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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Using Flow Regime Lightning and Sounding Climatologies to Initialize Gridded Lightning Threat Forecasts for East Central Florida

Each morning, the forecasters at the National Weather Service in Melbourne, FL (NWS MLB) produce an experimental cloud-to-ground (CG) lightning threat index map for their county warning area (CWA) that is posted to their web site (httl://www.srh.weather.gov/mlb/ghwo/lightning.shtml) . Given the hazardous nature of lightning in East Central Florida, especially during the warm season months of May September, these maps help users factor the threat of lightning, relative to their location, into their daily plans. The maps are color-coded in five levels from Very Low to Extreme, with threat level definitions based on the probability of lightning occurrence and the expected amount of CG activity. On a day in which thunderstorms are expected, there are typically two or more threat levels depicted spatially across the CWA. The locations of relative lightning threat maxima and minima often depend on the position and orientation of the low-level ridge axis, forecast propagation and interaction of sea/lake/outflow boundaries, expected evolution of moisture and stability fields, and other factors that can influence the spatial distribution of thunderstorms over the CWA. The lightning threat index maps are issued for the 24-hour period beginning at 1200 UTC each day with a grid resolution of 5 km x 5 km. Product preparation is performed on the AWIPS Graphical Forecast Editor (GFE), which is the standard NWS platform for graphical editing. Until recently, the forecasters created each map manually, starting with a blank map. To improve efficiency of the forecast process, NWS MLB requested that the Applied Meteorology Unit (AMU) create gridded warm season lightning climatologies that could be used as first-guess inputs to initialize lightning threat index maps. The gridded values requested included CG strike densities and frequency of occurrence stratified by synoptic-scale flow regime. The intent was to improve consistency between forecasters while allowing them to focus on the mesoscale detail of the forecast. Several studies took place at the Florida State University (FSU) and NWS Tallahassee (TAE) in which they created daily flow regimes using Florida 1200 UTC synoptic soundings and CG strike densities, or number of strikes per specified area. The soundings used to determine the flow regimes were taken at Miami (MIA), Tampa (TBW), and Jacksonville (JAX), FL, and the lightning data for the strike densities came from the National Lightning Detection Network (NLDN). The densities were created on a 2.5 km x 2.5 km grid for every hour of every day during the warm seasons in the years 1989-2004. The grids encompass an area that includes the entire state of Florida and adjacent Atlantic and Gulf of Mexico waters. Personnel at FSU and NWS TAE provided this data and supporting software for the work performed by the AMU.

Lambert, Winifred↗
NASA NTRS2005

Using Cloud-to-Ground Lightning Climatologies to Initialize Gridded Lightning Threat Forecasts for East Central Florida

Each morning, the forecasters at the National Weather Service in Melbourn, FL (NWS MLB) produce an experimental cloud-to-ground (CG) lightning threat index map for their county warning area (CWA) that is posted to their web site (http://www.srh.weather.gov/mlb/ghwo/lightning.shtml) . Given the hazardous nature of lightning in central Florida, especially during the warm season months of May-September, these maps help users factor the threat of lightning, relative to their location, into their daily plans. The maps are color-coded in five levels from Very Low to Extreme, with threat level definitions based on the probability of lightning occurrence and the expected amount of CG activity. On a day in which thunderstorms are expected, there are typically two or more threat levels depicted spatially across the CWA. The locations of relative lightning threat maxima and minima often depend on the position and orientation of the low-level ridge axis, forecast propagation and interaction of sea/lake/outflow boundaries, expected evolution of moisture and stability fields, and other factors that can influence the spatial distribution of thunderstorms over the CWA. The lightning threat index maps are issued for the 24-hour period beginning at 1200 UTC (0700 AM EST) each day with a grid resolution of 5 km x 5 km. Product preparation is performed on the AWIPS Graphical Forecast Editor (GFE), which is the standard NWS platform for graphical editing. Currently, the forecasters create each map manually, starting with a blank map. To improve efficiency of the forecast process, NWS MLB requested that the Applied Meteorology Unit (AMU) create gridded warm season lightning climatologies that could be used as first-guess inputs to initialize lightning threat index maps. The gridded values requested included CG strike densities and frequency of occurrence stratified by synoptic-scale flow regime. The intent is to increase consistency between forecasters while enabling them to focus on the mesoscale detail of the forecast, ultimately benefiting the end-users of the product. Several studies took place at the Florida State University (FSU) and NWS Tallahassee (TAE) for which they created daily flow regimes using Florida 1200 UTC synoptic soundings and CG strike densities from National Lightning Detection Network (NLDN) data. The densities were created on a 2.5 km x 2.5 km grid for every hour of every day during the warm seasons in the years 1989-2004. The grids encompass an area that includes the entire state of Florida and adjacent Atlantic and Gulf of Mexico waters. Personnel at the two organizations provided this data and supporting software for the work performed by the AMU. The densities were first stratified by flow regime, then by time in 1-, 3-, 6-, 12-, and 24-hour increments while maintaining the 2.5 km x 2.5 km grid resolution. A CG frequency of occurrence was calculated for each stratification and grid box by counting the number of days with lightning and dividing by the total number of days in the data set. New CG strike densities were calculated for each stratification and grid box by summing the strike number values over all warm seasons, then normalized by dividing the summed values by the number of lightning days. This makes the densities conditional on whether lightning occurred. The frequency climatology values will be used by forecasters as proxy inputs for lightning prObability, while the density climatology values will be used for CG amount. In addition to the benefits outlined above, these climatologies will provide improved temporal and spatial resolution, expansion of the lightning threat area to include adjacent coastal waters, and potential to extend the forecast to include the day-2 period. This presentation will describe the lightning threat index map, discuss the work done to create the maps initialized with climatological guidance, and show examples of the climatological CG lightning densities and frequencies of occurren based on flow regime.

Lambert, Winnie↗
NASA NTRS1991

Viscous flow simulations of internal store carriage and separation

The internal carriage of stores by the military aircraft is an option for possible reductions in the aerodynamic drag and the observability. Trade studies of this option require considering the aircraft and the stores together. In an effort to develop a computational fluid dynamic (CFD) code for such studies, an investigation was conducted from 1986 to 1990. The study was divided into five building-block steps. First, a full Navier-Stokes code was developed to simulate the unsteady, three-dimensional cavity flow. As the second step, this code was then used to simulate the flows past various missile configurations at angles of attack up to 44 deg. The effects of incidence as well as the turbulence on the leeside flows were computationally captured. The objective of this study has involved the interference flows of rather complex configurations with multiple, joint or disjoint, components of nonsimilar geometries. Hence, a hybrid domain decomposition (HDD) method was developed as the third step of the investigation. The strengths of the multiblock, zonal, and overlapped grids were judiciously combined and employed for the present problem. In the fourth step, the interference flow past a missile near a flat-plate wing was simulated using the HDD method. Finally, the fifth step involved the simulation of the internal store carriage and separation. Four different cases for two different configurations were simulated. The computational results of all five steps were successfully compared with the available wind tunnel test data. The unsteady aerodynamic forces on the separating store were computationally predicted. The CFD code developed for this project is called Viscous Internal Store Carriage Code (VISCC).

Baysal, Oktay↗
DOE OSTI2023

A cost comparison of various hourly-reliable and net-zero hydrogen production pathways in the United States

Hydrogen (H 2 ) as an energy carrier may play a role in various hard-to-abate subsectors, but to maximize emission reductions, supplied hydrogen must be reliable, low-emission, and low-cost. Here, we build a model that enables direct comparison of the cost of producing net-zero, hourly-reliable hydrogen from various pathways. To reach net-zero targets, we assume upstream and residual facility emissions are mitigated using negative emission technologies. For the United States (California, Texas, and New York), model results indicate next-decade hybrid electricity-based solutions are lower cost ($2.02-$2.88/kg) than fossil-based pathways with natural gas leakage greater than 4% ($2.73-$5.94/kg). These results also apply to regions outside of the U.S. with a similar climate and electric grid. However, when omitting the net-zero emission constraint and considering the U.S. regulatory environment, electricity-based production only achieves cost-competitiveness with fossil-based pathways if embodied emissions of electricity inputs are not counted under U.S. Tax Code Section 45V guidance.

08 HYDROGEN↗
DOE OSTI2018

2014-2018 Summary of NCAR activities in the Earth Energy Exascale System Model (E3SM) project

NCAR participation in E3SM activities as part of this funded collaborative project has been successful in leveraging the existing atmosphere model development experience from CESM scientists and applying it to initial v1 atmosphere model (EAM) development and analysis. NCAR partners collectively had many decades of experience in parameterization development, running and tuning coupled models and building the required software infrastructure to support ongoing model developments. Furthermore, collaboration between E3SM and CESM developers was of mutual benefit to both modeling endeavors. In the earlier periods of the project, participation in E3SM both complemented core critical path DOE activities and advanced individual parameterization development; including orographic drag, convection parameterization, convective gustiness and cloud and microphysical processes. Significant progress has been made implementing model capabilities for separating out the physics and dynamics grids, and providing the infrastructure for including orographic elevation class communication between the land and atmosphere models. Our activities working with the E3SM workflow and software engineering teams have established efficient protocols and infrastructure for the sharing of CESM and E3SM model codes of interest to both modeling groups, a large component of which is the mutual communication of common code bugs. As well as these specific project tasks all NCAR project members have been regular participants in atmosphere and coupled group telecons, as well as PI meetings. We have been fully engaged with and contributed to decisions regarding v1 atmosphere model developments, coupled model simulations, model tunings, and software engineering infrastructure. NCAR’s contribution to more recent E3SM development activities has centered on analysis of v1 release and pre-release simulations in order to address outstanding systematic biases and communicate climate improvements. Of particularly note is the work in understanding clouds and cloud feedbacks, shortcomings in ENSO and sub-seasonal variability; in particular the Madden Julian Oscillation (MJO). Contributions have been made to a number of papers that are currently published or in preparation detailing model performance in CMIP6-protocal experiments. They outline the simulations of mean climate, clouds and convection processes, convective gustiness, atmospheric blocking coupled climates. The contributions of NCAR’s funded activities to the E3SM atmosphere in the initial years of the project have had a positive impact on many aspects of the model simulations described in these papers.

58 GEOSCIENCES↗
NASA NTRS1991

Mach number validation of a new zonal CFD method (ZAP2D) for airfoil simulations

A closed-loop overlapped velocity coupling procedure has been utilized to combine a two-dimensional potential-flow panel code and a Navier-Stokes code. The fully coupled two-zone code (ZAP2D) has been used to compute the flow past a NACA 0012 airfoil at Mach numbers ranging from 0.3 to 0.84 near the two-dimensional airfoil C(lmax) point for a Reynolds number of 3 million. For these cases, the grid domain size can be reduced to 3 chord lengths with less than 3-percent loss in accuracy for freestream Mach numbers through 0.8. Earlier validation work with ZAP2D has demonstrated a reduction in the required Navier-Stokes computation time by a factor of 4 for subsonic Mach numbers. For this more challenging condition of high lift and Mach number, the saving in CPU time is reduced to a factor of 2.

Strash, Daniel J.↗
NASA NTRS1997

Charon Toolkit for Parallel, Implicit Structured-Grid Computations: Functional Design

Charon is a software toolkit that enables engineers to develop high-performing message-passing programs in a convenient and piecemeal fashion. Emphasis is on rapid program development and prototyping. In this report a detailed description of the functional design of the toolkit is presented. It is illustrated by the stepwise parallelization of two representative code examples.

VanderWijngaart, Rob F.↗
NASA NTRS1999

Numerical Predictions of Wind Turbine Power and Aerodynamic Loads for the NREL Phase II and IV Combined Experiment Rotor

Accurate, reliable and robust numerical predictions of wind turbine rotor power remain a challenge to the wind energy industry. The literature reports various methods that compare predictions to experiments. The methods vary from Blade Element Momentum Theory (BEM), Vortex Lattice (VL), to variants of Reynolds-averaged Navier-Stokes (RaNS). The BEM and VL methods consistently show discrepancies in predicting rotor power at higher wind speeds mainly due to inadequacies with inboard stall and stall delay models. The RaNS methodologies show promise in predicting blade stall. However, inaccurate rotor vortex wake convection, boundary layer turbulence modeling and grid resolution has limited their accuracy. In addition, the inherently unsteady stalled flow conditions become computationally expensive for even the best endowed research labs. Although numerical power predictions have been compared to experiment. The availability of good wind turbine data sufficient for code validation experimental data that has been extracted from the IEA Annex XIV download site for the NREL Combined Experiment phase II and phase IV rotor. In addition, the comparisons will show data that has been further reduced into steady wind and zero yaw conditions suitable for comparisons to "steady wind" rotor power predictions. In summary, the paper will present and discuss the capabilities and limitations of the three numerical methods and make available a database of experimental data suitable to help other numerical methods practitioners validate their own work.

Duque, Earl P. N.↗
NASA NTRS2003

The Development of the Ducted Fan Noise Propagation and Radiation Code CDUCT-LaRC

The development of the ducted fan noise propagation and radiation code CDUCT-LaRC at NASA Langley Research Center is described. This code calculates the propagation and radiation of given acoustic modes ahead of the fan face or aft of the exhaust guide vanes in the inlet or exhaust ducts, respectively. This paper gives a description of the modules comprising CDUCT-LaRC. The grid generation module provides automatic creation of numerical grids for complex (non-axisymmetric) geometries that include single or multiple pylons. Files for performing automatic inviscid mean flow calculations are also generated within this module. The duct propagation is based on the parabolic approximation theory of R. P. Dougherty. This theory allows the handling of complex internal geometries and the ability to study the effect of non-uniform (i.e. circumferentially and axially segmented) liners. Finally, the duct radiation module is based on the Ffowcs Williams-Hawkings (FW-H) equation with a penetrable data surface. Refraction of sound through the shear layer between the external flow and bypass duct flow is included. Results for benchmark annular ducts, as well as other geometries with pylons, are presented and compared with available analytical data.

Nark, Douglas M.↗
NASA NTRS1997

Coupling of Sph and Finite Element Codes for Multi-Layer Orbital Debris Shield Design

Particle-based hydrodynamics models offer distinct advantages over Eulerian and Lagrangian hydrocodes in particular shock physics applications. Particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of Lagrangian and Eulerian codes respectively. However conventional particle-in-cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points. A new particle-based modeling methodology, termed Hamiltonian particle hydrodynamics, was developed by Fahrenthold and Koo (1997) to provide an alternative, fully Lagrangian, energy-based approach to shock physics simulations. This alternative formulation avoids the tensile and boundary instabilities associated with standard smooth particle hydrodynamics formulations and the diffusive grid- to-particle mapping schemes characteristic of particle-in-cell methods. In the work described herein, the method of Fahrenthold and Koo has been extended, by coupling the aforementioned hydrodynamic particle model to a hexahedral finite element based description of the continuum dynamics. The resulting continuum model retains all of the features (including general contact-impact effects) of Hamiltonian particle hydrodynamics, while in addition accounting for tensile strength, plasticity, and damage effects important in the simulation of hypervelocity impact on orbital debris shielding. A three dimensional, vectorized, and autotasked implementation of the extended particle method described here has been coded for application to orbital debris shielding design. Source code for the pre-processor (PREP), analysis code (EXOS), post-processor (POST), and rezoner (ZONE), have been delivered separately, along with a User's Guide describing installation and application of the software.

Fahrenthold, Eric P.↗
NASA NTRS2005

Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

Batina, John T.↗
DOE OSTI2025

thermal-grid-jba v1.0.0

This is a software repository that contains models for a feasibility study of a thermal energy network for Joint Base Andrews. The work has been conducted under the ESTCP program in the project https://serdp-estcp.mil/projects/details/0694868a-3d58-4a14-a587-b8f638bfcd5c The repository contains models for energy system selection and for verification of design. The DoD management intends to give access to this code for future feasibility studies at Joint Base Andrews and possibly other bases.

Wetter, Michael [Lawrence Berkeley National Labora↗
NASA NTRS2000

Performance of an Optimized Eta Model Code on the Cray T3E and a Network of PCs

In the year 2001, NASA will launch the satellite TRIANA that will be the first Earth observing mission to provide a continuous, full disk view of the sunlit Earth. As a part of the HPCC Program at NASA GSFC, we have started a project whose objectives are to develop and implement a 3D cloud data assimilation system, by combining TRIANA measurements with model simulation, and to produce accurate statistics of global cloud coverage as an important element of the Earth's climate. For simulation of the atmosphere within this project we are using the NCEP/NOAA operational Eta model. In order to compare TRIANA and the Eta model data on approximately the same grid without significant downscaling, the Eta model will be integrated at a resolution of about 15 km. The integration domain (from -70 to +70 deg in latitude and 150 deg in longitude) will cover most of the sunlit Earth disc and will continuously rotate around the globe following TRIANA. The cloud data assimilation is supposed to run and produce 3D clouds on a near real-time basis. Such a numerical setup and integration design is very ambitious and computationally demanding. Thus, though the Eta model code has been very carefully developed and its computational efficiency has been systematically polished during the years of operational implementation at NCEP, the current MPI version may still have problems with memory and efficiency for the TRIANA simulations. Within this work, we optimize a parallel version of the Eta model code on a Cray T3E and a network of PCs (theHIVE) in order to improve its overall efficiency. Our optimization procedure consists of introducing dynamically allocated arrays to reduce the size of static memory, and optimizing on a single processor by splitting loops to limit the number of streams. All the presented results are derived using an integration domain centered at the equator, with a size of 60 x 60 deg, and with horizontal resolutions of 1/2 and 1/3 deg, respectively. In accompanying charts we report the elapsed time, the speedup and the Mflops as a function of the number of processors for the non-optimized version of the code on the T3E and theHIVE. The large amount of communication required for model integration explains its poor performance on theHIVE. Our initial implementation of the dynamic memory allocation has contributed to about 12% reduction of memory but has introduced a 3% overhead in computing time. This overhead was removed by performing loop splitting in some of the high demanding subroutines. When the Eta code is fully optimized in order to meet the memory requirement for TRIANA simulations, a non-negligeable overhead may appear that may seriously affect the efficiency of the code. To alleviate this problem, we are considering implementation of a new algorithm for the horizontal advection that is computationally less expensive, and also a new approach for marching in time.

Kouatchou, Jules↗
DOE OSTI2023

Calculated covariance matrices for fission product yields using BeoH

Fission product yields (FPY) are important for a variety of applications (reactor neutronics, spent fuel, dosimetry, radiochemistry, etc.) and are currently included in many of the evaluated libraries around the world. The FPYs in the current US evaluation, ENDF/B-VIII.0, are mainly based on the 1994 evaluation of England and Rider and have only had slight updates—such as the inclusion of a 2 MeV point for 239 Pu—since their development. Additionally, only mean values and uncertainties are included in the evaluation, not full correlations. Los Alamos National Laboratory, in collaboration with several other institutes, has been working on an updated evaluation for the FPYs of 239 Pu(n,f), 235 U(n,f), 238 U(n,f), and 252 Cf(sf) using the deterministic, Hauser-Feshbach, fission fragment decay code, BeoH. BeoH calculates the FPYs consistently with many other prompt and delayed fission observables, explicitly taking into account multi-chance fission and ensuring consistency between observables. In addition to providing updated means and uncertainties for the FPYs on a pointwise energy grid from thermal to 20 MeV, we calculate correlations between all FPYs at each incident energy and across incident energies. Here, we discuss the development of these covariance matrices, differences in the correlations between FPYs based on the parameters that are included in the model optimization, and correlations across incident energies for neutron-induced fission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Full wave modeling of radio-frequency beams in tokamaks in the electron cyclotron frequency range

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Monthly Quality-filtered Aggregation of NOAA Climate Data Record (CDR) of AVHRR (Version 5) and VIIRS (Version 1) Leaf Area Index (LAI) and Fraction of Absorbed Photosynthetically Active Radiation (FAPAR)

This dataset contains gridded monthly Leaf Area Index (LAI) derived from the daily NOAA Climate Data Record (CDR) of AVHRR (Version 5) and VIIRS (Version 1) Leaf Area Index (LAI) and Fraction of Absorbed Photosynthetically Active Radiation (FAPAR). This data record spans from 1981 to 2024 using data from NOAA polar orbiting satellites: NOAA-7, -9, -11, -14, -16, -17, -18, -19 and S-NPP. The data are projected on a 0.05 degree x 0.05 degree global grid, as in the original CDR. The original CDR is one of the Land Surface CDR products produced by the NASA Goddard Space Flight Center (GSFC) and the University of Maryland (UMD), which is accompanied by algorithm documentation, data flow diagram and source code for the NOAA CDR Program. This dataset is in the netCDF-4 file format following ACDD and CF Conventions. This dataset has applied quality assurance information to only include "OK" data from the original CDR in the monthly aggregation.

Vermote, Eric [NASA Goddard Space Flight Center (G↗
NASA NTRS1981

Model verification studies using accurate measurements of spin up

The reliability and accuracy of the numerical code for spin up flows in a cylinder by comparing the numerical results against high resolution laser Doppler velocimeter (LDV) measurements of the azimuthal flows were checked. A computer code to generate numerical solution for axisymmetric rotating fluid in a cylinder was obtained and amended for routine use at MSFC. The numerical simulations used the Navier-Stokes equations in axisymmetric form and employed finite difference techniques on both constant and variable grids. The numerical solutions are analyzed to gain further insight into the fundamental questions analyzed in rotating fluid dynamics.

Hyun, J. M.↗
NASA NTRS1994

An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension)

An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multidimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.

Powell, Kenneth G.↗