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NASA NTRS1976

Characteristics of wake vortex generated by a Boeing 727 jet transport during two-segment and normal ILS approach flight paths

A series of flight tests was conducted to evaluate the vortex wake characteristics of a Boeing 727 (B727-200) aircraft during conventional and two-segment ILS approaches. Twelve flights of the B727, which was equipped with smoke generators for vortex marking, were flown and its vortex wake was intentionally encountered by a Lear Jet model 23 (LR-23) and a Piper Twin Comanche (PA-30). Location of the B727 vortex during landing approach was measured using a system of photo-theodolites. The tests showed that at a given separation distance there were no readily apparent differences in the upsets resulting from deliberate vortex encounters during the two types of approaches. Timed mappings of the position of the landing configuration vortices showed that they tended to descend approximately 91 m(300 ft) below the flight path of the B727. The flaps of the B727 have a dominant effect on the character of the trailed wake vortex. The clean wing produces a strong, concentrated vortex but as the flaps are lowered, the vortex system becomes more diffuse. Pilot opinion and roll acceleration data indicate that 4.5 n.mi. would be a minimum separation distance at which roll control of light aircraft (less than 5,670 kg (12,500 lb) could be maintained during parallel encounters of the B727's landing configuration wake. This minimum separation distance is generally in scale with results determined from previous tests of other aircraft using the small roll control criteria.

Kurkowski, R. L.↗
NASA NTRSDate not supplied

Spatiotemporal Methane Emissions from Global Lakes and Reservoirs

Inland aquatic systems, such as lakes and reservoirs, contribute substantially to global methane (CH4) emissions; yet are among the most uncertain components of the total CH4 budget. Lakes and reservoirs have received recent attention as they may generate high CH4 fluxes. Improved quantification of these CH4 fluxes, particularly their spatiotemporal distribution, is key to realistically incorporating them in CH4 modeling and budget studies. Here we report on a new global, gridded (0.25° lat × 0.25° lon) study of lake and reservoir CH4 emissions, accounting for new knowledge regarding lake and reservoir areal extent and distribution, and spatiotemporal emission patterns influenced by diurnal variability, temperature-dependent seasonality, satellite-derived freeze-thaw dynamics, and eco-climatic and physical CH4-centric type classification. The results of this new data set comprise daily CH4 emissions from lake and reservoirs throughout the full annual cycle and are tightly anchored to field observations, in situ measurements, and remote-sensing observations. Results show that reservoirs cover 297 × 103 km2 globally and emit 10.1 Tg CH4 yr-1 from diffusive (1.2 Tg CH4 yr-1) and ebullitive (8.9 Tg CH4 yr-1) emission pathways. On a global scale, CH4 emitting areas of lakes cover 1853 × 103 km2 and emit 37.1 Tg CH4 yr-1 from diffusive (17.1 Tg CH4 yr-1) and ebullitive (23.0 Tg CH4 yr-1) emission pathways and an additional ebullition flux of 5.2 Tg CH4 yr-1 upon ice-melt due to the accumulation of bubbles during the freeze period. This analysis of lakes and reservoir CH4 emission addresses multiple gaps and uncertainties in previous studies and represents an important contribution to studies of the global CH4 budget. The new data sets and methodologies from this study provide a framework to better understand and model the current and future role of lakes and reservoirs in the global CH4 budget and to guide efforts to mitigate inland aquatic system CH4 emissions. This presentation will describe the methodologies applied and the major results of this study focusing on the spatiotemporal distribution of lake and reservoir type classification, processes driving lake and reservoir emission seasonality, and the contribution of individual lake and reservoir types to the annual cycle of inland aquatic CH4 emissions.

Spatiotemporal↗
NASA NTRS1992

Characterization of supersonic mixing in a nonreacting Mach 2 combustor

Planar measurements of the injection mole fraction distribution and the velocity field within a nonreacting model SCRAMJET combustor have been made using laser-induced iodine fluorescence. The combustor geometry investigated in this work is staged transverse injection of air into a Mach 2 freestream. A complete three-dimensional survey of the injectant mole fraction distribution has been generated and a single planar velocity measurement has been completed. The measurements reveal the dramatic effect of streamwise vortices on the mixing of the injectant in the near field of the injectors, as well as the rapid mixing generated by staging two field injectors. Analysis of the downstream decay of the maximum injectant mole fraction in this and other nonreacting combustor geometries indicates that the relative rate of injectant mixing well downstream of the injectors is independent of combustor geometry, combustor Mach number, and injectant molecular weight. Mixing within this region of the combustor is dominated by turbulent diffusion within the injectant plume. The transition of the dominant mixing mechanism, from vortex-driven mixing in the near field to turbulent diffusion in the far field, was found to occur in the region between 10 and 20 jet diameters downstream of the injectors.

Hollo, Steven D.↗
NASA NTRS2012

Vibroacoustic Characterization of a New Hybrid Wing-Body Fuselage Concept

A lighter, more robust airframe design is required to withstand the loading inherent to next generation non cylindrical commercial airliners. The Pultruded Rod Stitched Efficient Unitized Structure concept, a highly integrated composite design involving a stitched and co-cured substructure, has been developed to meet such requirements. While this structure has been shown to meet the demanding out-of-plane loading requirements of the flat-sided pressurized cabin design, there are concerns that the stiff co-cured details will result in relatively high acoustic radiation efficiencies at frequencies well below the thin skin acoustic coincidence frequency. To address this concern and establish a set of baseline vibroacoustic characteristics, a representative test panel was fabricated and a suite of tests were conducted that involved measurements of panel vibration and radiated sound power during point force and diffuse acoustic field excitations. Experimental results are shown and compared with Finite Element and Statistical Energy Analysis model predictions through the use of modal and energy correlation techniques among others. The behavior of the structure subject to turbulent boundary layer excitation is also numerically examined.

Allen, Albert R.↗
NASA NTRS1975

Experimentally determined aeroacoustic performance and control of several sonic inlets

Low speed wind tunnel tests were conducted to determine the aeroacoustic performance of several model sonic inlets. The results were analyzed to indicate how inlet aeroacoustic characteristics were affected by inlet design and operating conditions. A system for regulating sonic inlet noise reduction was developed and tested. Results indicate that pressure losses at forward velocity may be substantially less than those at static conditions. This is particularly true for translating centerbody inlets with the centerbody extended in the approach and landing position. Operation to simulated take-off incidence angles of 50 deg was demonstrated with good inlet performance. Results suggest that at takeoff, with 0 deg incidence angle, sonic inlet total pressure losses need not exceed those generated by skin friction for sound pressure level reductions to at least 15 dB. Inlet sound pressure level reduction was regulated to within approximately plus or minus 1 dB by controlling inlet surface static pressure measured at the diffuser exit.

Miller, B. A.↗
NASA NTRS1996

Application of the pressure sensitive paint technique to steady and unsteady flow

Pressure sensitive paint is a newly-developed optical measurement technique with which one can get a continuous pressure distribution in much shorter time and lower cost than a conventional pressure tap measurement. However, most of the current pressure sensitive paint applications are restricted to steady pressure measurement at high speeds because of the small signal-to-noise ratio at low speed and a slow response to pressure changes. In the present study, three phases of work have been completed to extend the application of the pressure sensitive paint technique to low-speed testing and to investigate the applicability of the paint technique to unsteady flow. First the measurement system using a commercially available PtOEP/GP-197 pressure sensitive paint was established and applied to impinging jet measurements. An in-situ calibration using only five pressure tap data points was applied and the results showed good repeatability and good agreement with conventional pressure tap measurements on the whole painted area. The overall measurement accuracy in these experiments was found to be within 0.1 psi. The pressure sensitive paint technique was then applied to low-speed wind tunnel tests using a 60 deg delta wing model with leading edge blowing slots. The technical problems encountered in low-speed testing were resolved by using a high grade CCD camera and applying corrections to improve the measurement accuracy. Even at 35 m/s, the paint data not only agreed well with conventional pressure tap measurements but also clearly showed the suction region generated by the leading edge vortices. The vortex breakdown was also detected at alpha=30 deg. It was found that a pressure difference of 0.2 psi was required for a quantitative pressure measurement in this experiment and that temperature control or a parallel temperature measurement is necessary if thermal uniformity does not hold on the model. Finally, the pressure sensitive paint was applied to a periodically changing pressure field with a 12.8s time period. A simple first-order pole model was applied to deal with the phase lag of the paint. The unsteady pressure estimated from the time-changing pressure sensitive paint data agreed well with the pressure transducer data in regions of higher pressure and showed the possibility of extending the technique to unsteady pressure measurements. However, the model still needs further refinement based on the physics of the oxygen diffusion into the paint layer and the oxygen quenching on the paint luminescence.

Shimbo, Y.↗
NASA NTRS2020

Satellite Beach Energy - Restructuring the Energy Balance in Satellite Beach, Florida, by Quantifying Solar Energy Production Potential using NASA POWER Data Products and LiDAR

The City of Satellite Beach, Florida, has committed to supplying 100% of its energy use from renewable energy, primarily solar, by the year 2050. The team created a methodology for estimating rooftop solar power potential using a high-resolution Light Detection and Ranging (LiDAR) dataset and the NASA Prediction of Worldwide Energy Resources (POWER) dataset to assist Satellite Beach in reaching their solar renewable energy goals. The POWER dataset provides information on direct and diffuse solar irradiation on horizontal surfaces, surface albedo, and effects of local meteorology, such as clouds. The team integrated the solar irradiance data with the LiDAR data to model slope, aspect, and shadowing in the 7 km2 study area to find suitable roof segments for solar panel installation and estimate the solar potential of each segment. This process was supplemented by an analysis of land surface temperature and urban greenness measured through the Normalized Difference Vegetation Index (NDVI) from Landsat 8 Operational Land Imager and Thermal Infrared Sensor (OLI/TIRS) observations. These metrics serve to target areas for cooling initiatives aimed at reducing Satellite Beach’s overall energy consumption. The team found the total rooftop solar potential throughout the city to be 221,919,330KWh per year with an average annual rooftop photovoltaic, or PV, potential of 55,647KWh per building. As such, the average building could generate over five times the annual energy needs for an average household if PV panels were installed on all viable areas of its roof.

Spencer Nelson↗
NASA NTRSDate not supplied

TPSAS-NF1676L-16988-DND

There has been renewed interest to uniformly recalibrate historical geostationary (GEO) data records to aid in climate monitoring. GEO sensors have annual repeatable angular sampling over a given location. The view angle is fixed and the imaging schedule is usually constant through its lifetime. Given the fact that colocated GEOs are always share the same sub-satellite point and maintain their imaging schedules provides repeatable angular sampling over decades. One of the biggest challenges in transferring a reference sensor calibration using invariant desert targets to another sensor is the accuracy of the bidirectional reflectance distribution function (BDRF). A well-calibrated GEO can be used to predict the daily exoatmospheric radiance model (DERM) over a desert target for a given GMT that is valid for any GEO sensor at the same location. The advantage of this method is that a BRDF is not needed. Another challenge of invariant target calibration is the unique spectra signature of the desert. However, since most GEOs are built in batches, the spectral response functions (SRF) are very similar for most historical GEOs, the spectral band adjustment factor (SBAF) between GEO sensors is much smaller than for MODIS and GEO sensors. Since the water vapor burden over the desert is seasonal, both the TOA and desert surface can be considered invariant for a given day of the year. The reference GEO can be inter-calibrated with MODIS or VIIRS, which have onboard visible calibration using solar diffusers, using other methods, such as ray-matching or deep convective clouds. Also the next generation GEOs will have onboard visible calibration, which will increase the accuracy of this method. Three Meteosats over the Libyan desert will be used to illustrate the DERM method. The reference Meteosat will be inter-calibrated against Aqua-MODIS. The reference GEO DERM will be constructed and used to calibrate the remaining Meteosats. The DERM calibration will be validated by comparing the calibration using Aqua-MODIS ray-matching. Similarly, two GOES sensors using the Sonoran desert will also be highlighted. An uncertainty analysis will also be performed with emphasis on the SBAF, derived over the desert targets using both SCIAMACHY and Hyperion hyper-spectral radiances.

David Doelling↗
NASA NTRS1986

Operating envelope charts for the Langley 0.3-meter transonic cryogenic wind tunnel

To take full advantage of the unique Reynolds number capabilities of the 0.3-meter Transonic Cryogenic Tunnel (0.3-m TCT) at the NASA Langley Research Center, it was designed to accommodate test sections other than the original, octagonal, three-dimensional test section. A 20- by 60-cm two-dimensional test section was installed in 1976 and was extensively used, primarily for airfoil testing, through the fall of 1984. The tunnel was inactive during 1985 so that a new test section and improved high speed diffuser could be installed in the tunnel circuit. The new test section has solid adaptive top and bottom walls to reduce or eliminate wall interference for two-dimensional testing. The test section is 33- by 33-cm in cross section at the entrance and is 142 cm long. In the planning and running of past airfoil tests in the 0.3-m TCT, the use of operating envelope charts have proven very useful. These charts give the variation of total temperature and pressure with Mach number and Reynolds number. The operating total temperature range of the 0.3-m TCT is from about 78 K to 327 K with total pressures ranging from about 17.5 psia to 88 psia. This report presents the operating envelope charts for the 0.3-m TCT with the adaptive wall tes t section installed. They were all generated based on a 1-foot chord model. The Mach numbers vary from 0.1 to 0.95.

Rallo, R. A.↗
NASA NTRS2000

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Bisset, David K.↗
NASA NTRS1990

Coupled effects of conduction in the crystal and thermo-solutal convection in a rectangular inclined enclosure

To date modeling of crystal growth of optoelectronic materials using Physical Vapor Transport has been limited to the study of the fluid phase. To achieve it, the equations of coupled heat, mass and momentum transfer in the gas have to be solved. The first objective of this study is to examine the effect of heat conduction in the crystal on the fluid flow in the neighborhood of the interface. Heat transfer boundary conditions on both interfaces were modified to take into account the additional heat flux between gas and solid. It is proved that heat conduction does not affect the fluid flow. In the presence of gravity, density gradients in the fluid phase generate convection responsible for the problem of a nonplanar growth of the interface. The second objective is to study systematically under one-g the different possible flows in order to solve this problem. Depending on the parameters, a diffusive mode and three convective modes (thermal, solutal and thermo-solutal) are observed. The competition between thermal and solutal convections leads to a mathematical condition which can be used to achieve a planar growth. It is proven that, under the physical conditions chosen, this mathematical condition cannot be thermodynamically satisfied.

Mennetrier, Christophe↗
NASA NTRS1997

Annual Research Briefs

This report contains the 1997 annual progress reports of the research fellows and students supported by the Center for Turbulence Research (CTR). Titles include: Invariant modeling in large-eddy simulation of turbulence; Validation of large-eddy simulation in a plain asymmetric diffuser; Progress in large-eddy simulation of trailing-edge turbulence and aeronautics; Resolution requirements in large-eddy simulations of shear flows; A general theory of discrete filtering for LES in complex geometry; On the use of discrete filters for large eddy simulation; Wall models in large eddy simulation of separated flow; Perspectives for ensemble average LES; Anisotropic grid-based formulas for subgrid-scale models; Some modeling requirements for wall models in large eddy simulation; Numerical simulation of 3D turbulent boundary layers using the V2F model; Accurate modeling of impinging jet heat transfer; Application of turbulence models to high-lift airfoils; Advances in structure-based turbulence modeling; Incorporating realistic chemistry into direct numerical simulations of turbulent non-premixed combustion; Effects of small-scale structure on turbulent mixing; Turbulent premixed combustion in the laminar flamelet and the thin reaction zone regime; Large eddy simulation of combustion instabilities in turbulent premixed burners; On the generation of vorticity at a free-surface; Active control of turbulent channel flow; A generalized framework for robust control in fluid mechanics; Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries; and DNS of shock boundary-layer interaction - preliminary results for compression ramp flow.

Spinks, Debra↗
NASA NTRS2017

The First Fermi-LAT SNR Catalog and Cosmic Ray Implications

While supernova remnants (SNRs) are widely thought to be powerful cosmic-ray accelerators, indirect evidence comes from a small number of well-studied cases. Here we systematically determine the gamma-ray emission detected by the Fermi Large Area Telescope (LAT) from all known Galactic SNRs, disentangling them from the sea of cosmic-ray generated photons in the Galactic plane. Using LAT data we have characterized the 1-100 GeV emission in 279 regions containing SNRs, accounting for systematic uncertainties caused by source misattribution and instrumental response. We classified 30 sources as SNRs, using spatial overlap with the radio emission position. For all the remaining regions we evaluated upper limits on SNRs' emission. In the First Fermi-LAT SNR Catalog there is a study of the common characteristics of these SNRs, such as comparisons between GeV, radio and TeV quantities. We show that previously satisfactory models of SNRs' GeV emission no longer adequately describe the data. To address the question of cosmic ray (CR) origins, we also examine the SNRs' maximal CR contribution assuming the GeV emission arises solely from proton interactions. Improved breadth and quality of multiwavelength (MW) data, including distances and local densities, and more, higher resolution gamma-ray data with correspondingly improved Galactic diffuse models will strengthen this constraint.

de Palma, F.↗
NASA NTRS2016

The First Fermi-LAT SNR Catalog and Cosmic Ray Implications

While supernova remnants (SNRs) are widely thought to be powerful cosmicray accelerators, indirect evidence comes from a small number of well-studied cases. Here we systematically determine the gamma-ray emission detected by the ermi Large Area Telescope (LAT) from all known Galactic SNRs, disentangling them from the sea of cosmic-ray generated photons in the Galactic plane. Using LAT data we have characterized the 1-100 GeV emission in 279 regions containing SNRs, accounting for systematic uncertainties caused by source misattribution and instrumental response. We classified 30 sources as SNRs, using spatial overlap with the radio emission position. For all the remaining regions we evaluated upper limits on SNRs' emission. In the First Fermi-LAT SNR Catalog there is a study of the common characteristics of these SNRs, such as comparisons between GeV, radio and TeV quantities. We show that previously satisfactory models of SNRs' GeV emission no longer adequately describe the data. To address the question of cosmic ray (CR) origins, we also examine the SNRs' maximal CR contribution assuming the GeV emission arises solely from proton interactions. Improved breadth and quality of multiwavelength (MW) data, including distances and local densities, and more, higher resolution gamma-ray data with correspondingly improved Galactic diffuse models will strengthen this constraint.

de Palma, F.↗
NASA NTRS2006

An Overview of Inter-comparison Methodologies for Terra and Aqua MODIS Calibration

With increasing efforts on data fusion and long-term climate data records (CDR) using observations made by multiple sensors, on the same or different platforms, their cross-calibration and validation work has become more and more important. The uncertainties of the climate models and data records depend not only on the calibration quality of individual sensors but also on their calibration consistency. This paper provides an overview of methodologies used by the MODIS Characterization Support Team (MCST) at NASA GSFC for the inter-comparison studies of Terra and Aqua MODIS on-orbit calibration. Each MODIS was built with a set of onboard calibrators (OBC) that include a blackbody (BB), a solar diffuser (SD), and a solar diffuser stability monitor (SDSM). The BB is primarily used for the thermal emissive bands (TEB) calibration and the SD/SDSM system for the reflective solar bands (RSB) calibration. Although the-instrument design and calibration approach are nearly identical for both Terra and Aqua MODIS and they all went through an extensive and similar pre-launch calibration and characterization process, still their on-orbit calibration consistency needs to be carefully examined and validated as many science products have been generated from observations made by both instruments. Methodologies discussed in this paper include inter-comparison studies using the Moon, a third sensor, and ground targets. Our results show that Terra and Aqua reflective solar bands and thermal emissive bands have been calibrated consistently with excellent long-term stabilities. For the 11 and 12 micrometers sea surface temperature (SST) bands, the calibration difference of Terra and Aqua MODIS is less than 0.2K.

Xiong, X.↗
NASA NTRS1993

Numerical investigations in three-dimensional internal flows

In the present reporting period, the 3D version of the OVERFLOW code was used to solve the flow within the internal portion of the supersonic inlet. The internal portion of this inlet is bounded by an inflow plane containing the leading edge of the sidewalls, the sidewalls, the ramp and cowl surfaces and an outflow plane just downstream of the minimum geometric area of the inlet. Boundary layer bleed was used in the two-dimensional calculations discussed in the previous progress report and that same bleed was applied in the present study. For reference, this bleed corresponds to locations designated as R2 and R3 in the Mach 5 inlet model test. Using the GRIDGEN code, a three dimensional grid was generated that accounted for the viscous effects expected to occur on the sidewall, as well as those known to occur on the ramp and cowl surfaces. The internal flow grid size was 141 streamwise by 101 cross stream by 71 in the lateral direction between sidewalls. Since the flow entering the inlet was not symmetrical, the inlet was solved from sidewall to sidewall (without using a symmetry plane). In addition to the short sidewalls proposed in the Langley geometry database, a set of shorter sidewalls was also investigated in the present study and was shown to have beneficial effects with respect to the flow distortion exiting the supersonic inlet. In addition to these calculations, additional 3D solutions using the OVERFLOW code were obtained for the flow downstream of the throat of the supersonic inlet, including a terminal shock wave system produced by a backpressured subsonic diffuser.

Rose, William C.↗
NASA NTRS2012

Optimal Inlet Shape Design of N2B Hybrid Wing Body Configuration

The N2B hybrid wing body aircraft was conceptually designed to meet environmental and performance goals for the N+2 generation transport set by the Subsonic Fixed Wing project of NASA Fundamental Aeronautics Program. In the present study, flow simulations are conducted around the N2B configuration by a Reynolds-averaged Navier-Stokes flow solver using unstructured meshes. Boundary conditions at engine fan face and nozzle exhaust planes are provided by the NPSS thermodynamic engine cycle model. The flow simulations reveal challenging design issues arising from boundary layer ingestion offset inlet and airframe-propulsion integration. Adjoint-based optimal designs are then conducted for the inlet shape to minimize the airframe drag force and flow distortion at fan faces. Design surfaces are parameterized by NURBS, and the cowl lip geometry is modified by a spring analogy approach. By the drag minimization design, flow separation on the cowl surfaces are almost removed, and shock wave strength got remarkably reduced. For the distortion minimization design, a circumferential distortion indicator DPCP(sub avg) is adopted as the design objective and diffuser bottom and side wall surfaces are perturbed for the design. The distortion minimization results in a 12.5 % reduction in the objective function.

Kim, Hyoungjin↗
NASA NTRS1994

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

Chang, Sin-Chung↗