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NASA NTRS1995

Technical report series on global modeling and data assimilation. Volume 6: A multiyear assimilation with the GEOS-1 system: Overview and results

The Data Assimilation Office (DAO) at Goddard Space Flight Center has produced a multiyear global assimilated data set with version 1 of the Goddard Earth Observing System Data Assimilation System (GEOS-1 DAS). One of the main goals of this project, in addition to benchmarking the GEOS-1 system, was to produce a research quality data set suitable for the study of short-term climate variability. The output, which is global and gridded, includes all prognostic fields and a large number of diagnostic quantities such as precipitation, latent heating, and surface fluxes. Output is provided four times daily with selected quantities available eight times per day. Information about the observations input to the GEOS-1 DAS is provided in terms of maps of spatial coverage, bar graphs of data counts, and tables of all time periods with significant data gaps. The purpose of this document is to serve as a users' guide to NASA's first multiyear assimilated data set and to provide an early look at the quality of the output. Documentation is provided on all the data archives, including sample read programs and methods of data access. Extensive comparisons are made with the corresponding operational European Center for Medium-Range Weather Forecasts analyses, as well as various in situ and satellite observations. This document is also intended to alert users of the data about potential limitations of assimilated data, in general, and the GEOS-1 data, in particular. Results are presented for the period March 1985-February 1990.

Suarez, Max J.↗
NASA NTRS2015

Computational Fluid Dynamics Simulation of Dual Bell Nozzle Film Cooling

Marshall Space Flight Center (MSFC) and Armstrong Flight Research Center (AFRC) are working together to advance the technology readiness level (TRL) of the dual bell nozzle concept. Dual bell nozzles are a form of altitude compensating nozzle that consists of two connecting bell contours. At low altitude the nozzle flows fully in the first, relatively lower area ratio, nozzle. The nozzle flow separates from the wall at the inflection point which joins the two bell contours. This relatively low expansion results in higher nozzle efficiency during the low altitude portion of the launch. As ambient pressure decreases with increasing altitude, the nozzle flow will expand to fill the relatively large area ratio second nozzle. The larger area ratio of the second bell enables higher Isp during the high altitude and vacuum portions of the launch. Despite a long history of theoretical consideration and promise towards improving rocket performance, dual bell nozzles have yet to be developed for practical use and have seen only limited testing. One barrier to use of dual bell nozzles is the lack of control over the nozzle flow transition from the first bell to the second bell during operation. A method that this team is pursuing to enhance the controllability of the nozzle flow transition is manipulation of the film coolant that is injected near the inflection between the two bell contours. Computational fluid dynamics (CFD) analysis is being run to assess the degree of control over nozzle flow transition generated via manipulation of the film injection. A cold flow dual bell nozzle, without film coolant, was tested over a range of simulated altitudes in 2004 in MSFC's nozzle test facility. Both NASA centers have performed a series of simulations of that dual bell to validate their computational models. Those CFD results are compared to the experimental results within this paper. MSFC then proceeded to add film injection to the CFD grid of the dual bell nozzle. A series of nozzle pressure ratios and film coolant flow rates are investigated to determine the effect of the film injection on the nozzle flow transition behavior. The results of this CFD study of a dual bell with film injection are presented in this paper.

Braman, Kalen↗
NASA NTRS2012

Preliminary Results of a U.S. Deep South Modeling Experiment Using NASA SPoRT Initialization Datasets for Operational National Weather Service Local Model Runs

A joint collaborative modeling effort among the NWS offices in Mobile, AL, and Houston, TX, and NASA Short-term Prediction Research and Transition (SPoRT) Center began during the 2011-2012 cold season, and continued into the 2012 warm season. The focus was on two frequent U.S. Deep South forecast challenges: the initiation of deep convection during the warm season; and heavy precipitation during the cold season. We wanted to examine the impact of certain NASA produced products on the Weather Research and Forecasting Environmental Modeling System in improving the model representation of mesoscale boundaries such as the local sea-, bay- and land-breezes (which often leads to warm season convective initiation); and improving the model representation of slow moving, or quasi-stationary frontal boundaries (which focus cold season storm cell training and heavy precipitation). The NASA products were: the 4-km Land Information System, a 1-km sea surface temperature analysis, and a 4-km greenness vegetation fraction analysis. Similar domains were established over the southeast Texas and Alabama coastlines, each with an outer grid with a 9 km spacing and an inner nest with a 3 km grid spacing. The model was run at each NWS office once per day out to 24 hours from 0600 UTC, using the NCEP Global Forecast System for initial and boundary conditions. Control runs without the NASA products were made at the NASA SPoRT Center. The NCAR Model Evaluation Tools verification package was used to evaluate both the positive and negative impacts of the NASA products on the model forecasts. Select case studies will be presented to highlight the influence of the products.

Wood, Lance↗
NASA NTRS1998

Exploration of the Moon with Remote Sensing, Ground-Penetrating Radar, and the Regolith-Evolved Gas Analyzer (REGA)

There are two important reasons to explore the Moon. First, we would like to know more about the Moon itself: its history, its geology, its chemistry, and its diversity. Second, we would like to apply this knowledge to a useful purpose. namely finding and using lunar resources. As a result of the recent Clementine and Lunar Prospector missions, we now have global data on the regional surface mineralogy of the Moon, and we have good reason to believe that water exists in the lunar polar regions. However, there is still very little information about the subsurface. If we wish to go to the lunar polar regions to extract water, or if we wish to go anywhere else on the Moon and extract (or learn) anything at all, we need information in three dimensions an understanding of what lies below the surface, both shallow and deep. The terrestrial mining industry provides an example of the logical steps that lead to an understanding of where resources are located and their economic significance. Surface maps are examined to determine likely locations for detailed study. Geochemical soil sample surveys, using broad or narrow grid patterns, are then used to gather additional data. Next, a detailed surface map is developed for a selected area, along with an interpretation of the subsurface structure that would give rise to the observed features. After that, further sampling and geophysical exploration are used to validate and refine the original interpretation, as well as to make further exploration/ mining decisions. Integrating remotely sensed, geophysical, and sample datasets gives the maximum likelihood of a correct interpretation of the subsurface geology and surface morphology. Apollo-era geophysical and automated sampling experiments sought to look beyond the upper few microns of the lunar surface. These experiments, including ground-penetrating radar and spectrometry, proved the usefulness of these methods for determining the best sites for lunar bases and lunar mining operations.

Cooper, B. L.↗
NASA NTRS1991

Solar powered Stirling cycle electrical generator

Under NASA's Civil Space Technology Initiative (CSTI), the NASA Lewis Research Center is developing the technology needed for free-piston Stirling engines as a candidate power source for space systems in the late 1990's and into the next century. Space power requirements include high efficiency, very long life, high reliability, and low vibration. Furthermore, system weight and operating temperature are important. The free-piston Stirling engine has the potential for a highly reliable engine with long life because it has only a few moving parts, non-contacting gas bearings, and can be hermetically sealed. These attributes of the free-piston Stirling engine also make it a viable candidate for terrestrial applications. In cooperation with the Department of Energy, system designs are currently being completed that feature the free-piston Stirling engine for terrestrial applications. Industry teams were assembled and are currently completing designs for two Advanced Stirling Conversion Systems utilizing technology being developed under the NASA CSTI Program. These systems, when coupled with a parabolic mirror to collect the solar energy, are capable of producing about 25 kW of electricity to a utility grid. Industry has identified a niche market for dish Stirling systems for worldwide remote power application. They believe that these niche markets may play a major role in the introduction of Stirling products into the commercial market.

Shaltens, Richard K.↗
NASA NTRS2011

Analysis of Ultra High Resolution Sea Surface Temperature Level 4 Datasets

Sea surface temperature (SST) studies are often focused on improving accuracy, or understanding and quantifying uncertainties in the measurement, as SST is a leading indicator of climate change and represents the longest time series of any ocean variable observed from space. Over the past several decades SST has been studied with the use of satellite data. This allows a larger area to be studied with much more frequent measurements being taken than direct measurements collected aboard ship or buoys. The Group for High Resolution Sea Surface Temperature (GHRSST) is an international project that distributes satellite derived sea surface temperatures (SST) data from multiple platforms and sensors. The goal of the project is to distribute these SSTs for operational uses such as ocean model assimilation and decision support applications, as well as support fundamental SST research and climate studies. Examples of near real time applications include hurricane and fisheries studies and numerical weather forecasting. The JPL group has produced a new 1 km daily global Level 4 SST product, the Multiscale Ultrahigh Resolution (MUR), that blends SST data from 3 distinct NASA radiometers: the Moderate Resolution Imaging Spectroradiometer (MODIS), the Advanced Very High Resolution Radiometer (AVHRR), and the Advanced Microwave Scanning Radiometer ? Earth Observing System(AMSRE). This new product requires further validation and accuracy assessment, especially in coastal regions.We examined the accuracy of the new MUR SST product by comparing the high resolution version and a lower resolution version that has been smoothed to 19 km (but still gridded to 1 km). Both versions were compared to the same data set of in situ buoy temperature measurements with a focus on study regions of the oceans surrounding North and Central America as well as two smaller regions around the Gulf Stream and California coast. Ocean fronts exhibit high temperature gradients (Roden, 1976), and thus satellite data of SST can be used in the detection of these fronts. In this case, accuracy is less of a concern because the primary focus is on the spatial derivative of SST. We calculated the gradients for both versions of the MUR data set and did statistical comparisons focusing on the same regions.

sea surface temperature SST)↗
NASA NTRSDate not supplied

The System Modeling and Analysis of Resiliency in STEReO (SMARt-STEReO)

Wildfire emergency response has remained rooted in relatively low-tech solutions for coordination between ground and aerial assets. These low-tech solutions are robust for the remote environments in which wildfires are usually fought, but limit strategic cross-organizational support and the ability to deploy and effectively utilize aerial assets. As aircraft become more advanced and new technology, including drones, become available to firefighters, a new, more modern method of asset coordination is needed. NASA is working on a project called ‘Scalable Traffic Management for Emergency Response Operations’ (STEReO) to integrate unmanned aerial systems (UAS)and UAS traffic management (UTM)into wildfire response. STEReO’s goals include simplifying the coordination of aerial assets, improving the existing UAS framework, and increasing the role of additional autonomous systems to reduce human risk and to increase system resilience. This paper describes the development of the ‘System Modeling and Analysis of Resiliency in STEReO’ (SMARt-STEReO) project, which aims to model wildfire response and to quantify the additional system resilience that STEReO technology provides firefighters. This paper verifies SMARt-STEReO and defines its scope; it includes experimental and statistical analysis of the impact that the addition of UAS has on both performance metrics and also on performance resiliency response to a given fault. SMARt-STEReO is a grid-based model of fire propagation that incorporates varying crew responses. Through the use of a Python package called ‘fmdtools’, the model easily allows for the addition of faults to the system. These faults allow analysts to investigate various response parameters. Factors including terrain, fuel type and wind speed can be modified to affect the fire propagation; additionally, the number of ground crews, engines, fixed wing aircraft, helicopters, and UAS can be changed to affect the crew response. The communication lines between actors mimic those used in real life situations. This paper explains the development of SMARt-STEReO including background research, verification and validation, and preliminary experimental analysis of system resilience to both a minor and major fault in systems with and without UAS.

Resiliency↗
NASA NTRS2002

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes with incremental studies was initiated. Here we further refine the analysis on, and improve the understanding of the adaptive numerical dissipation control strategy. Basically, the development of these schemes focuses on high order nondissipative schemes and takes advantage of the progress that has been made for the last 30 years in numerical methods for conservation laws, such as techniques for imposing boundary conditions, techniques for stability at shock waves, and techniques for stable and accurate long-time integration. We concentrate on high order centered spatial discretizations and a fourth-order Runge-Kutta temporal discretizations as the base scheme. Near the bound-aries, the base scheme has stable boundary difference operators. To further enhance stability, the split form of the inviscid flux derivatives is frequently used for smooth flow problems. To enhance nonlinear stability, linear high order numerical dissipations are employed away from discontinuities, and nonlinear filters are employed after each time step in order to suppress spurious oscillations near discontinuities to minimize the smearing of turbulent fluctuations. Although these schemes are built from many components, each of which is well-known, it is not entirely obvious how the different components be best connected. For example, the nonlinear filter could instead have been built into the spatial discretization, so that it would have been activated at each stage in the Runge-Kutta time stepping. We could think of a mechanism that activates the split form of the equations only at some parts of the domain. Another issue is how to define good sensors for determining in which parts of the computational domain a certain feature should be filtered by the appropriate numerical dissipation. For the present study we employ a wavelet technique introduced in as sensors. Here, the method is briefly described with selected numerical experiments.

Sjoegreen, Bjoern↗
NASA NTRS2011

Evaluating the Use of Remote Sensing Data in the USAID Famine Early Warning Systems Network

The US Agency for International Development (USAID) s Famine Early Warning System Network (FEWS NET) provides monitoring and early warning support to decision makers responsible for responding to food insecurity emergencies on three continents. FEWS NET uses satellite remote sensing and ground observations of rainfall and vegetation in order to provide information on drought, floods and other extreme weather events to decision makers. Previous research has presented results from a professional review questionnaire with FEWS NET expert end-users whose focus was to elicit Earth observation requirements. The review provided FEWS NET operational requirements and assessed the usefulness of additional remote sensing data. Here we analyzed 1342 food security update reports from FEWS NET. The reports consider the biophysical, socioeconomic, and contextual influences on the food security in 17 countries in Africa from 2000-2009. The objective was to evaluate the use of remote sensing information in comparison with other important factors in the evaluation of food security crises. The results show that all 17 countries use rainfall information, agricultural production statistics, food prices and food access parameters in their analysis of food security problems. The reports display large scale patterns that are strongly related to history of the FEWS NET program in each country. We found that rainfall data was used 84% of the time, remote sensing of vegetation 28% of the time, and gridded crop models 10%, reflecting the length of use of each product in the regions. More investment is needed in training personnel on remote sensing products to improve use of data products throughout the FEWS NET system.

Brown, Molly E.↗
NASA NTRS2000

Patch Network for Power Allocation and Distribution in Smart Materials

The power allocation and distribution (PAD) circuitry is capable of allocating and distributing a single or multiple sources of power over multi-elements of a power user grid system. The purpose of this invention is to allocate and distribute power that is collected by individual patch rectennas to a region of specific power-user devices, such as actuators. The patch rectenna converts microwave power into DC power. Then this DC power is used to drive actuator devices. However, the power from patch rectennas is not sufficient to drive actuators unless all the collected power is effectively used to drive another group by allocation and distribution. The power allocation and distribution (PAD) circuitry solves the shortfall of power for devices in a large array. The PAD concept is based on the networked power control in which power collected over the whole array of rectennas is allocated to a sub domain where a group of devices is required to be activated for operation. Then the allocated power is distributed to individual element of power-devices in the sub domain according to a selected run-mode.

Golembiewski, Walter T.↗
NASA NTRS2004

SIM PlanetQuest: Science with the Space Interferometry Mission

SIM - the Space Interferometry Mission - will perform precision optical astrometry on objects as faint as R magnitude 20. It will be the first space-based astrometric interferometer, operating in the optical band with a 10-m baseline. The Project is managed by the Jet Propulsion Laboratory, California Institute of Technology, in close collaboration with two industry partners, Lockheed Martin Missiles and Space, and TRW Inc., Space and Electronics Group. Launch of SIM is currently planned for 2009. In its wide-angle astrometric mode, SIM will yield 4 microarcsecond absolute position and parallax measurements. Astrometric planet searches will be done in a narrow-angle mode, with an accuracy of 4 microarcseconds or better in a single measurement. As a pointed rather than a survey instrument, SIM will maintain.its astrometric accuracy down to the faintest, magnitudes, opening up the opportunity for astrometry of active galactic nuclei to better than 10 pas. SIM will define a new astrometric reference frame, using a grid of approximately 1500 stars with positions accurate to 4 microarcseconds. The SIM Science Team comprises the Principal Investigators of ten Key Projects, and five Mission Scientists contributing their expertise to specific areas of the mission. Their science programs cover a wide range of topics in Galactic and extragalactic astronomy. They include: searches for low-mass planets - including analogs to our own solar system - tlie formation and dynamics of our Galaxy, calibration of the cosmic distance scale, and fundamental stellar astrophysics. All of the science observing on SIM is competitively awarded; the Science Team programs total about 40% of the total available, and the remainder will be assigned via future NASA competitions. This report is a compilation of science summaries by members of the Science Team, and it illustrates the wealth of scientific problems that microarcsecond-precision astrometry can contribute to. More information on SIM, including copies of this report, may be obtained from the project web site, at http://sim. jpl.nasa.gov.

Unwin, Stephen↗
NASA NTRS2012

Evaluating the Use of Remote Sensing Data in the U.S. Agency for International Development Famine Early Warning Systems Network

The U.S. Agency for International Development (USAID)'s Famine Early Warning System Network (FEWS NET) provides monitoring and early warning support to decision makers responsible for responding to food insecurity emergencies on three continents. FEWS NET uses satellite remote sensing and ground observations of rainfall and vegetation in order to provide information on drought, floods, and other extreme weather events to decision makers. Previous research has presented results from a professional review questionnaire with FEWS NET expert end-users whose focus was to elicit Earth observation requirements. The review provided FEWS NET operational requirements and assessed the usefulness of additional remote sensing data. We analyzed 1342 food security update reports from FEWS NET. The reports consider the biophysical, socioeconomic, and contextual influences on the food security in 17 countries in Africa from 2000 to 2009. The objective was to evaluate the use of remote sensing information in comparison with other important factors in the evaluation of food security crises. The results show that all 17 countries use rainfall information, agricultural production statistics, food prices, and food access parameters in their analysis of food security problems. The reports display large-scale patterns that are strongly related to history of the FEWS NET program in each country. We found that rainfall data were used 84% of the time, remote sensing of vegetation 28% of the time, and gridded crop models 10% of the time, reflecting the length of use of each product in the regions. More investment is needed in training personnel on remote sensing products to improve use of data products throughout the FEWS NET system.

USAID↗
NASA NTRS2016

Development of a Prototype Model-Form Uncertainty Knowledge Base

Uncertainties are generally classified as either aleatory or epistemic. Aleatory uncertainties are those attributed to random variation, either naturally or through manufacturing processes. Epistemic uncertainties are generally attributed to a lack of knowledge. One type of epistemic uncertainty is called model-form uncertainty. The term model-form means that among the choices to be made during a design process within an analysis, there are different forms of the analysis process, which each give different results for the same configuration at the same flight conditions. Examples of model-form uncertainties include the grid density, grid type, and solver type used within a computational fluid dynamics code, or the choice of the number and type of model elements within a structures analysis. The objectives of this work are to identify and quantify a representative set of model-form uncertainties and to make this information available to designers through an interactive knowledge base (KB). The KB can then be used during probabilistic design sessions, so as to enable the possible reduction of uncertainties in the design process through resource investment. An extensive literature search has been conducted to identify and quantify typical model-form uncertainties present within aerospace design. An initial attempt has been made to assemble the results of this literature search into a searchable KB, usable in real time during probabilistic design sessions. A concept of operations and the basic structure of a model-form uncertainty KB are described. Key operations within the KB are illustrated. Current limitations in the KB, and possible workarounds are explained.

Green, Lawrence L.↗
NASA NTRS2001

Computational Aeroacoustic Analysis System Development

Many industrial and commercial products operate in a dynamic flow environment and the aerodynamically generated noise has become a very important factor in the design of these products. In light of the importance in characterizing this dynamic environment, Rocketdyne has initiated a multiyear effort to develop an advanced general-purpose Computational Aeroacoustic Analysis System (CAAS) to address these issues. This system will provide a high fidelity predictive capability for aeroacoustic design and analysis. The numerical platform is able to provide high temporal and spatial accuracy that is required for aeroacoustic calculations through the development of a high order spectral element numerical algorithm. The analysis system is integrated with well-established CAE tools, such as a graphical user interface (GUI) through PATRAN, to provide cost-effective access to all of the necessary tools. These include preprocessing (geometry import, grid generation and boundary condition specification), code set up (problem specification, user parameter definition, etc.), and postprocessing. The purpose of the present paper is to assess the feasibility of such a system and to demonstrate the efficiency and accuracy of the numerical algorithm through numerical examples. Computations of vortex shedding noise were carried out in the context of a two-dimensional low Mach number turbulent flow past a square cylinder. The computational aeroacoustic approach that is used in CAAS relies on coupling a base flow solver to the acoustic solver throughout a computational cycle. The unsteady fluid motion, which is responsible for both the generation and propagation of acoustic waves, is calculated using a high order flow solver. The results of the flow field are then passed to the acoustic solver through an interpolator to map the field values into the acoustic grid. The acoustic field, which is governed by the linearized Euler equations, is then calculated using the flow results computed from the flow solver.

Hadid, A.↗
NASA NTRS2006

Volumetric Acoustic Vector Intensity Probe

A new measurement tool capable of imaging the acoustic intensity vector throughout a large volume is discussed. This tool consists of an array of fifty microphones that form a spherical surface of radius 0.2m. A simultaneous measurement of the pressure field across all the microphones provides time-domain near-field holograms. Near-field acoustical holography is used to convert the measured pressure into a volumetric vector intensity field as a function of frequency on a grid of points ranging from the center of the spherical surface to a radius of 0.4m. The volumetric intensity is displayed on three-dimensional plots that are used to locate noise sources outside the volume. There is no restriction on the type of noise source that can be studied. The sphere is mobile and can be moved from location to location to hunt for unidentified noise sources. An experiment inside a Boeing 757 aircraft in flight successfully tested the ability of the array to locate low-noise-excited sources on the fuselage. Reference transducers located on suspected noise source locations can also be used to increase the ability of this device to separate and identify multiple noise sources at a given frequency by using the theory of partial field decomposition. The frequency range of operation is 0 to 1400Hz. This device is ideal for the study of noise sources in commercial and military transportation vehicles in air, on land and underwater.

Klos, Jacob↗
NASA NTRS2022

Predicting Antarctic Net Snow Accumulation at the Kilometer Scale and Its Impact on Observed Height Changes

Sub-grid-scale processes occurring at or near the surface of an ice sheet have a potentially large impact on local and integrated net accumulation of snow via redistribution and sublimation. Given observational complexity, they are either ignored or parameterized over large-length scales. Here, we train random forest (RF) models to predict variability in net accumulation over the Antarctic Ice Sheet using atmospheric variables and topographic characteristics as predictors at 1 km resolution. Observations of net snow accumulation from both in situ and airborne radar data provide the input observable targets needed to train the RF models. We find that local net accumulation deviates by as much as 172% of the atmospheric model mean. The correlation in space between the predicted net accumulation variability and satellite-derived surface-height change indicates that surface processes operate differently through time, driven largely by the seasonal anomalies in snow accumulation.

Antarctic↗
NASA NTRS1995

Zero side force volute development

Collector scrolls on high performance centrifugal pumps are currently designed with methods which are based on very approximate flowfield models. Such design practices result in some volute configurations causing excessive side loads even at design flowrates. The purpose of this study was to develop and verify computational design tools which may be used to optimize volute configurations with respect to avoiding excessive loads on the bearings. The new design methodology consisted of a volute grid generation module and a computational fluid dynamics (CFD) module to describe the volute geometry and predict the radial forces for a given flow condition, respectively. Initially, the CFD module was used to predict the impeller and the volute flowfields simultaneously; however, the required computation time was found to be excessive for parametric design studies. A second computational procedure was developed which utilized an analytical impeller flowfield model and an ordinary differential equation to describe the impeller/volute coupling obtained from the literature, Adkins & Brennen (1988). The second procedure resulted in 20 to 30 fold increase in computational speed for an analysis. The volute design analysis was validated by postulating a volute geometry, constructing a volute to this configuration, and measuring the steady radial forces over a range of flow coefficients. Excellent agreement between model predictions and observed pump operation prove the computational impeller/volute pump model to be a valuable design tool. Further applications are recommended to fully establish the benefits of this new methodology.

Anderson, P. G.↗
NASA NTRS2002

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗