials Project. Recognizing that thermodynamic screening alone is insufficient, we addressed kinetic limitations by developing a suite of tools to estimate transition state (TS) energies for key redox reactions. We implemented a novel bounding approach that provides lower and upper estimates of TS energies with dramatically reduced computational cost, requiring less than 10% of the CPU time of a full nudged elastic band (NEB) calculation while maintaining high accuracy. This enabled rapid evaluation of over 200 reaction pathways across 90 materials. To further accelerate screening, we developed a SISSO-based ML model to predict diffusion barriers with a 96.7% success rate in classifying fast vs. slow materials, supporting a robust, data-driven framework for assessing redox kinetics. Experimental validation was critical to confirming the predictive power of our models. We synthesized and tested a wide array of candidate materials, including Mn-doped hercynite and several Gd- and La-based perovskites. Notably, Sr 0.4 Gd 0.6 Mn 0.6 Al 0.4 O 3 (SGMA) and Gd 0.5 La 0.5 Co 0.5 Fe 0.5 O 3 (GLCF) emerged as leading STCH materials, exhibiting robust redox cycling and high hydrogen yields exceeding 150 µmol H 2 /g per cycle. These materials also retained over 50% of their hydrogen productivity under high-conversion conditions (H 2 O:H 2 = 1333:1), demonstrating strong thermodynamic favorability and promising performance under industrially relevant scenarios. Additional candidates, such as La 2 MnNiO 6 (L2MN), were found to produce even higher yields than ceria under standard STCH conditions. Our collaborators at Sandia National Laboratories confirmed these findings using high-temperature X-ray diffraction and thermogravimetric analysis, observing stable phase evolution and reversible redox activity. In several respects, the project went beyond the goals initially outlined in the SOPO. We published 17 peer-reviewed articles, including a large dataset of over 66,000 theoretical perovskites and a new structure prediction method (SPuDS-DFT) that accurately identifies ground-state structures at a fraction of the cost of traditional DFT. We demonstrated that our machine-learned G(T) model offers accuracy rivaling quasiharmonic calculations while being orders of magnitude faster. In partnership with the Materials Project, we made our datasets openly available, providing a powerful new resource for the broader materials science community. The combined computational and experimental advances of this project represent a significant advance in STCH materials discovery. By creating a robust, generalizable, and open workflow for thermodynamic and kinetic screening, and validating key findings through synthesis and reactor testing, we have provided a practical and scalable pathway for the rapid identification of new redox-active materials. The tools, data, and materials developed under this project are already supporting ongoing research and have laid the groundwork for the next generation of solar fuel technologies.

08 HYDROGEN↗

Integrating DOE ASCR Computing into HEPCloud through GlideinWMS

Fermilab's HEPCloud facility expands the laboratory's computing capacity by provisioning resources beyond the local grid, using GlideinWMS to deliver pilots to where experiments such as CMS and DUNE run. The High-Performance Computing (HPC) facilities of the DOE Office of Advanced Scientific Computing Research (ASCR) are a growing part of that pool. HEPCloud currently provisions NERSC over SSH, but NERSC is moving away from that path as it adopts multi-factor authentication and directs automated access to its Superfacility API and the DOE Integrated Research Infrastructure (IRI) APIs. Maintaining and extending access across the ASCR ecosystem now requires provisioning through these interfaces. This work adds new pilot submission paths to GlideinWMS for the NERSC Superfacility API, IRI, and Globus Compute. Each uses the provisioning model GlideinWMS already applies to batch resources, so experiments can run on ASCR computing resources without changes to their existing workflows. This work finally presents a comparison of the paths to guide which interfaces are best suited for different workflows.

Majumder, Meghanto [U. Houston (main)]↗

Scalable Computation of 2D-Minkowski Sum of Arbitrary Non-Convex Domains: Modeling Flexibility in Energy Resources

The flexibility of active ($p$) and reactive power ($q$) consumption in distributed energy resources (DERs) can be represented as a (potentially non-convex) set of points in the $p$-$q$ plane. Modeling of the aggregated flexibility in a heterogeneous ensemble of DERs as a Minkowski sum (M-sum) is computationally intractable even for moderately sized populations. In this article, we propose a scalable method of computing the M-sum of the flexibility domains of a heterogeneous ensemble of DERs, which are allowed to be non-convex, non-compact. In particular, the proposed algorithm computes a guaranteed superset of the true M-sum, with desired accuracy. The worst-case complexity of the algorithm is computed. Special cases are considered, and it is shown that under certain scenarios, it is possible to achieve a complexity that is linear with the size of the ensemble. Numerical examples are provided by computing the aggregated flexibility of different mix of DERs under varying scenarios.

Kundu, Soumya↗

Quantum Solver Using Singular Value Decomposition for Computational Fluid Dynamics

Numerical solutions for fluid flow problems are challenging and have been focus of Computational Fluid Dynamics (CFD) research for past several decades. The advent of quantum computing promises exponential speedup in comparison to existing classical methods and alleviate computational constraints posed by CFD problems. Although solutions for most problems of interest in fluid dynamics using quantum computing are distant, recent advances in algorithms, software and hardware provide a path towards realizing this goal. Quantum linear solver algorithms (QLSA) such as Harrow–Hassidim–Lloyd (HHL) and Variational Quantum Linear Solver (VQLS) have been successfully implemented to solve for canonical problems such as Hele-Shaw flow. However, these algorithms still suffer to scale and address problems with ill-conditioned Jacobians. In the current paper, we alleviate these restrictions with a new quantum solver based on Singular Value Decomposition (SVD) and simulate flow past a 2D cylinder. The fidelity of the SVD based quantum solver in predicting the flow past 2D cylinder is computed along with an assessment of errors. Classical and quantum solutions for the flow are compared for different resolutions. Finally, we discuss variation in the solutions based on number of shots used.

Gottiparthi, Kalyan [ORNL] (ORCID:0000000213540255↗

Role of Computational Parameters on Predicting Self-Consistent Residual Stress and Distortion during Wire Arc Additive Manufacturing

Production of three-dimensional metallic parts through integration of an articulated robot and gas metal arc welding, also known as wire arc additive manufacturing (WAAM), can produce large-scale components with moderate geometrical complexity. This technology is particularly appealing due to its high deposition rates, scalability, and cost-effective feedstock compared to other AM processes. Despite its advantages, WAAM adoption is hindered by challenges in ensuring geometric conformity without extensive distortion, defect-free structures, and consistent mechanical properties. Finite element analysis (FEA) is often used to address the challenge of geometrical conformity. As the size of parts increases, the best practices for mesh size and temporal resolution known in the literature become computationally unviable. This research examined the effects of mesh and time-step resolutions during transient FEA of a large-scale (248 layers) metallic part. The impact of computational parameters on the thermal history, displacement, and residual stress distributions were evaluated. The results showed that predicted distortion was consistent across resolutions, while time-step length significantly affected predicted thermal history, and mesh size influenced residual stress distributions. To investigate this relationship further, directionally biased meshes were considered and analyzed. The results indicated that increasing mesh resolution perpendicular to the welding path yielded stress predictions that aligned closely with higher-resolution models while offering substantial computational savings. In conclusion, the significances of this research are related to verification and validation of WAAM models for widespread industrial adoption and pragmatic guidelines for optimizing computation parameters for balancing computational efficiency and predictive accuracy of residual stress and distortion.

Solsbee, Brandon [Univ. of Tennessee, Knoxville, T↗

Comparing computational times for simulations when using PBPK model template and stand-alone implementations of PBPK models

Introduction We previously developed a PBPK model template that consists of a single model “superstructure” with equations and logic found in many physiologically based pharmacokinetic (PBPK) models. Using the template, one can implement PBPK models with different combinations of structures and features. Methods To identify factors that influence computational time required for PBPK model simulations, we conducted timing experiments using various implementations of PBPK models for dichloromethane and chloroform, including template and stand-alone implementations, and simulating four different exposure scenarios. For each experiment, we measured the required computational time and evaluated the impacts of including various model features (e.g., number of output variables calculated) and incorporating various design choices (e.g., different methods for estimating blood concentrations). Results We observed that model implementations that treat body weight and dependent quantities as constant (fixed) parameters can result in a 30% time savings compared with options that treat body weight and dependent quantities as time-varying. We also observed that decreasing the number of state variables by 36% in our PBPK model template led to a decrease of 20–35% in computational time. Other factors, such as the number of output variables, the method for implementing conditional statements, and the method for estimating blood concentrations, did not have large impacts on simulation time. In general, simulations with PBPK model template implementations of models required more time than simulations with stand-alone implementations, but the flexibility and (human) time savings in preparing and reviewing a model implemented using the PBPK model template may justify the increases in computational time requirements. Conclusion Our findings concerning how PBPK model design and implementation decisions impact computational speed can benefit anyone seeking to develop, improve, or apply a PBPK model, with or without the PBPK model template.

Bernstein, Amanda S.↗

Advances in Computational Approaches for Estimating Passive Permeability in Drug Discovery

Passive permeation of cellular membranes is a key feature of many therapeutics. The relevance of passive permeability spans all biological systems as they all employ biomembranes for compartmentalization. A variety of computational techniques are currently utilized and under active development to facilitate the characterization of passive permeability. These methods include lipophilicity relations, molecular dynamics simulations, and machine learning, which vary in accuracy, complexity, and computational cost. This review briefly introduces the underlying theories, such as the prominent inhomogeneous solubility diffusion model, and covers a number of recent applications. Various machine-learning applications, which have demonstrated good potential for high-volume, data-driven permeability predictions, are also discussed. Due to the confluence of novel computational methods and next-generation exascale computers, we anticipate an exciting future for computationally driven permeability predictions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A viscous starter solution for shuttle flow field computations

A time dependent numerical procedure that calculates the viscous flow in the shock layer around the shuttle nose has been developed. It has been applied to the free stream conditions that may be encountered in the shuttle flight trajectory and found to be efficient and in satisfactory agreement with other steady and unsteady techniques. Two features associated with the present formulation are responsible for its successful applications. The first is that the flow field computation is made within the shock layer; the second is that the mapping of the computational region places proportionately more mesh points in the vicinity of the wall than in the remaining computational region. The numerical results may be used for low altitude flight to determine the edge conditions for a thin boundary layer, to provide initial boundary layer profiles for downstream boundary layer calculations, and to start supersonic computations. For high altitude flight, it may be used to determine the complete flow field in the nose region and also provide a starter solution for subsequent supersonic flow computations.

Li, C. P.↗

Applications of symbolic computing methods to the dynamic analysis of large systems

Since the symbolic computing language is very well suited to the operations with algebraic equations, techniques use the transfer function concept as a tool for the analysis of large linear dynamic systems. Techniques were coded in the experimental symbolic computer language FORMAC. The first of these approaches, REDUCE 1, establishes the techniques and a computer program to symbolically reduce arbitrary block diagrams associated with large systems for desired transfer functions. Symbolic closed form solutions are determined in several forms including an expanded form in terms of the driving frequencies and system constants. Programs are also written to numerically evaluate the symbolic solutions. A second computer program, REDUCE 2, is also based on the use of symbolic computing methods and was written to accommodate large engineering systems.

Lorenzo, C. F.↗