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At least 991 records · Page 55

Using Remotely Sensed Data and Watershed and Hydrodynamic Models to Evaluate the Effects of Land Cover Land Use Change on Aquatic Ecosystems in Mobile Bay, AL

Alabama coastal systems have been subjected to increasing pressure from a variety of activities including urban and rural development, shoreline modifications, industrial activities, and dredging of shipping and navigation channels. The impacts on coastal ecosystems are often observed through the use of indicator species. One such indicator species for aquatic ecosystem health is submerged aquatic vegetation (SAV). Watershed and hydrodynamic modeling has been performed to evaluate the impact of land cover land use (LCLU) change in the two counties surrounding Mobile Bay (Mobile and Baldwin) on SAV stressors and controlling factors (temperature, salinity, and sediment) in the Mobile Bay estuary. Watershed modeling using the Loading Simulation Package in C++ (LSPC) was performed for all watersheds contiguous to Mobile Bay for LCLU scenarios in 1948, 1992, 2001, and 2030. Remotely sensed Landsat-derived National Land Cover Data (NLCD) were used in the 1992 and 2001 simulations after having been reclassified to a common classification scheme. The Prescott Spatial Growth Model was used to project the 2030 LCLU scenario based on current trends. The LSPC model simulations provided output on changes in flow, temperature, and sediment for 22 discharge points into the estuary. These results were inputted in the Environmental Fluid Dynamics Computer Code (EFDC) hydrodynamic model to generate data on changes in temperature, salinity, and sediment on a grid throughout Mobile Bay and adjacent estuaries. The changes in the aquatic ecosystem were used to perform an ecological analysis to evaluate the impact on SAV habitat suitability. This is the key product benefiting the Mobile Bay coastal environmental managers that integrates the influences of temperature, salinity, and sediment due to LCLU driven flow changes with the restoration potential of SAVs. Data products and results are being integrated into NOAA s EcoWatch and Gulf of Mexico Data Atlas online systems for dissemination to coastal resource managers and stakeholders.

Al-Hamdan, Mohammad Z.↗

Using Remotely Sensed Data and Watershed and Hydrodynamic Models to Evaluate the Effects of Land Cover Land Use Change on Aquatic Ecosystems in Mobile Bay, AL

Alabama coastal systems have been subjected to increasing pressure from a variety of activities including urban and rural development, shoreline modifications, industrial activities, and dredging of shipping and navigation channels. The impacts on coastal ecosystems are often observed through the use of indicator species. One such indicator species for aquatic ecosystem health is submerged aquatic vegetation (SAV). Watershed and hydrodynamic modeling has been performed to evaluate the impact of land cover land use (LCLU) change in the two counties surrounding Mobile Bay (Mobile and Baldwin) on SAV stressors and controlling factors (temperature, salinity, and sediment) in the Mobile Bay estuary. Watershed modeling using the Loading Simulation Package in C++ (LSPC) was performed for all watersheds contiguous to Mobile Bay for LCLU scenarios in 1948, 1992, 2001, and 2030. Remotely sensed Landsat-derived National Land Cover Data (NLCD) were used in the 1992 and 2001 simulations after having been reclassified to a common classification scheme. The Prescott Spatial Growth Model was used to project the 2030 LCLU scenario based on current trends. The LSPC model simulations provided output on changes in flow, temperature, and sediment for 22 discharge points into the estuary. These results were inputted in the Environmental Fluid Dynamics Computer Code (EFDC) hydrodynamic model to generate data on changes in temperature, salinity, and sediment on a grid throughout Mobile Bay and adjacent estuaries. The changes in the aquatic ecosystem were used to perform an ecological analysis to evaluate the impact on SAV habitat suitability. This is the key product benefiting the Mobile Bay coastal environmental managers that integrates the influences of temperature, salinity, and sediment due to LCLU driven flow changes with the restoration potential of SAVs. Data products and results are being integrated into NOAA s EcoWatch and Gulf of Mexico Data Atlas online systems for dissemination to coastal resource managers and stakeholders. Objective 1: Develop and utilize Land Use scenarios for Mobile and Baldwin Counties, AL as input to models to predict the affects on water properties (temperature,salinity,)for Mobile Bay through 2030. Objective 2: Evaluate the impact of land use change on seagrasses and SAV in Mobile Bay. Hypothesis: Urbanization will significantly increase surface flows and impact salinity and temperature variables that effect seagrasses and SAVs.

Al-Hamdan, Mohammad↗

Application of Rotor Disk Model in the Overflow CFD Code

To reduce the complexity and to reduce the cost of turnaround time of simulating unsteady flows of rotating blades with moving overset grids, amid-fidelity option is provided in the OVERFLOW computational fluid dynamics analysis to model rotors and propellers as infinitely thin disks. The effect of the flow through the disk is represented by the momentum source terms in the governing Navier-Stokes equations. The model is loosely coupled with the rotorcraft comprehensive analysis CAMRADII. A brief description of the coupling algorithm is provided. Simulations of a single rotor and multiple rotors are shown, including comparisons with measurements and with the full rotor where all blades are modeled, and unsteady simulation performed with moving grids for rotating geometry,

ARMD↗

A High Angle of Attack Inviscid Shuttle Orbiter Computation

An accurate description of the aerothermal environment is required to minimize the weight of the Thermal Protection System required on the leeside of winged reentry vehicles. The inability of ground-test facilities to reproduce the high enthalpy, separated flow present during reentry flight conditions, coupled with the prohibitive expense of flight tests, leads to the use of an analytical method - namely Computational Fluid Dynamics (CFD) - to describe the flow. While the ultimate goal of this work is to accurately predict the leeside flow and its associated thermal environment, an essential and reasonable first step towards that goal is a comparison of pressure predictions by a code with wind-tunnel data. Until such CFD pressure predictions agree with wind-tunnel test cases, there is little hope of accurately predicting the thermal environment at flight conditions. Thus, the objective of this study is to compare the pressure distributions predicted by inviscid, perfect gas CFD to Shuttle Orbiter wind-tunnel data and to address any significant issues encountered during the computation. While flight data is available for the Shuttle Orbiter, a wind-tunnel case is chosen for this study to allow a tractable problem for preliminary investigation. A wind-tunnel case allows the perfect gas assumption for the flow chemistry. This provides a significant computational savings over a several species finite-rate chemistry model which would be necessary if high-temperature effects present at flight conditions were to be included. In addition, by concentrating on the surface pressures, the analysis need only consider inviscid flow for general evaluation of the code capability. This further reduces the computational expense due to the absence of viscous terms and the associated decrease in the number of points required for the computational grid. Previous computational efforts (such as STEIN and HALIS) have been directed toward the windward surface quantities, primarily due to restrictions in treating either the winged geometry or its associated subsonic regions at high angle of attack. The code used for this study, the LAURA (Langley Aerothermodynamic Upwind Relaxation Algorithm) code of Gnoffo, represents a state-of-the-art code for computing the flow over complex configurations at hypersonic speeds. In the study, the LAURA code is applied to a wind-tunnel condition to initiate the assessment of the code's ability to predict the flow over a relatively complex hypersonic vehicle at high angles of attack. This presentation is used to highlight the pertinent results of a more detailed investigation of the inviscid calculation over the Shuttle Orbiter with the LAURA code.

William L. Kleb↗

The efficient solution of transonic wing flow fields

An evaluation of the transonic-wing-analysis computer code TWING is presented. TWING utilizes a fully implicit, approximate-factorization iteration scheme to solve the full-potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations have been analyzed, and comparisons of computed results have been made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative, full-potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations, including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Holst, T. L.↗

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. Here, this study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Toward the routine aerodynamic analysis of complex configurations

An evaluation is made of the ability of the TranAir CFD code to routinely compute the aerodynamic characteristics of complex subsonic and supersonic aircraft configurations. TranAir solves the full-potential equation for transonic flow about completely arbitrary geometries, using the surface-paneling PanAir technique in geometry definition. The uniform global grid may be locally refined in regions where flow properties are rapidly changing, such as regions where shocks arise, and around wing leading edges. Unlike panel method codes, TranAir solutions are not undermined by small-perturbation assumptions. Illustrative results are presented for such configurations as the F-16A with wingtip-mounted missiles and underwing fuel tanks, a generic fighter configuration, and a model of NASA-Ames' 12-ft Pressure Wind Tunnel.

Madson, Michael D.↗

Task 7: ADPAC User's Manual

The overall objective of this study was to develop a 3-D numerical analysis for compressor casing treatment flowfields. The current version of the computer code resulting from this study is referred to as ADPAC (Advanced Ducted Propfan Analysis Codes-Version 7). This report is intended to serve as a computer program user's manual for the ADPAC code developed under Tasks 6 and 7 of the NASA Contract. The ADPAC program is based on a flexible multiple- block grid discretization scheme permitting coupled 2-D/3-D mesh block solutions with application to a wide variety of geometries. Aerodynamic calculations are based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. Steady flow predictions are accelerated by a multigrid procedure. An iterative implicit algorithm is available for rapid time-dependent flow calculations, and an advanced two equation turbulence model is incorporated to predict complex turbulent flows. The consolidated code generated during this study is capable of executing in either a serial or parallel computing mode from a single source code. Numerous examples are given in the form of test cases to demonstrate the utility of this approach for predicting the aerodynamics of modem turbomachinery configurations.

Hall, E. J.↗

UNH TDP - Voltsys Raw Data and Processing Scripts - Fall 2021

This submission contains raw Voltsys rectifier data and processing scripts associated with MHKDR submission 394 (UNH TDP - Concurrent Measurements of Inflow, Power Performance, and Loads for a Grid-Synchronized Vertical Axis Cross-Flow Turbine Operating in a Tidal Estuary, DOI: 10.15473/1973860) from the University of New Hampshire and Atlantic Marine Energy Center (AMEC) turbine deployment platform. The user is directed to the MHKDR submission 394 for relevant context and detail of this deployment; see link below. The 394_READ_ME file here provides the description from that submission for quick reference. The READ_ME file for this specific instrument from the 394 submission is also available here. This submission contains a zipped folder structure containing raw data in its original format and MATLAB (2019a) processing scripts used to process and manipulate the data into its final form. The final data products are submitted in the 394 submission.

16 TIDAL AND WAVE POWER↗

Parallelization of the Physical-Space Statistical Analysis System (PSAS)

Atmospheric data assimilation is a method of combining observations with model forecasts to produce a more accurate description of the atmosphere than the observations or forecast alone can provide. Data assimilation plays an increasingly important role in the study of climate and atmospheric chemistry. The NASA Data Assimilation Office (DAO) has developed the Goddard Earth Observing System Data Assimilation System (GEOS DAS) to create assimilated datasets. The core computational components of the GEOS DAS include the GEOS General Circulation Model (GCM) and the Physical-space Statistical Analysis System (PSAS). The need for timely validation of scientific enhancements to the data assimilation system poses computational demands that are best met by distributed parallel software. PSAS is implemented in Fortran 90 using object-based design principles. The analysis portions of the code solve two equations. The first of these is the "innovation" equation, which is solved on the unstructured observation grid using a preconditioned conjugate gradient (CG) method. The "analysis" equation is a transformation from the observation grid back to a structured grid, and is solved by a direct matrix-vector multiplication. Use of a factored-operator formulation reduces the computational complexity of both the CG solver and the matrix-vector multiplication, rendering the matrix-vector multiplications as a successive product of operators on a vector. Sparsity is introduced to these operators by partitioning the observations using an icosahedral decomposition scheme. PSAS builds a large (approx. 128MB) run-time database of parameters used in the calculation of these operators. Implementing a message passing parallel computing paradigm into an existing yet developing computational system as complex as PSAS is nontrivial. One of the technical challenges is balancing the requirements for computational reproducibility with the need for high performance. The problem of computational reproducibility is well known in the parallel computing community. It is a requirement that the parallel code perform calculations in a fashion that will yield identical results on different configurations of processing elements on the same platform. In some cases this problem can be solved by sacrificing performance. Meeting this requirement and still achieving high performance is very difficult. Topics to be discussed include: current PSAS design and parallelization strategy; reproducibility issues; load balance vs. database memory demands, possible solutions to these problems.

Larson, J. W.↗

Computation of asymmetric supersonic flows around cones at large incidence

The Schiff-Steger parabolized Navier-Stokes (PNS) code has been modified to allow computation of conical flowfields around cones at high incidence. The improved algorithm of Degani and Schiff has been incorporated with the PNS code. This algorithm adds the cross derivative and circumferential viscous terms to the original PNS code and modifies the algebraic eddy viscosity turbulence model to take into account regions of so called cross-flow separation. Assuming the flowfield is conical (but not necessarily symmetric) a marching stepback procedure is used: the solution is marched one step downstream using improved PNS code and the flow variables are then scaled to place the solution back to the original station. The process is repeated until no change in the flow variables is observed with further marching. The flow variables are then constant along rays of the flowfield. The experiments obtained by Bannik and Nebbeling were chosen as a test case. In these experiments a cone of 7.5 deg. half angle at Mach number 2.94 and Reynolds number 1.372 x 10(7) was tested up 34 deg. angle of attack. At high angle of attack nonconical asymmetric leeward side vortex patterns were observed. In the first set of computations, using an earlier obtained solution of the above cone for angle of attack of 22.6 deg. and at station x=0.5 as a starting solution, the angle of attack was gradually increased up to 34 deg. During this procedure the grid was carfully adjusted to capture the bow shock. A stable, converged symmetric solution was obtained. Since the numerical code converged to a symmetric solution which is not the physical one, the stability was tested by a random perturbation at each point. The possible effect of surface roughness or non perfect body shape was also investigated. It was concluded that although the assumption of conical viscous flows can be very useful for certain cases, it can not be used for the present case. Thus the second part of the investigation attempted to obtain a marching (in space) solution with the PNS method using the conical solution as initial data. Finally, the solution of the full Navier-Stokes equations was carried out.

Degani, David↗

Interference Lattice-based Loop Nest Tilings for Stencil Computations

A common method for improving performance of stencil operations on structured multi-dimensional discretization grids is loop tiling. Tile shapes and sizes are usually determined heuristically, based on the size of the primary data cache. We provide a lower bound on the numbers of cache misses that must be incurred by any tiling, and a close achievable bound using a particular tiling based on the grid interference lattice. The latter tiling is used to derive highly efficient loop orderings. The total number of cache misses of a code is the sum of (necessary) cold misses and misses caused by elements being dropped from the cache between successive loads (replacement misses). Maximizing temporal locality is equivalent to minimizing replacement misses. Temporal locality of loop nests implementing stencil operations is optimized by tilings that avoid data conflicts. We divide the loop nest iteration space into conflict-free tiles, derived from the cache miss equation. The tiling involves the definition of the grid interference lattice an equivalence class of grid points whose images in main memory map to the same location in the cache-and the construction of a special basis for the lattice. Conflicts only occur on the boundaries of the tiles, unless the tiles are too thin. We show that the surface area of the tiles is bounded for grids of any dimensionality, and for caches of any associativity, provided the eccentricity of the fundamental parallelepiped (the tile spanned by the basis) of the lattice is bounded. Eccentricity is determined by two factors, aspect ratio and skewness. The aspect ratio of the parallelepiped can be bounded by appropriate array padding. The skewness can be bounded by the choice of a proper basis. Combining these two strategies ensures that pathologically thin tiles are avoided. They do not, however, minimize replacement misses per se. The reason is that tile visitation order influences the number of data conflicts on the tile boundaries. If two adjacent tiles are visited successively, there will be no replacement misses on the shared boundary. The iteration space may be covered with pencils larger than the size of the cache while avoiding data conflicts if the pencils are traversed by a scanning-face method. Replacement misses are incurred only on the boundaries of the pencils, and the number of misses is minimized by maximizing the volume of the scanning face, not the volume of the tile. We present an algorithm for constructing the most efficient scanning face for a given grid and stencil operator. In two dimensions it is based on a continued fraction algorithm. In three dimensions it follows Voronoi's successive minima algorithm. We show experimental results of using the scanning face, and compare with canonical loop orderings.

VanderWijngaart, Rob F.↗

Development of an implicit electromagnetic capability for a hybrid gyrokinetic ion-fluid electron model

Here we report on the development and implementation of a hybrid kinetic ion–fluid electron model for electromagnetic COGENT simulations of edge plasmas. COGENT is a finite-volume gyrokinetic code that employs a locally field-aligned coordinate system combined with a mapped multi-block grid technology to handle strongly anisotropic edge plasma turbulence. The simulation model involves the long-wavelength limit of the ion gyrokinetic equation coupled to the vorticity and Ohm's law equations for the electromagnetic field perturbations. In order to handle the fast Alfvén wave time scales, an implicit-explicit time integration approach with a physics-based preconditioner is used. The model is successfully applied to the simulations of ion-scale resistive-drift ballooning turbulence in a toroidal annulus geometry. Substantial speed-up over a fully explicit time integration approach is observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

AGILE GETRS

AGILE GETRS provides an optimized implementation of DETRS that is faster than vendor optimized libraries for small (< 4000) problem sizes. These small problems sizes are of interest to researchers in the Grid Research Integration and Deployment Center (GRID-C) researching real-time power electronics simulations. In addition to our implementation of DETRS, this code provides a test using Google Benchmark which generates matrices of various sizes, fills them with random numbers, runs GETRS, verifies the solution is correct and reports average runtime and other performance metrics.

Hahn, Steven [Oak Ridge National Laboratory (ORNL)↗

Transient Physical Modelling for the Coupling of a High Temperature Gas Reactor with Thermal Energy Storage

Improving the flexibility of nuclear reactors to meet fluctuating demand on grids with high renewable energy generation penetration is key to improving reactor economics. Economic optimization using the code HERON gives maximum profit of coupling high temperature gas reactors (HTGRs) to thermal energy storage (TES) systems in the configuration shown in Figure 1 when following the demand in Figure 3. We look to model the physics of operation for a HTGR-TES using the HYBRID library in the code Modelica.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

INTEGRATE - Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements

The INTEGRATE (Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements) project is developing a new inverse-design capability for the aerodynamic design of wind turbine rotors using invertible neural networks. This AI-based design technology can capture complex non-linear aerodynamic effects while being 100 times faster than design approaches based on computational fluid dynamics. This project enables innovation in wind turbine design by accelerating time to market through higher-accuracy early design iterations to reduce the levelized cost of energy. INVERTIBLE NEURAL NETWORKS Researchers are leveraging a specialized invertible neural network (INN) architecture along with the novel dimension-reduction methods and airfoil/blade shape representations developed by collaborators at the National Institute of Standards and Technology (NIST) learns complex relationships between airfoil or blade shapes and their associated aerodynamic and structural properties. This INN architecture will accelerate designs by providing a cost-effective alternative to current industrial aerodynamic design processes, including: - Blade element momentum (BEM) theory models: limited effectiveness for design of offshore rotors with large, flexible blades where nonlinear aerodynamic effects dominate - Direct design using computational fluid dynamics (CFD): cost-prohibitive - Inverse-design models based on deep neural networks (DNNs): attractive alternative to CFD for 2D design problems, but quickly overwhelmed by the increased number of design variables in 3D problems AUTOMATED COMPUTATIONAL FLUID DYNAMICS FOR TRAINING DATA GENERATION - MERCURY FRAMEWORK The INN is trained on data obtained using the University of Marylands (UMD) Mercury Framework, which has with robust automated mesh generation capabilities and advanced turbulence and transition models validated for wind energy applications. Mercury is a multi-mesh paradigm, heterogeneous CPU-GPU framework. The framework incorporates three flow solvers at UMD, 1) OverTURNS, a structured solver on CPUs, 2) HAMSTR, a line based unstructured solver on CPUs, and 3) GARFIELD, a structured solver on GPUs. The framework is based on Python, that is often used to wrap C or Fortran codes for interoperability with other solvers. Communication between multiple solvers is accomplished with a Topology Independent Overset Grid Assembler (TIOGA). NOVEL AIRFOIL SHAPE REPRESENTATIONS USING GRASSMAN SPACES We developed a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation as an analytic generative model, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data , (ii) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes. TECHNOLOGY TRANSFER DEMONSTRATION - COUPLING WITH NREL WISDEM Researchers have integrated the inverse-design tool for 2D airfoils (INN-Airfoil) into WISDEM (Wind Plant Integrated Systems Design and Engineering Model), a multidisciplinary design and optimization framework for assessing the cost of energy, as part of tech-transfer demonstration. The integration of INN-Airfoil into WISDEM allows for the design of airfoils along with the blades that meet the dynamic design constraints on cost of energy, annual energy production, and the capital costs. Through preliminary studies, researchers have shown that the coupled INN-Airfoil + WISDEM approach reduces the cost of energy by around 1% compared to the conventional design approach. This page will serve as a place to easily access all the publications from this work and the repositories for the software developed and released through this pr...

aerodynamics↗

Experiences with explicit finite-difference schemes for complex fluid dynamics problems on STAR-100 and CYBER-203 computers

Several two- and three-dimensional external and internal flow problems solved on the STAR-100 and CYBER-203 vector processing computers are described. The flow field was described by the full Navier-Stokes equations which were then solved by explicit finite-difference algorithms. Problem results and computer system requirements are presented. Program organization and data base structure for three-dimensional computer codes which will eliminate or improve on page faulting, are discussed. Storage requirements for three-dimensional codes are reduced by calculating transformation metric data in each step. As a result, in-core grid points were increased in number by 50% to 150,000, with a 10% execution time increase. An assessment of current and future machine requirements shows that even on the CYBER-205 computer only a few problems can be solved realistically. Estimates reveal that the present situation is more storage limited than compute rate limited, but advancements in both storage and speed are essential to realistically calculate three-dimensional flow.

Kumar, A.↗

Interacting boundary-layer solutions for laminar separated flow past airfoils

Numerical solutions of the interacting laminar boundary layer equations are presented for two symmetric airfoils at zero incidence: the NACA 0012 and the NACA 66 sub 3-108 airfoils. The potential flow was computed using Carlson's code, and viscous interaction was treated following a Hilbert integral scheme due to Veldman. Effects of various grid parameters are studied, and pressure and skin friction distributions are compared at several Reynolds numbers. For the NACA 0012 airfoil, Reynolds number is varied from a value just below separation (R sub N = 3000) to a value for which extensive separation occurs (R sub N = 100,000). For the 66 sub 3-018 airfoil, results are given at intermediate values (R sub N - 10,000 and 40,000). The method fails to converge for greater values of Reynolds number, corresponding to the development of very thin well separated shear layers where transition to turbulence would occur naturally.

Burggraf, O. R.↗