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Results for “differential transformation”

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NASA NTRS1989

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Meade, Andrew James, Jr.↗

DOE OSTI2020

Thermal Analysis of High Entropy Rare Earth Oxides

Phase transformations in multicomponent rare earth sesquioxides were studied by splat quenching from the melt, high temperature differential thermal analysis and synchrotron X-ray diffraction on laser-heated samples. Three compositions were prepared by the solution combustion method: (La,Sm,Dy,Er,RE) 2 O 3 , where all oxides are in equimolar ratios and RE is Nd or Gd or Y. After annealing at 800 °C, all powders contained mainly a phase of C-type bixbyite structure. After laser melting, all samples were quenched in a single-phase monoclinic B-type structure. Thermal analysis indicated three reversible phase transitions in the range 1900–2400 °C, assigned as transformations into A, H, and X rare earth sesquioxides structure types. Unit cell volumes and volume changes on C-B, B-A, and H-X transformations were measured by X-ray diffraction and consistent with the trend in pure rare earth sesquioxides. The formation of single-phase solid solutions was predicted by Calphad calculations. The melting point was determined for the (La,Sm,Dy,Er,Nd) 2 O 3 sample as 2456 ± 12 °C, which is higher than for any of constituent oxides. An increase in melting temperature is probably related to nonideal mixing in the solid and/or the melt and prompts future investigation of the liquidus surface in Sm 2 O 3 -Dy 2 O 3 , Sm 2 O 3 -Er 2 O 3 , and Dy 2 O 3 -Er 2 O 3 systems.

36 MATERIALS SCIENCE↗

NASA NTRS1992

A method of smooth bivariate interpolation for data given on a generalized curvilinear grid

A method of locally bicubic interpolation is presented for data given at the nodes of a two-dimensional generalized curvilinear grid. The physical domain is transformed to a computational domain in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. The metrics of the transformation are obtained by finite differences in the computational domain. Metric derivatives are determined by repeated application of the chain rule for partial differentiation. Given the metrics and the metric derivatives, the partial derivatives required to determine a locally bicubic interpolant can be estimated at each data point using finite differences in the computational domain. A bilinear transformation is used to analytically transform the individual quadrilateral cells in the physical domain into unit squares, thus allowing the use of simple formulas for bicubic interpolation.

Zingg, David W.↗

NASA NTRS1981

Products of multiple Fourier series with application to the multiblade transformation

A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.

Kunz, D. L.↗

DOE OSTI2023

Determination of the regeneration energy of direct air capture solvents/sorbents using calorimetric methods

Regeneration energy and recyclability are important parameters that dictate the viability of a CO 2 direct air capture (DAC) process. In this study, differential scanning calorimetry (DSC) is used in conjunction with thermogravimetric analysis (TGA) and Fourier Transform Infrared Spectroscopy (FTIR) to evaluate the regeneration energy required for CO 2 -loaded 3 M aqueous potassium sarcosinate (K-SAR) solvent and crystalline methyl-glyoxal-bisiminoguanidine (MGBIG) sorbent. Based on calorimetric measurements, for aqueous K-SAR, the sensible heat amounts to 1.5 GJ/tCO 2 and the enthalpy of desorption is estimated at 3.68 GJ/tCO 2 . The total energy of regeneration will also include the enthalpy of solvent vaporization, which will depend on the thermodynamic conditions and the level of regeneration. For MGBIG, the total regeneration energy required was measured at approximately 7.0 GJ/tCO 2 . Further, FTIR measurements were used to observe CO 2 and H 2 O release during the thermal regeneration process. For K-SAR, CO 2 release is seen to take place at temperatures greater than 80 °C and, for MGBIG, the CO 2 release takes place at temperatures greater than 100 °C. The moderate temperatures required for K-SAR and MGBIG regenerations compared to other DAC solvents/sorbents suggest that low-cost sources of heat, such as geothermal heat, could potentially be used for regeneration to drive down the cost of direct air capture.

42 ENGINEERING↗

DOE OSTI2022

Crystal Chemistry and Thermodynamics of HREE (Er, Yb) Mixing in a Xenotime Solid Solution

Rare earth elements (REEs), the 15 naturally occurring lanthanides plus yttrium and scandium, are ubiquitously used in modern life as they are critical components of many advanced devices and technologies. However, the demand for REEs is not equal, with the heavy rare earth elements (HREEs) having a higher demand. Xenotime (HREEPO 4 ) is an important HREE ore mineral and globally is an economical source of HREE. Most of the crystallographic and thermodynamic properties of xenotime endmembers have been elucidated by calorimetric, solubility, and high-pressure studies. Yet, in natural systems, endmembers are rarely encountered, and instead, REE solid solutions are more commonly observed. Here, we characterize the crystal chemistry, thermodynamics of HREE mixing, and high-temperature material behaviors and thermochemistry of a synthetic erbium (Er)-ytterbium (Yb) binary xenotime solid solution (Er (x) Yb (1-x) PO 4 ) using a suite of experimental techniques, including X-ray fluorescence spectroscopy, synchrotron X-ray powder diffraction implemented with Rietveld analysis, Fourier transform infrared spectroscopy coupled with attenuated total reflectance, Raman spectroscopy, thermogravimetric analysis coupled with differential scanning calorimetry, and high-temperature oxide melt drop solution calorimetry. Our results shed light on the formation of natural xenotimes and lay the foundation for their industrial applications as thermal coating materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Scalable Federated Learning for Scientific Foundation Models on Leadership-Class Systems

Federated learning (FL) at leadership-class HPC systems remains largely unexplored, despite growing interest in deploying federated workflows on modern HPC systems. This paper provides the first system-level empirical characterization of federated fine-tuning of pretrained foundation models on an exascale supercomputer under a multi-node deployment. Using up to 96 concurrent FL clients deployed across Frontier nodes, we study the impact of client scale, model size, data heterogeneity, partial participation, and differential privacy on runtime, communication overhead, and convergence stability. Our results show that pretrained transformer models remain robust to heterogeneity, client dropout, and privacy noise, while system efficiency degrades rapidly with scale as synchronizat and orchestration dominate runtime. We further demonstrate that system-aware execution strategies, including intra-node aggregation and early aggregation, significantly reduce wall-clock time without degrading model quality. These findings establish a practical performance baseline and inform the design of communication-efficient FL systems on leadership-class HPC platforms.

Kotevska, Olivera [ORNL] (ORCID:0000000316772243)↗

DOE OSTI2024

Synchrophasor-Based Zonal Current Differential Protection for Secondary Low Voltage Networks

This report describes an approach to utilizing phasor measurement unit (PMU) data from multiple Intelligent Electronics Devices (IEDs) in a low-voltage network to produce a differential scheme for protecting the medium-voltage feeder and low-voltage network transformers. The proposed protection scheme is designed and prototyped on a real-time automation controller. Its performance is evaluated using real-time controller hardware-in-the-loop simulation. Lab testing results indicate that the proposed protection scheme allows significant distributed energy resources (DER) backfeed and enables selective and fast protection of medium voltage feeders.

42 ENGINEERING↗

DOE OSTI2021

PNNL DataHub Project: Omics Lethal Human Viruses Project Profiling of the Host Response to Ebola Virus Infection, Processed Experimental Dataset Catalog

Ebola virus (EBOV) is high risk biological agent, classified as a Category A priority pathogen (Flaviviridae) by the National Institute of Allergy and Infectious Diseases (NIAID), known to cause hemorrhagic fever with high mortality rates in humans. Lethal host-pathogen invasion mechanisms and the cellular intricacies behind these fatal infections still remain unclear. The NIAID Modeling Host Responses to Understand Severe Human Virus Infections Research Program project (2013-2018) aimed to develop an improved comprehensive understanding of the host response to a suite of viruses causing lethal infections leveraging a systems biology approach. Herein, PNNL sub-projects provide a never before released comprehensive infectious disease collection of primary and secondary transformation multi-Omics data profiling a series of priority pathogen primary experimental studies for enhanced open-access to viral Omics datasets and project lifecycle metadata. Secondary host-pathogen viral dataset downloads contain one or more statistically processed (normalization data transformation) quantitative dataset collections resulting in qualitative expression analyses of primary host-pathogen experimental study designs. Leveraging unique high-resolution Omics capabilities for proteomics (P), metabolomics (M), lipidomics (L), and transcriptomics (T) dataset downloads each have a direct relationship to a primary sample submission corresponding to a specific Ebola virus [NCBITAXON:186536] (Zaire/Makona or Zaire/Mayinga) experimental infection study. Human host samples types include peripheral blood mononuclear cells isolated from blood plasma ["PBMC", BTO:0001025], human hepatoma carcinoma cells ["HUH", BTO:0001950], human umbilical vein endothelial cells ["HUVEC", BTO:0001949], immortalized human hepatocyte cells ["IHH", BTO:0006147], and human histiocytic lymphoma cells ["U937", BTO:0001412].

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

PNNL DataHub Project: Omics Lethal Human Viruses Project Profiling of the Host Response to Influenza A Virus Infection, Processed Experimental Dataset Catalog

Influenza A virus (IAV) is a high risk biological agent, classified as a Category C priority pathogen (Orthomyxoviridae) by the National Institute of Allergy and Infectious Diseases (NIAID), and is known to cause severe respiratory disease with high mortality rates in humans. Lethal host-pathogen invasion mechanisms and the cellular intricacies behind these fatal infections still remain unclear. The NIAID Modeling Host Responses to Understand Severe Human Virus Infections Research Program project (2013-2018) aimed to develop an improved comprehensive understanding of the host response to a suite of viruses causing lethal infections leveraging a systems biology approach. Herein, PNNL sub-projects provide a never before released comprehensive infectious disease collection of primary and secondary transformation multi-Omics data profiling a series of priority pathogen primary experimental studies for enhanced open-access to viral Omics datasets and project lifecycle metadata. Secondary host-pathogen viral dataset downloads contain one or more statistically processed (normalization data transformation) quantitative dataset collections resulting in qualitative expression analyses of primary host-pathogen experimental study designs. Leveraging unique high-resolution Omics capabilities for proteomics (P), metabolomics (M), lipidomics (L), and transcriptomics (T) dataset downloads each have a direct relationship to a primary sample submission corresponding to a specific Influenza A virus [NCBITAXON:11320] experimental infection study. Host sample types include human lung adenocarcinoma cells ["Calu-3", BTO:0002750] and whole mouse lung [BTO:0000763] tissue collections.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

PNNL DataHub Project: Omics Lethal Human Viruses Project Profiling of the Host Interferon-Stimulated Response to Virus Infection, Processed Experimental Dataset Catalog

Human Interferon (IFN) alpha, beta, and gamma participate in the body's natural immune response to lethal virus infection and disease.The NIAID Modeling Host Responses to Understand Severe Human Virus Infections Research Program project (2013 - 2018) aimed to develop an improved comprehensive understanding of the host response to a suite of viruses causing lethal infections leveraging a systems biology approach. The NIAID Modeling Host Responses to Understand Severe Human Virus Infections Research Program project (2013-2018) aimed to develop an improved comprehensive understanding of the host response to a suite of viruses causing lethal infections leveraging a systems biology approach. Herein, PNNL sub-projects provide a never before released comprehensive infectious disease collection of primary and secondary transformation multi-Omics data profiling a series of priority pathogen primary experimental studies for enhanced open-access to viral Omics datasets and project lifecycle metadata. Secondary host-associated viral dataset downloads contain one or more statistically processed (normalization data transformation) quantitative dataset collections resulting in qualitative expression analyses of primary host-pathogen experimental study designs. Transcriptomics (T) dataset downloads each have a direct relationship to a primary sample submission corresponding to a specific Human Interferon (IFN), interferon alpha (IFNα), interferon beta (IFNβ), and/or interferon gamma (IFNγ) stimulated response to an experimental virus infection treatment study. Host sample types include cerebellum ["CB", BTO:0000232], cortical neurons ["CN", BTO:0004102], cortex ["CT", BTO:0000233], dendritic cells ["DC", BTO:0002042], granule cell neurons ["GCN", BTO:0003393], lymph node ["LN", BTO:0000784], and serum ["SE", BTO:0001239] from mouse (Mus musculus) tissue collections.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Omics Lethal Human Viruses Project Profiling of the Host Response to MERS-CoV Infection, Processed Experimental Dataset Catalog

Middle East Respiratory Syndrome coronavirus (MERS-CoV) is classified as a Category C priority pathogen (Coronaviridae) by the National Institute of Allergy and Infectious Diseases (NIAID), and is known to cause severe respiratory disease with high mortality rates in humans. Lethal host-pathogen invasion mechanisms and the cellular intricacies behind these fatal infections still remain unclear. The NIAID Modeling Host Responses to Understand Severe Human Virus Infections Research Program project (2013-2018) aimed to develop an improved comprehensive understanding of the host response to a suite of viruses causing lethal infections leveraging a systems biology approach. Herein, PNNL sub-projects provide a never before released comprehensive infectious disease collection of primary and secondary transformation multi-Omics data profiling a series of priority pathogen primary experimental studies for enhanced open-access to viral Omics datasets and project lifecycle metadata. Secondary host-pathogen viral dataset downloads contain one or more statistically processed (normalization data transformation) quantitative dataset collections resulting in qualitative expression analyses of primary host-pathogen experimental study designs. Leveraging unique high-resolution Omics capabilities for proteomics (P), metabolomics (M), lipidomics (L), and transcriptomics (T) dataset downloads each have a direct relationship to a primary sample submission corresponding to a specific MERS-CoV [NCBITAXON:1335626] experimental infection study. Host sample types include human lung adenocarcinoma cells ["Calu-3", BTO:0002750], human bronchial epithelial cells ["Calu-3 clone 2B4"; BTO:0002022], primary human fibroblasts ["FB"; BTO:0000452], primary human airway epithelial cells ["HAE"; BTO:0005571], human microvascular endothelial cells ["HMVE"; BTO:0003123], and whole mouse lung [BTO:0000763] tissue collections.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

PNNL DataHub Project: Omics Lethal Human Viruses Project Profiling of the Host Response to West Nile Virus Infection, Processed Experimental Dataset Catalog

West Nile virus (WNV) is classified as a Category B priority pathogen (mosquito-borne Flavivirus) by the National Institute of Allergy and Infectious Diseases (NIAID), and are known to cause severe infections in humans where lethal host-associated mechanisms are not clearly defined. The NIAID Modeling Host Responses to Understand Severe Human Virus Infections Research Program project (2013 - 2018) aimed to develop an improved comprehensive understanding of the host response to a suite of viruses causing lethal infections leveraging a systems biology approach. The NIAID Modeling Host Responses to Understand Severe Human Virus Infections Research Program project (2013-2018) aimed to develop an improved comprehensive understanding of the host response to a suite of viruses causing lethal infections leveraging a systems biology approach. Herein, PNNL sub-projects provide a never before released comprehensive infectious disease collection of primary and secondary transformation multi-Omics data profiling a series of priority pathogen primary experimental studies for enhanced open-access to viral Omics datasets and project lifecycle metadata. Secondary host-pathogen viral dataset downloads contain one or more statistically processed (normalization data transformation) quantitative dataset collections resulting in qualitative expression analyses of primary host-pathogen experimental study designs. Leveraging unique high-resolution Omics capabilities for proteomics (P), metabolomics (M), lipidomics (L), and transcriptomics (T) dataset downloads each have a direct relationship to a primary sample submission corresponding a specific West Nile virus [NCBITAXON:11082] (WNV-NY99 382) experimental infection study. Host sample types include cerebellum ["CB", BTO:0000232], cortical neurons ["CN", BTO:0004102], cortex ["CT", BTO:0000233], dendritic cells ["DC", BTO:0002042], granule cell neurons ["GCN", BTO:0003393], lymph node ["LN", BTO:0000784], and serum ["SE", BTO:0001239] from mouse (Mus musculus) tissue collections.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

PNNL DataHub NIAID Program Project: Modeling Host Responses to Understand Severe Human Virus Infections, Multi-Omic Viral Dataset Catalog Collection

The National Institute of Allergy and Infectious Diseases (NIAID) "Modeling Host Responses to Understand Severe Human Virus Infections" program project was a highly integrated and comprehensive systems biology research core, funded by the National Institute of Health (U19AI106772) from 2013-06-01 to 2018-05-31, investigating the complex host response to category A, B, and C priority pathogen infections. Resulting project deliverables include an extensive comprehensive collections of linked primary and secondary transformation viral experimental infection data. Here we provide a never before released comprehensive infectious disease collection of primary and secondary transformation multi-Omics data profiling a series of priority pathogen primary experimental studies for enhanced open access to viral Omics lifecycle datasets and project metadata. Using a highly integrated and multidisciplinary approach, linked primary data and metadata supporting secondary normalization datasets, provide critical information necessary for research reproducibility and long-term preservation. Enabling on-demand data access for research community consumption and developer reuse, serves to support new mechanistic insights and discoveries into host-pathogen interactions for aiding future biohazard data preparedness efforts in emergency response to global health crises involving viral infection.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group

The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg (IWH) group. The group IWH connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the IWH group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

Synthesis and Characterization of Copolymers and Nanocomposites from Limonene, Styrene and Organomodified-Clay Using Ultrasonic Assisted Method

In the present work, we report a simple synthesis method for preparation of copolymers and nanocomposites from limonene and styrene using clay as a catalyst. The copolymerization reaction is carried out by using a proton exchanged clay as a catalyst called Mag-H+. The effect of temperature, reaction time and amount of catalyst were studied, and the obtained copolymer structure (lim-co-sty) is characterized by Fourier transform infrared spectroscopy (FT-IR), nuclear magnetic resonance spectroscopy (1H-NMR) and differential scanning calorimetry (DSC). The molecular weight of the obtained copolymer is determined by gel permeation chromatography (GPC) and is about 4500 g·mol−1. The (lim-co-sty/Mag 1%, 3%, 7% and 10% by weight of clay) nanocomposites were prepared through polymer/clay mixture in solution method using ultrasonic irradiation, in the presence of Mag-CTA+ as green nano-reinforcing filler. The Mag-CTA+ is organophilic silicate clay prepared through a direct exchange process, using cetyltrimethylammonuim bromide (CTAB). The prepared lim-co-sty/Mag nanocomposites have been extensively characterized by FT-IR spectroscopy, X-ray diffraction (XRD), scanning electronic microscopy (SEM) and transmission electronic microscopy (TEM). TEM analysis confirms the results obtained by XRD and clearly show that the obtained nanocomposites are partially exfoliated for the lower amount of clay (1% and 3% wt) and intercalated for higher amounts of clay (7% and 10% wt). Moreover, thermogravimetric analysis (TGA) indicated an enhancement of thermal stability of nanocomposites compared with the pure copolymer.

Derdar, Hodhaifa↗

DOE OSTI2023

Autonomous Inversion of In Situ Deformation Measurement Data for Injection-Induced Stress Change

Geologic carbon storage (GCS) is likely to play a key part of the global effort to dramatically reduce CO2 emissions and perhaps even reduce atmospheric CO2 concentrations through carbon negative operations. A critical part of effort to commercialize and widely deploy this technology is developing the capability to rapidly assimilate real-time monitoring data into a form that will enable site operators to make decisions to manage the safe and efficient operations. Two of the risks associate with GCS are the risk of inducing fractures in the sealing formations that can create leakage pathways and the risk of inducing earthquakes of sufficient magnitude to cause public concern, property damage, or safety risks. To properly manage these risks the site operator needs to know the initial state of stress, the change in stress induced by injection, and the relationship between operational parameters such as injection rate and pressure and the change in stress. Current methods of estimating the change in stress require choosing the type of constitutive model and the model parameters based on core, log, and geophysical data during the characterization phase, with little feedback from operational observations to validate or refine these choices. These characterization methods interrogate the geologic formations using length scales, loading rates or magnitudes that are quite different from those encountered by the actual storage system. It is shown that errors in the assumed constitutive response, even when informed by laboratory tests on core samples, are likely to be common, large, and underestimate the magnitude of stress change caused by injection. Recent advances in borehole-based strain instruments and borehole and surface-based tilt and displacement instruments have now enabled monitoring of the deformation of the storage system throughout its operational lifespan. This data can enable validation and refinement of the knowledge of the geomechanical properties and state of the system, but brings with it a challenge to transform the raw data into actionable knowledge. We demonstrate a method that uses automatic differentiation and a finite-element based geomechanical model perform a gradient-based deterministic inversion of geomechanical monitoring data. This approach allows autonomous integration of the instrument data without the need for time consuming manual interpretation and selection of updated model parameters. Furthermore, only isotropic linear elasticity is considered in this paper, the approach presented is very flexible as to what type of geomechanical constitutive response can be used. The approach is easily adaptable to nonlinear physics-based constitutive models to account for common rock behaviors such as creep and plasticity. The approach also enables training of machine learning-based constitutive models by allowing back propagation of errors through the finite element calculations. This enables strongly enforcing known physics, such as conservation of momentum and continuity, while allowing data-driven models to learn the truly unknown physics such as the constitutive or petrophysical responses.

Burghardt, Jeffrey A.↗

NASA NTRS1973

Numerical calculation of the three dimensional transonic flow over a yawed wing.

Results are presented of calculations of the three dimensional steady transonic flow over a finite yawed wing. The full potential flow equation is solved in a transformed coordinate system which permits the boundary conditions to be satisfied exactly. The correct differential properties are enforced by rotating the difference scheme to conform with the flow direction, and fast convergence is assured by simulating a time dependent equation designed to settle quickly to a steady state. Computed lift drag ratios are consistent with the results of wind tunnel tests of a yawed wing conducted by R. T. Jones (1972).-

Jameson, A.↗