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NASA NTRS1999

Impact of a Merged Precipitation Data on Global Soil Moisture Variability

Accurate soil moisture information has proved to be important to climate simulations and climate and weather forecasts. However, many difficulties exist that limit our understanding of soil moisture distribution and variability. One of them is the lack of accurate precipitation with appropriate spatial and temporal resolution. Precipitation as an input forcing to the land surface greatly influences soil moisture characteristics and variability. To improve precipitation data quality, an algorithm has been developed to generate a spatially and temporally continuous 3-hourly global precipitation data for the period of 1987 to present. This precipitation product is a combination of the precipitation from Special Sensor Microwave Imager (SSMI) with the Goddard Earth Observing System-1 Data Assimilation System (GEOS-1 DAS) employing a Physical-space Statistical Analysis System (PSAS). In this study we investigate the impact of this merged/analyzed precipitation data on the global soil moisture variability using an Off-line Land-surface GEOS Assimilation (OLGA) system. Two OLGA integrations starting from 1987 to 1993 are performed forced with the analyzed and GEOS-1 DAS precipitation respectively. We examine the spatial and temporal characteristics of soil moisture variability in response to the analyzed precipitation. The influence of this merged precipitation on the soil moisture variability and regional hydrological budget is estimated throughout the comparison with the results forced with the GEOS-1 DAS precipitation only. In the OLGA the sut@-grid scale horizontal heterogeneity is explicitly represented on the tile space. This provides a means to assess the role of the surface moisture heterogeneity in the interaction with the surface atmosphere and surface hydrological budget, and to validate OLGA results at tile space with in situ observation. ABRACOS (Anglo-Brazilian Amazonian Climate Observation Study), FIFE (First ISLSCP Field Experiment) I and HAPEX data will be used in the validation.

Yang, Runhua↗

NASA NTRS1977

A computer software system for integration and analysis of grid-based remote sensing data with other natural resource data. Remote Sensing Project

A computer-based information system is described designed to assist in the integration of commonly available spatial data for regional planning and resource analysis. The Resource Analysis Program (RAP) provides a variety of analytical and mapping phases for single factor or multi-factor analyses. The unique analytical and graphic capabilities of RAP are demonstrated with a study conducted in Windsor Township, Eaton County, Michigan. Soil, land cover/use, topographic and geological maps were used as a data base to develope an eleven map portfolio. The major themes of the portfolio are land cover/use, non-point water pollution, waste disposal, and ground water recharge.

Tilmann, S. E.↗

NASA NTRS2021

Geomagnetically Induced Currents at Middle Latitudes: 1. Quiet-Time Variability

Geomagnetically induced currents (GICs) at middle latitudes have received increased attention after reported power grid disruptions due to geomagnetic disturbances. However, quantifying the risk to the electric power grid at middle latitudes is difficult without understanding how the GIC sensors respond to geomagnetic activity on a daily basis. Therefore, in this study the question “Do measured GICs have distinguishable and quantifiable long-period and short-period characteristics?” is addressed. The study focuses on the long-term variability of measured GIC, and establishes the extent to which the variability relates to quiet-time geomagnetic activity. GIC quiet-day curves (QDCs) are computed from measured data for each GIC node, covering all four seasons, and then compared with the seasonal variability of thermosphere-ionosphere-electrodynamics general circulation model (TIE- GCM)-simulated neutral wind and height-integrated current density. The results show strong evidence that the middle-latitude nodes routinely respond to the tidal-driven Sq variation, with a local time and seasonal dependence on the direction of the ionospheric currents, which is specific to each node. The strong dependence of GICs on the Sq currents demonstrates that the GIC QDCs may be employed as a robust baseline from which to quantify the significance of GICs during geomagnetically active times and to isolate those variations to study independently. The QDC-based significance score computed in this study provides power utilities with a node-specific measure of the geomagnetic significance of a given GIC observation. Finally, this study shows that the power grid acts as a giant sensor that may detect ionospheric current systems.

Adam C Kellerman↗

NASA NTRS2014

The D8 Aircraft: An Aerodynamics Study of Boundary Layer and Wake Ingestion Benefit

Goal: Quantify benefits of BLI (Boundary Layer Ingesting) and wake ingestion for the D8. Approach: Overset CFD (Computational Fluid Dynamics) using CGT (Chimera Grid Tools software package) and Overflow-‐2; CFD validation; NASA LaRC (Langley Research Center) 14x22 WT (wind tunnel) data for a 1:11 scale model; Quantifying the BLI and wake ingestion benefit - Direct Comparison between: Efficient conventional (podded nacelle) configuration; BLI (integrated nacelle) configuration.

D8↗

NASA NTRS2004

Surface Modeling and Grid Generation for Iced Airfoils (SmaggIce)

Many of the troubles associated with problem solving are alleviated when there is a model that can be used to represent the problem. Through the Advanced Graphics and Visualization (G-VIS) Laboratory and other facilities located within the Research Analysis Center, the Computer Services Division (CSD) is able to develop and maintain programs and software that allow for the modeling of various situations. For example, the Icing Research Branch is devoted to investigating the effect of ice that forms on the wings and other airfoils of airplanes while in flight. While running tests that physically generate ice and wind on airfoils within the laboratories and wind tunnels on site are done, it would be beneficial if most of the preliminary work could be done outside of the lab. Therefore, individuals from within CSD have collaborated with Icing Research in order to create SmaggIce. This software allows users to create ice patterns on clean airfoils or open files containing a variety of icing situations, manipulate and measure these forms, generate, divide, and merge grids around these elements for more explicit analysis, and specify and rediscretize subcurves. With the projected completion date of Summer 2005, the majority of the focus of the Smagglce team is user-functionality and error handling. My primary responsibility is to test the Graphical User Interface (GUI) in SmaggIce in order to ensure the usability and verify the expected results of the events (buttons, menus, etc.) within the program. However, there is no standardized, systematic way in which to test all the possible combinations or permutations of events, not to mention unsolicited events such as errors. Moreover, scripting tests, if not done properly and with a view towards inevitable revision, can result in more apparent errors within the software and in effect become useless whenever the developers of the program make a slight change in the way a specific process is executed. My task therefore requires a brief yet intense study into GUI coverage criteria and creating algorithms for GUI implementation. Nevertheless, there are still heavily graphical features of SmaggIceSmaggIce that must be either corrected or redesigned before its release. A particular feature of SmaggIce is the ability to smooth out curves created by control points that form an arbitrary shape into something more acquiescent to gridding (while maintaining the integrity of the data). This is done by a mathematical model known as Non-Uniform Rational B-Spline (NURBS) curves. Existing NURBS code is written in FORTRAN-77 with static arrays for holding information. My new assignment is to allow for dynamic memory allocation within the code and to make it possible for the developers to call out functions from the NURBS code using C.

Hammond, Brandy M.↗

NASA NTRS2000

Development and Testing of Coupled Land-surface, PBL and Shallow/Deep Convective Parameterizations within the MM5

The objective of this investigation was to study the role of shallow convection on the regional water cycle of the Mississippi and Little Washita Basins using a 3-D mesoscale model, the PSUINCAR MM5. The underlying premise of the project was that current modeling of regional-scale climate and moisture cycles over the continents is deficient without adequate treatment of shallow convection. It was hypothesized that an improved treatment of the regional water cycle can be achieved by using a 3-D mesoscale numerical model having a detailed land-surface parameterization, an advanced boundary-layer parameterization, and a more complete shallow convection parameterization than are available in most current models. The methodology was based on the application in the MM5 of new or recently improved parameterizations covering these three physical processes. Therefore, the work plan focused on integrating, improving, and testing these parameterizations in the MM5 and applying them to study water-cycle processes over the Southern Great Plains (SGP): (1) the Parameterization for Land-Atmosphere-Cloud Exchange (PLACE) described by Wetzel and Boone; (2) the 1.5-order turbulent kinetic energy (TKE)-predicting scheme of Shafran et al.; and (3) the hybrid-closure sub-grid shallow convection parameterization of Deng. Each of these schemes has been tested extensively through this study and the latter two have been improved significantly to extend their capabilities.

Stauffer, David R.↗

NASA NTRS2012

Effects of Real-Time NASA Vegetation Data on Model Forecasts of Severe Weather

The NASA Short-term Prediction Research and Transition (SPoRT) Center has developed a Greenness Vegetation Fraction (GVF) dataset, which is updated daily using swaths of Normalized Difference Vegetation Index data from the Moderate Resolution Imaging Spectroradiometer (MODIS) data aboard the NASA-EOS Aqua and Terra satellites. NASA SPoRT started generating daily real-time GVF composites at 1-km resolution over the Continental United States beginning 1 June 2010. A companion poster presentation (Bell et al.) primarily focuses on impact results in an offline configuration of the Noah land surface model (LSM) for the 2010 warm season, comparing the SPoRT/MODIS GVF dataset to the current operational monthly climatology GVF available within the National Centers for Environmental Prediction (NCEP) and Weather Research and Forecasting (WRF) models. This paper/presentation primarily focuses on individual case studies of severe weather events to determine the impacts and possible improvements by using the real-time, high-resolution SPoRT-MODIS GVFs in place of the coarser-resolution NCEP climatological GVFs in model simulations. The NASA-Unified WRF (NU-WRF) modeling system is employed to conduct the sensitivity simulations of individual events. The NU-WRF is an integrated modeling system based on the Advanced Research WRF dynamical core that is designed to represents aerosol, cloud, precipitation, and land processes at satellite-resolved scales in a coupled simulation environment. For this experiment, the coupling between the NASA Land Information System (LIS) and the WRF model is utilized to measure the impacts of the daily SPoRT/MODIS versus the monthly NCEP climatology GVFs. First, a spin-up run of the LIS is integrated for two years using the Noah LSM to ensure that the land surface fields reach an equilibrium state on the 4-km grid mesh used. Next, the spin-up LIS is run in two separate modes beginning on 1 June 2010, one continuing with the climatology GVFs while the other uses the daily SPoRT/MODIS GVFs. Finally, snapshots of the LIS land surface fields are used to initialize two different simulations of the NU-WRF, one running with climatology LIS and GVFs, and the other running with experimental LIS and NASA/SPoRT GVFs. In this paper/presentation, case study results will be highlighted in regions with significant differences in GVF between the NCEP climatology and SPoRT product during severe weather episodes.

Case, Jonathan L.↗

NASA NTRS1990

Time scales and variability of area-averaged tropical oceanic rainfall

A statistical analysis of time series of area-averaged rainfall over the oceans has been conducted around the diurnal time scale. The results of this analysis can be applied directly to the problem of establishing the magnitude of expected errors to be incurred in the estimation of monthly area-averaged rain rate from low orbiting satellites. Such statistics as the mean, standard deviation, integral time scale of background red noise, and spectral analyses were performed on time series of the GOES precipitation index taken at 3-hour intervals during the period spanning December 19, 1987 to March 31, 1988 over the central and eastern tropical Pacific. The analyses have been conducted on 2.5 x 2.5 deg and 5 x 5 deg grid boxes, separately. The study shows that rainfall measurements by a sun-synchronous satellite visiting a spot twice per day will include a bias due to the existence of the semidiurnal cycle in the SPCZ ranging from 5 to 10 percentage points. The bias in the ITCZ may be of the order of 5 percentage points.

Shin, Kyung-Sup↗

NASA NTRS2017

A Comparative Study of Simulated and Measured Main Landing Gear Noise for Large Civil Transports

Computational results for the NASA 26%-scale model of a six-wheel main landing gear with and without a toboggan-shaped noise reduction fairing are presented. The model is a high-fidelity representation of a Boeing 777-200 aircraft main landing gear. A lattice Boltzmann method was used to simulate the unsteady flow around the model in isolation. The computations were conducted in free-air at a Mach number of 0.17, matching a recent acoustic test of the same gear model in the Virginia Tech Stability Wind Tunnel in its anechoic configuration. Results obtained on a set of grids with successively finer spatial resolution demonstrate the challenge in resolving/capturing the flow field for the smaller components of the gear and their associated interactions, and the resulting effects on the high-frequency segment of the farfield noise spectrum. Farfield noise spectra were computed based on an FWH integral approach, with simulated pressures on the model solid surfaces or flow-field data extracted on a set of permeable surfaces enclosing the model as input. Comparison of these spectra with microphone array measurements obtained in the tunnel indicated that, for the present complex gear model, the permeable surfaces provide a more accurate representation of farfield noise, suggesting that volumetric effects are not negligible. The present study also demonstrates that good agreement between simulated and measured farfield noise can be achieved if consistent post-processing is applied to both physical and synthetic pressure records at array microphone locations.

Konig, Benedikt↗

NASA NTRS2023

Robustness of Gridded Precipitation Products for Vietnam Basins using the Comprehensive Assessment Framework of Rainfall

The use of satellite–based precipitation products (SPPs) have become increasingly prevalent as key inputs to provide regional rainfall for improving hydrological simulations in data–spare regions. This study introduces a new approach – Comprehensive Assessment Framework of Rainfall (CAFR) to evaluate six satellite–based precipitation products (SPPs) for eleven basins with different sizes across Vietnam (2007–2015). These SPPs include the Global Precipitation Mission (GPM) Integrated Multi-satellitE Retrievals for Global Precipitation Measurement Final run Version 6 (GPM IMERGF V6), Multi–Source Weighted–Ensemble Precipitation (MSWEP) V2.2, Soil Moisture to Rain (SM2RAIN) – Advanced SCATterometer (ASCAT) V1.5, Asian Precipitation–Highly–Resolved Observational Data Integration Towards Evaluation (APHRODITE) V1901, Climate Hazards group Infrared Precipitation with Stations (CHIRPS) V2.0, and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) – Climate Data Record (CDR) V1.0. With the proposed CAFR: (1) IMERGF is suggested to have the best performance overall, especially when simulating flood peaks; (2) SM2RAIN–ASCAT demonstrates the best skills in metrics related to the dry season; (3) For streamflow simulations, SPPs' performance is sensitive to basin size, with larger basins showing better performance skills. In this study, we demonstrate the capability of our proposed framework to better understand SPP applications in hydrological modeling.

Comprehensive Assessment Framework of Rainfall (CA↗

NASA NTRS2018

LAVA Simulations for the 3rd AIAA CFD High Lift Prediction Workshop with Body Fitted Grids

In response to the 3rd AIAA CFD High Lift Prediction Workshop, the workshop cases were analyzed using Reynolds-averaged Navier-Stokes flow solvers within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework. For the workshop cases the advantages and limitations of both overset-structured an unstructured polyhedral meshes were assessed. The workshop included 3 cases: a 2D airfoil validation case, a mesh convergence study using the High Lift Common Research Model, and a nacelle/pylon integration study using the JAXA (Japan Aerospace Exploration Agency) Standard Model. The 2D airfoil case from the workshop is used to verify the implementation of the Spalart-Allmaras turbulence model along with some of its variants within the solver. The High Lift Common Research Model case is used to assess solver performance and accuracy at varying mesh resolutions, as well as identify the minimum mesh fidelity required for LAVA on this class of problem. The JAXA Standard Model case is used to assess the solver's sensitivity to the turbulence model and to compare the structured and unstructured mesh paradigms. These workshop cases have helped establish best practices for high lift flow configurations for the LAVA solver.

LAVA↗

NASA NTRS2016

Towards a Viscous Wall Model for Immersed Boundary Methods

Immersed boundary methods are frequently employed for simulating flows at low Reynolds numbers or for applications where viscous boundary layer effects can be neglected. The primary shortcoming of Cartesian mesh immersed boundary methods is the inability of efficiently resolving thin turbulent boundary layers in high-Reynolds number flow application. The inefficiency of resolving the thin boundary is associated with the use of constant aspect ratio Cartesian grid cells. Conventional CFD approaches can efficiently resolve the large wall normal gradients by utilizing large aspect ratio cells near the wall. This paper presents different approaches for immersed boundary methods to account for the viscous boundary layer interaction with the flow-field away from the walls. Different wall modeling approaches proposed in previous research studies are addressed and compared to a new integral boundary layer based approach. In contrast to common wall-modeling approaches that usually only utilize local flow information, the integral boundary layer based approach keeps the streamwise history of the boundary layer. This allows the method to remain effective at much larger y+ values than local wall modeling approaches. After a theoretical discussion of the different approaches, the method is applied to increasingly more challenging flow fields including fully attached, separated, and shock-induced separated (laminar and turbulent) flows.

Immersed↗

NASA NTRSDate not supplied

The Effect of Trailing Edge Grid Resolution in Large-Eddy Simulations

Ceramic Matrix Composite (CMC) with environmental barrier coating can tolerate significantly higher temperatures compared with the conventional metal alloy blades and thus can help achieve higher thermal efficiency in gas turbine engines. Due to the complex fabrication process of CMC blades, larger blade trailing edge thicknesses and larger leading-edge radii of curvature are expected. These features significantly alter aerodynamic performance especially near the trailing edge and thus the loss profile. In previous studies, the authors used the large eddy simulation (LES) as well as the Reynolds Averaged Navier-Stokes (RANS) coupled with an intermittency function-based transition model to simulate an aerodynamics performance of three different CMC blades and compared the predictions against the data acquired at NASA Glenn Transonic Turbine Blade Cascade Rig. Although we were able to successfully predict different characteristics of aerodynamic performance among three different blades (e.g., pressure loading and integrated losses), LES consistently predicted a small recirculation bubble at the end of the suction side. This was not inconsistent with the physics of the flow, but the pressure loading, locally, near the trailing edge, and as a result, the measured wake profiles did not match the experimental data. To delve further into these issues, a new LES grid with a much finer mesh near the trailing edge was generated where the spanwise extent of the grid was increased by 50%. An LES simulation for the CMC blade with the largest trailing edge thicknesses at the high-freestream turbulence (Tu=13%) condition showed that using such a mesh is necessary for LES to accurately capture the transition phenomena on the suction side. The resulting total pressure coefficient profile and the shift of the wake profile were greatly improved.

CMC↗

NASA NTRSDate not supplied

The Effect of Trailing Edge Grid Resolution in Large-Eddy Simulations

LES↗

NASA NTRS2009

Forecasting Lightning Threat using Cloud-resolving Model Simulations

As numerical forecasts capable of resolving individual convective clouds become more common, it is of interest to see if quantitative forecasts of lightning flash rate density are possible, based on fields computed by the numerical model. Previous observational research has shown robust relationships between observed lightning flash rates and inferred updraft and large precipitation ice fields in the mixed phase regions of storms, and that these relationships might allow simulated fields to serve as proxies for lightning flash rate density. It is shown in this paper that two simple proxy fields do indeed provide reasonable and cost-effective bases for creating time-evolving maps of predicted lightning flash rate density, judging from a series of diverse simulation case study events in North Alabama for which Lightning Mapping Array data provide ground truth. One method is based on the product of upward velocity and the mixing ratio of precipitating ice hydrometeors, modeled as graupel only, in the mixed phase region of storms at the -15\dgc\ level, while the second method is based on the vertically integrated amounts of ice hydrometeors in each model grid column. Each method can be calibrated by comparing domainwide statistics of the peak values of simulated flash rate proxy fields against domainwide peak total lightning flash rate density data from observations. Tests show that the first method is able to capture much of the temporal variability of the lightning threat, while the second method does a better job of depicting the areal coverage of the threat. A blended solution is designed to retain most of the temporal sensitivity of the first method, while adding the improved spatial coverage of the second. Weather Research and Forecast Model simulations of selected North Alabama cases show that this model can distinguish the general character and intensity of most convective events, and that the proposed methods show promise as a means of generating quantitatively realistic fields of lightning threat. However, because models tend to have more difficulty in correctly predicting the instantaneous placement of storms, forecasts of the detailed location of the lightning threat based on single simulations can be in error. Although these model shortcomings presently limit the precision of lightning threat forecasts from individual runs of current generation models, the techniques proposed herein should continue to be applicable as newer and more accurate physically-based model versions, physical parameterizations, initialization techniques and ensembles of cloud-allowing forecasts become available.

McCaul, E. W., Jr.↗

NASA NTRSDate not supplied

Wall-Modeled Large Eddy Simulations of Transonic Buffet Over a Supercritical Airfoil

A series of scale-resolving simulations of flow over the ONERA OAT15A airfoil have been performed at an angle of attack of 3.5◦, just past the onset of buffet. The focus of this study is to document the sensitivity of the wall-modeled large eddy simulation (WMLES) methodology for curvilinear structured overset grids within the Launch, Ascent, and Vehicle Aerodynamics (LAVA) framework to mesh spacing, mesh distribution, and domain size. A secondary purpose of the study is to compare the results from WMLES to unsteady Reynolds-averaged Navier Stokes (URANS) simulations and hybrid RANS-LES (HRLES) within the same LAVA solver framework. The study provides a unique perspective regarding comparisons between different turbulence modeling approaches, time-integration methods, and computational performance since many of the same numerical routines are used for all three types of simulations. The results are compared with experiments and previous numerical studies of the same geometry and flow conditions.

TTT↗

NASA NTRS1995

The NAS Computational Aerosciences Archive

In order to further the state-of-the-art in computational aerosciences (CAS) technology, researchers must be able to gather and understand existing work in the field. One aspect of this information gathering is studying published work available in scientific journals and conference proceedings. However, current scientific publications are very limited in the type and amount of information that they can disseminate. Information is typically restricted to text, a few images, and a bibliography list. Additional information that might be useful to the researcher, such as additional visual results, referenced papers, and datasets, are not available. New forms of electronic publication, such as the World Wide Web (WWW), limit publication size only by available disk space and data transmission bandwidth, both of which are improving rapidly. The Numerical Aerodynamic Simulation (NAS) Systems Division at NASA Ames Research Center is in the process of creating an archive of CAS information on the WWW. This archive will be based on the large amount of information produced by researchers associated with the NAS facility. The archive will contain technical summaries and reports of research performed on NAS supercomputers, visual results (images, animations, visualization system scripts), datasets, and any other supporting meta-information. This information will be available via the WWW through the NAS homepage, located at http://www.nas.nasa.gov/, fully indexed for searching. The main components of the archive are technical summaries and reports, visual results, and datasets. Technical summaries are gathered every year by researchers who have been allotted resources on NAS supercomputers. These summaries, together with supporting visual results and references, are browsable by interested researchers. Referenced papers made available by researchers can be accessed through hypertext links. Technical reports are in-depth accounts of tools and applications research projects performed by NAS staff members and collaborators. Visual results, which may be available in the form of images, animations, and/or visualization scripts, are generated by researchers with respect to a certain research project, depicting dataset features that were determined important by the investigating researcher. For example, script files for visualization systems (e.g. FAST, PLOT3D, AVS) are provided to create visualizations on the user's local workstation to elucidate the key points of the numerical study. Users can then interact with the data starting where the investigator left off. Datasets are intended to give researchers an opportunity to understand previous work, 'mine' solutions for new information (for example, have you ever read a paper thinking "I wonder what the helicity density looks like?"), compare new techniques with older results, collaborate with remote colleagues, and perform validation. Supporting meta-information associated with the research projects is also important to provide additional context for research projects. This may include information such as the software used in the simulation (e.g. grid generators, flow solvers, visualization). In addition to serving the CAS research community, the information archive will also be helpful to students, visualization system developers and researchers, and management. Students (of any age) can use the data to study fluid dynamics, compare results from different flow solvers, learn about meshing techniques, etc., leading to better informed individuals. For these users it is particularly important that visualization be integrated into dataset archives. Visualization researchers can use dataset archives to test algorithms and techniques, leading to better visualization systems, Management can use the data to figure what is really going on behind the viewgraphs. All users will benefit from fast, easy, and convenient access to CFD datasets. The CAS information archive hopes to serve as a useful resource to those interested in computational sciences. At present, only information that may be distributed internationally is made available via the archive. Studies are underway to determine security requirements and solutions to make additional information available. By providing access to the archive via the WWW, the process of information gathering can be more productive and fruitful due to ease of access and ability to manage many different types of information. As the archive grows, additional resources from outside NAS will be added, providing a dynamic source of research results.

Miceli, Kristina D.↗

NASA NTRS2001

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible; (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred; (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used; and (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

Yee, Helen C.↗