Search NASA⌕ Search

SEARCH · Search NASA

Results for “Balanced convergence rate”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

30 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

A spectral multi-domain technique with application to generalized curvilinear coordinates

Spectral collocation methods have proven to be efficient discretization schemes for many aerodynamic and fluid mechanic problems. The high order accuracy and resolution shown by these methods allows one to obtain engineering accuracy solutions on coarse meshes, or alternatively, to obtain solutions with very small error. One drawback to these techniques was the requirement that a complicated physical domain must map into a simple computational domain for discretization. This mapping must be smooth if the high order accuracy and expontential convergence rates associated with spectral methods are to be preserved. Additionally even smooth stretching transformations can decrease the accuracy of a spectral method, if the stretching is severe. A further difficulty with spectral methods was in their implementation on parallel processing computers, where efficient spectral algorithms were lacking. The above restrictions are overcome by splitting the domain into regions, each of which preserve the advantages of spectral collocation, and allow the ratio of the mesh spacing between regions to be several orders of magnitude higher than allowable in a single domain. Such stretchings would be required to resolve the thin viscous region in an external aerodynamic problem. Adjoining regions are interfaced by enforcing a global flux balance which preserves high-order continuity of the solution, regardless of the type of the equations being solved.

Macaraeg, M. G.↗
NASA NTRS2013

Prediction of Ablation Rates from Solid Surfaces Exposed to High Temperature Gas Flow

A mathematical model and a solution algorithm is developed to study the physics of high temperature heat transfer and material ablation and identify the problems associated with the flow of hydrogen gas at very high temperatures and velocities through pipes and various components of Nuclear Thermal Rocket (NTR) motors. Ablation and melting can be experienced when the inner solid surface of the cooling channels and the diverging-converging nozzle of a Nuclear Thermal Rocket (NTR) motor is exposed to hydrogen gas flow at temperatures around 2500 degrees Kelvin and pressures around 3.4 MPa. In the experiments conducted on typical NTR motors developed in 1960s, degradation of the cooling channel material (cracking in the nuclear fuel element cladding) and in some instances melting of the core was observed. This paper presents the results of a preliminary study based on two types of physics based mathematical models that were developed to simulate the thermal-hydrodynamic conditions that lead to ablation of the solid surface of a stainless steel pipe exposed to high temperature hydrogen gas near sonic velocities. One of the proposed models is one-dimensional and assumes the gas flow to be unsteady, compressible and viscous. An in-house computer code was developed to solve the conservations equations of this model using a second-order accurate finite-difference technique. The second model assumes the flow to be three-dimensional, unsteady, compressible and viscous. A commercial CFD code (Fluent) was used to solve the later model equations. Both models assume the thermodynamic and transport properties of the hydrogen gas to be temperature dependent. In the solution algorithm developed for this study, the unsteady temperature of the pipe is determined from the heat equation for the solid. The solid-gas interface temperature is determined from an energy balance at the interface which includes heat transfer from or to the interface by conduction, convection, radiation, and ablation. Two different ablation models are proposed to determine the heat loss from the solid surface due to the ablation of the solid material. Both of them are physics based. Various numerical simulations were carried out using both models to predict the temperature distribution in the solid and in the gas flow, and then predict the ablation rates at a typical NTR motor hydrogen gas temperature and pressure. Solid mass loss rate per foot of a pipe was also calculated from these predictions. The results are presented for fully developed turbulent flow conditions in a sample SS pipe with a 6 inch diameter.

Akyuzlu, Kazim M.↗
NASA NTRS1984

Radiative heating rates near the stratospheric fountain

Radiative heating rates are computed for various sets of conditions thought to be appropriate to the stratospheric fountain region: with and without a layer of cirrus cloud between 100 and 150 mbar; with standard ozone and with decreased ozone in the lower stratosphere, again with and without the cirrus cloud; and with different temperatures in the tropopause region. The presence of the cloud decreases the radiative cooling below the cloud in the upper troposphere and increases the cooling above it in the lower stratosphere. The cloud is heated at the base and cooled at the top and thus radiatively destabilized; overall it gains energy by radiation. Decreasing ozone above the cloud also tends to cool the lower stratosphere. The net effect is a tendency for vertical convergence and horizontal divergence in the cloud region. High resolution profiles of temperature, ozone, and cloudiness within the fountain region are required in order to assess the final balance of the various processes.

Doherty, G. M.↗
NASA NTRS2023

The Sensitivity of the Equatorial Pacific ODZ to Particulate Organic Matter Remineralization in A Climate Model Under Pre-Industrial Conditions

Marine oxygen plays a fundamental role in regulating the transfer of organic carbon and nutrients to their dissolved inorganic forms, serving as the terminal electron acceptor for heterotrophic respiration. Oxygen can become limiting to these processes in coastal and open-ocean oxygen deficient zones (ODZs). The maintenance of ODZs depends on the balance between physical processes such as ventilation and biogeochemical processes such as remineralization. These two processes act in opposing directions on ODZs, with ventilation responsible for transporting oxygen from the surface, where it is near saturation with the partial pressure of O2 in the atmosphere, to deeper oxygen-depleted layers, and remineralization acting to consume oxygen through biogeochemical processes such as microbial degradation throughout the water column. Remineralization is represented in all CMIP6 models, but the actual parameterizations, as well as their magnitude, are widely varying. In this study, we examine the sensitivity to remineralization of the equatorial Pacific ODZ O2 ol/kg) in a model; the NASA GISS Ocean Biogeochemical Model (NOBM-G) embedded in the NASA-GISS coupled atmosphere-ocean model. We find that increasing the remineralization rate shoals the ODZ onset depth (i.e. the regionally averaged upper bound of the ODZ), and decreases ODZ volume and regional-averaged thickness. Changes in biological consumption and vertical convergence of oxygen are identified as the primary contributors to changes in ODZ onset depth. ODZ thickness is mainly influenced by the shoaling of the bottom boundary of the ODZ, which decreases with maximum remineralization rate due to decreasing oxygen consumption and increasing horizontal oxygen convergence in deep waters. On the other hand, vertically-averaged ODZ area has a more complex, non-monotonic relationship with maximum remineralization rate. While these findings suggest an important role for remineralization in determining the shape of the ODZ in our model, the relative importance of remineralization vs. other physical parameterizations remains to be established. While our results reflect the structure of our ocean biogeochemical model, the relationship of remineralization to ODZ characteristics in other models should be examined to better inform model inter-comparisons.

Oxygen-deficient zone↗
NASA NTRS1999

Three Paradigms of Lunar Regolith Evolution

Integration of diverse datasets on the Moon may render some paradigms of lunar science either better-defended or vulnerable. We will consider three paradigms commonly used for understanding the processes of lunar regolith evolution in light of new and accumulated data. Our premise is that all data-sets should converge to a single interpretation if a concept or model is to be accepted as a paradigm. If a convergence is lacking, the paradigm needs fresh scrutiny. SteadyState: Lunar regolith evolution is currently understood in terms of comminution, agglutination, and replenishment as described by McKay and coworkers). Briefly, the model envisages continued micrometeoritic bombardment to comminute exposed soil particles to finer sizes while continued agglutination consumes finer sizes to produce larger constructional particles. Eventually, a balance between these two opposing processes achieves a steady state; soils at steady state maintain their mean grain size (M(sub z)). Episodic higher-energy impacts excavate fresh coarse material from below the soil cover, disturb the steady state, and restart the process to achieve a new steady state. It follows that the thickness of the regolith at any site would control the frequency of replenishment; indeed, the thickness of the regolith at Apollo landing sites was predicted by McKay et al. from the average M(sub z) of local soils. However, replenishment may come also from disintegrating boulders and cobbles at the lunar surface, and rates of comminution and agglutination may depend on the properties of target material. Regression between M(sub z) and I(sub s)/Fe(sup 0) (a measure of maturity or total surface exposure) of Apollo soils at different sites shows the following relations and estimated M(sub z) at a high maturity of I(sub s)/Fe(sup 0)= 100. It is possible that Apollo 12 and 15 sites have the thickest regolith and the Apollo 16 site has the thinnest. It is also possible that Apollo 12 and 15 basalts are comminuted faster than Apollo 16 highland rocks and Apollo 14 and 17 soils are products of mixed parentage. If a soil becomes continually finer as it matures until agglutination catches up, and if comminution is differential-dependent on the physical properties of the constituents, then the composition of the bulk soil has to match the composition of some "fulcrum" grain size fraction, say X Grain size fractions >X and <X will complement each other; their mass balance is the bulk soil. It appears that the 10-20-micron size fraction may be the fulcrum. In general, trace-element chemistry and IR reflectance spectra of this size fraction are closest to that of the bulk soil, regardless of maturity that is surprising. Disaggregated products of regolith breccias may also show similar relationships. If the 10-20 gm is the fulcrum (i.e., X as above) for many soil properties (e.g., major element composition, FMR, solar-wind-implanted elements), then this may be the ultimate mean grain size of lunar soils at steady state. However, different properties of soils may find steady states at different grain size fractions. The steady state of solar-wind-implanted elements, on the other hand, will climb up the grain-size scale as agglutinates transfer surface-correlated components into volume correlated components until a saturation level is reached or the rates of replenishment and implantation become equal. The same will be the case with vapor-deposited reduced metals as they too are incorporated inside constructional particles. Properties that are directly affected by soil-maturation processes will thus have different pathways of achieving steady states. Maturity, i.e., cumulative surface exposure, of lunar soils is best quantified by the amount of nanophase superparamagnetic Fe(sup 0) (np-Fe(sup 0)) normalized to Fe content (=I(sub s)/Fe(sup 0). The majority consensus (paradigm?) for the production of np-Fe(sup 0) is associated with the production of agglutinates. Because large doses of solar-wind H are implanted in all lunar soils upon exposure, any melting (e.g., during agglutinate production) triggers a chemical reduction of Fe-bearing minerals resulting in np-Fe(sup 0) production. The quantity of np-Fe(sup 0) is thus dependent on melting events, (i.e., exposure), and limited by the Fe content of the soil. All freshly produced np-Fe(sup 0) resides in agglutinitic glass, as new TEM images show. Apparently, the correction procedure developed by Lucey et al. to estimate the Fe content of the lunar surface from IR-reflectance spectra depends on accepting the above. However, the process of producing np-Fe(sup 0) may be physical rather than chemical. All np-Fe(sup 0) could be deposits from a vapor produced by micrometeoritic impact on lunar soils. If metal-O bonds in target phases are broken, O being "most volatile" will escape leaving an O-deficient vapor to facilitate the production of np-Fe(sup 0). If so, the quantity of np-Fe(sup 0) is dependent on the vaporizing events, (i.e., exposure), and limited by the efficiency of breaking metal-O bonds and the escape of 0. To the extent that strengths of metal-O bonds are dependent on the local crystal field, production of np-Fe(sup 0) may be limited by the mineral composition of target soils and not by their total Fe content. According to this model, vapor-deposited np-Fe(sup 0) should be found at any retentive sites on lunar soil grains. Indeed, TEM images show np-Fe(sup 0) on plagioclase and ilmenite. Incorporation of such pre-irradiated np-Fe(sup 0)-bearing grains into agglutinates may account for eventual increased emplacement of np-Fe(sup 0) in agglutinates. Such a paradigm shift in understanding the origin of np-Fe(sup 0) will raise questions ranging from the unquestionable use of Is/FeO as the universal maturity parameter of lunar soils to global elemental maps of the Moon from remote-sensing data. Additional information is contained in the original.

Basu, A.↗
NASA NTRS1998

Ma'adim Vallis Estuarine Delta in Elysium Basin and Its Relevance as a Landing Site for Exobiology Exploration on Mars

The debouche of Ma'adim Vallis in the Elysium Basin generated a transitional transported sediment structure, which planimetric shape is controlled by the enclosing topography of a deep reentrant gulf of the Basin into the highland. We defined it as an estuarine delta. The location and the importance of this estuarine delta is supported by the theoretical model of graded profile constructed for Ma'adim Vallis, and by two approaches: (i) the reconstruction of Ma'adim Vallis downstream course from Gusev to Elysium Basin, and (ii) the survey of the sediment deposit in the alleged estuary. The longitudinal graded profile of Ma'adim Vallis finds its base-level in the Elysium Basin, at a about 1000 m elevation, which is in agreement with the observed Basin shoreline. This model is supported by observational evidence of flow between the northern rim of Gusev crater, and the Elysium Basin shoreline. This downstream course of Ma'adim Vallis can be divided into three hydrogeologic regions. into three hydrogeologic regions. (a) The first region is a flooded plain (Zephiria Mensae), consisting in chaotic terrain formed by highland rocks, and disintegrated lava of the western flank of Apollinaris. Morphologic indicators of the flood process are: (1) the sediment deposit over the Gusev crater northern rim that reflects the overspilling of the crater-lake water through a 40-km wide gap provided by an ancient impact crater, (2) the tear-drop shaped feature on the northeastern flank of Apollinaris Patera, and (3) the chaotic terrain that suggest the emergence of ground water generated by the seepage of the crater lake through high-permeable broken rampart material. This underground water circulation sustained by the hydrostatic pressure of the crater-lake has likely generated a hydrothermal system in the volcanic environment of Apollinaris Patera. The stratigraphy of the flooded area is identified as Hesperian age, with occurrences of Noachian hilly individual features, and as Amazonian flooded plain and chaotic material, (b) The second region is located on the western flank of Apollinaris Patera. It is surrounded by relics of deep valleys that suggest a former downstream course of Ma'adim Vallis. The geologic setting of this region (Lucus Planum) is interpreted to be an Amazonian formation composed by the middle and lower members of the Medusae Formation., c) The third region corresponds to the convergence of the west and east branches of Ma'adirn Vallis into a deep re-entrant wide gulf that penetrates about 100 km into the highland. This topographic depression is delineated by the 1000 in elevation contour. This gulf has formed an estuarine configuration centered at 3S/190W within the Elysium Basin. This configuration has favored the formation of a estuarine sedimentary delta, because of topographically controlled lateral migration. This estuarine structure is strongly dominated by the incoming supply of Ma'adim Vallis fluvial sediment extracted from Zephiria Mensae and Lucus Planum. The obtuse-angle geometry of the estuary increases the sedimentation rate, which is higher than in the course of the channel. The sediment deposition process is governed by the estuarine water circulation. The inflowing loaded fluvial water enters the estuary as a bottom current, and mixes with the relatively less-loaded water of the receiving basin. When they mixed. the inflowing fluvial material, and the landward basin circulating water generate an accumulation of highly-diversified estuarine deposit stratification. This accumulation of material is mostly centered in the transitional zone of the delta. The sediment trapping efficiency of the estuary is function of the energy balance between the inflowing fluvial water, and the ingoing basin current. The submergence of the delta by the rising of the water-level increases the estuary water-depth, and consequently the sediment entrapment is favored. The locus of sediment accumulation moves landward in the zone of inflowing fluvial water. This results in the rising of the channel base-level, thus in the increase of the length of the longitudinal graded-profile. The sediment deposit facies of the zone A shows a generally smooth surface. The longitudinal deposit is bordered by alluvial terraces that reflect the variations of the channel level. The waning of the Elysium Basin caused the erosion of the Basin estuarine zone by small channels, this episode being characterized by dissected tear-drop shaped mesa-like morphologies in the delta. Our estuarine delta model predicts a lithostratigraphic depositional sequence associated with the water submergence and the transgression of Elysium Basin. The thickness of the estuarine sediment corresponds to the Elysium Basin levels changes relatively to the bed floor of the estuary, The depositional sequence of Ma'adim Vallis are described: (1) a pro-current filled region (A), where fluvial are longitudinally accumulated by the inflowing water, (2) inverse current from Elysium Basin (B), where fluvial and lacustrine sediments are accumulated, and (3) zone of current equilibrium (C), where the sediments are distributed as a shoreline at the boundary of the estuarine delta. The estuary sedimentology dynamics collects and keeps the record of the geologic unit material crossed by Ma'adim Vallis, and those of the lakebed deposit of Elysium Basin. The predicted mixed stratigraphic sequence from fluvial and lacustrine sediment makes this site an exceptional environment to concentrate potential multi-origin biologic records. We envision four possible strategies to explore this sedimentologic record: (1) longitudinal surface and subsurface traverses in region A to investigate outcrop levees, (2) exploration of the mesa walls in region B, (3) deep drilling hole lodging of the sequential deposits in the zones A and B, and (4) surface and subsurface exploration of the shoreline delta. The expected results for each of these strategies are: (1) in the deepest layers of region A are predicted frequent and abundant coarse material, sandy lenses lamination grading downward from sand to cobbles. Volcanic debris from the Noachian crustal Plateau unit material, hydrothermal altered rocks, carbonates, Hesperian and possibly Amazonian volcanic material, from Apollinaris Patera, altered rocks and carbonates from Zephiria Mensae are expected. As a favorable environment for inception of life, possible biological records are expected in transported rock, (2) At the surface, and subsurface (<=100 m), large deposits sandy to silted material from Elysium paleolake basin mixed with fine-grained sediments from Ma'adim Vallis are expected mostly in the upstream part of region B, (3) on the shoreline of the estuarine delta, abundant fine material from Elysium paleolake basin (evaporites, carbonates), mostly Amazonian in age are expected. The Ma'adini estuary is a favorable landing site for all the above mentioned science aspects, and .for its location. The site lies near the equator, which is favorable for the rover solar power supply, and at 1000m elevation, which is a favorable configuration for the descent system braking. Another advantage is the extent of the area of high scientific interest (33,000 sq km), which provides a good ellipse, and potential long study traverses.

Grin, E. A.↗
NASA NTRS1985

Estimation of precipitation from GOES IR imagery during FGGE: Application to diagnostic studies

The objectives were to (1) develop a method of estimating open-ocean rainfall and associated latent heat release via GOES IR satellite imagery; (2) to use remote precipitation estimates to investigate the role of diabatic forcing in the maintenance of the South Pacific Convergence Zone (SPCZ) during FGGE SOP-1/; and (3) to assess the significance of non-quasigeostrophic transports of energy in several cyclogenetic events preceding the development of a North Atlantic blocking episode during FGGE SOP-1. The bulk of the early FY-85 work was directed toward development of the single pixel indexing technique (SPI) which assigns a rain rate to GOES IR black-body temperatures, T sub b, via a non-linear statistical relationship developed with raingauge measurements. The method was tested against radar-derived rainfall during GATE raingauge measurements over coastal North Carolina and island stations in the South Pacific Ocean. Skill was found comparable to Arkin's method (1979 MWR) in convective situations. The results suggest that transferring a rain algorithm from one oceanic regime to another may not require substantial modification of coefficients or tunable parameters. Twelve H mean rainfall amounts were produced for the region bounded by 10 deg. N, 50 deg. S, 120 deg W and 170 deg. E during the period January 10 to 16, 1979. These estimates constitute a basic input to diagnostic calculations of diabatic heating over the SPCZ region. ECMWF level III-b data analyses was used to compute several components of the APE balance in the South Pacific during the period January 10 to 18, 1979.

Robertson, F. R.↗
NASA NTRS2020

Intercomparison of Precipitation Estimates Over the Southern Ocean from Atmospheric Reanalyses

Precipitation is a major component of the hydrologic cycle and plays a significant role in the sea-ice mass balance in the polar regions. Over the Southern Ocean, precipitation is particularly uncertain due to the lack of direct observations in this remote and harsh environment. Here we demonstrate that precipitation estimates from 8 global reanalyses produce similar spatial patterns between 2000-2010, although their annual means vary by about 250 mm yr -1 (or 26 percent of the median values) and there is little similarity in their representation of interannual variability. ERA-Interim produces the smallest and CFSR produces the largest amount of precipitation overall. Rainfall and snowfall are partitioned in five reanalyses; snowfall suffers from the same issues as the total precipitation comparison, with ERA-Interim producing about 128 mm less snowfall and JRA-55 about 103 mm more rainfall compared to the other reanalyses. When compared to CloudSat-derived snowfall, these five reanalyses indicate similar spatial patterns, but differ in their magnitude. All reanalyses indicate precipitation on nearly every day of the year, with spurious values occurring on an average of about 60 days yr -1 resulting in an accumulation of about 4.5 mm yr -1 . While similarities in spatial patterns among the reanalyses suggest a convergence, the large spread in magnitudes points to issues with the background models in adequately reproducing precipitation rates, and the differences in the model physics employed. Further improvements to model physics are required to achieve confidence in precipitation rate, as well as the phase and frequency of precipitation in these products.

Linette N. Boisvert↗
NASA NTRS1995

Actively Controlled Shaft Seals for Aerospace Applications

This study experimentally investigates an actively controlled mechanical seal for aerospace applications. The seal of interest is a gas seal, which is considerably more compact than previous actively controlled mechanical seals that were developed for industrial use. In a mechanical seal, the radial convergence of the seal interface has a primary effect on the film thickness. Active control of the film thickness is established by controlling the radial convergence of the seal interface with a piezoelectric actuator. An actively controlled mechanical seal was initially designed and evaluated using a mathematical model. Based on these results, a seal was fabricated and tested under laboratory conditions. The seal was tested with both helium and air, at rotational speeds up to 3770 rad/sec, and at sealed pressures as high as 1.48 x 10(exp 6) Pa. The seal was operated with both manual control and with a closed-loop control system that used either the leakage rate or face temperature as the feedback. The output of the controller was the voltage applied to the piezoelectric actuator. The seal operated successfully for both short term tests (less than one hour) and for longer term tests (four hours) with a closed-loop control system. The leakage rates were typically 5-15 slm (standard liters per minute), and the face temperatures were generally maintained below 100C. When leakage rate was used as the feedback signal, the setpoint leakage rate was typically maintained within 1 slm. However, larger deviations occurred during sudden changes in sealed pressure. When face temperature was used as the feedback signal, the setpoint face temperature was generally maintained within 3 C, with larger deviations occurring when the sealed pressure changes suddenly. the experimental results were compared to the predictions from the mathematical model. The model was successful in predicting the trends in leakage rate that occurred as the balance ratio and sealed pressure changed, although the leakage rates were not quantitatively predicted with a high degree of accuracy. This model could be useful in providing valuable design information for future actively controlled mechanical seals.

Salant, Richard F.↗
NASA NTRS1993

Massively parallel computation of RCS with finite elements

One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary steps expected to result in a robust low i/o system for very large finite element problems.

Parker, Jay↗
NASA NTRS2011

Contributions of GRACE to Climate Monitoring

The NASA/German Gravity Recovery and Climate Experiment (GRACE) was launched in March 2002. Rather than looking downward, GRACE continuously monitors the locations of and precise distance between twin satellites which orbit in tandem about 200 km apart. Variations in mass near Earth's surface cause heterogeneities in its gravity field, which in turn affect the orbits of satellites. Thus scientists can use GRACE data to map Earth's gravity field with enough accuracy to discern month to month changes caused by ocean circulation and redistribution of water stored on and in the land. Other gravitational influences, such as atmospheric circulation, post-glacial rebound, and solid earth movements are either independently determined and removed or are negligible on a monthly to sub-decadal timescale. Despite its coarse spatial (>150,000 sq km at mid-latitudes) and temporal (approx monthly) resolutions, GRACE has enabled significant advancements in the oceanic, hydrologic, and cryospheric science, and has great potential for climate monitoring, because it is the only global observing system able to measure ocean bottom pressures, total terrestrial water storage, and ice mass changes. The best known GRACE results are estimates of Greenland and Antarctic ice sheet loss rates. Previously, scientists had estimated ice mass losses using ground and satellite based altimetry and surface mass balance estimates based on snowfall accumulation and glacier discharge. While such measurements are still very useful for their spatial detail, they are imperfectly correlated with large-scale ice mass changes, due to snow and ice compaction and incomplete spatial coverage. GRACE enables scientists to generate monthly time series of Greenland and Antarctic ice mass, which have confirmed the shrinking of the polar ice sheets, one of the most obvious and indisputable manifestations of climate change. Further, GRACE has located and quantified hot spots of ice loss in southeastern Greenland and western Antarctica. For 2002 to present, the rate of ice mass loss has been 200 to 300 GT/yr in Greenland and 70 to 210 GT/yr in Antarctica, and some scientists are suggesting that the rates are accelerating. Similarly, GRACE has been used to monitor mass changes in alpine glaciers. Tamisiea et al. first characterized glacier melt along the southern coast of Alaska, more recently estimated to be occurring at a rate of 84 GT/yr. Chen et al. estimated that Patagonian glaciers are melting at a rate of 28 GT/yr, and estimated that the high mountains of central Asia lose ice at a rate of 47 GT/yr. Tapley et al. and Wahr et al. presented the first GRACE based estimates of changes in column-integrated terrestrial water storage (TWS; the sum of ground-water, soil moisture, surface waters, snow, ice, and water stored in vegetation) at continental scales. Since then, dozens of studies have shown that GRACE based estimates of regional to continental scale TWS variations agree with independent information, and some innovative uses of GRACE data have been developed. Rodell et al. (2004) and Swenson and Wahr (2006) demonstrated that by combining GRACE derived terrestrial water storage changes with observations of precipitation and runoff in a river basin scale water budget, it was possible to produce new estimates of evapotranspiration and atmospheric moisture convergence, essential climate variables that are difficult to estimate accurately. Similarly, GRACE has been used to constrain estimates of global river discharge and the contribution of changes in TWS to sea level rise. Crowley et al. observed a negative correlation between interannual TWS anomalies in the Amazon and the Congo River basin. Yeh et al. and Rodell et al. estimated regionally averaged groundwater storage variations based on GRACE and auxiliary observations. Rodell et al. and Tiwari et al. applied that method to quantify massive groundwater depletion in northern India caused by over reliance on aquifers for irration, and Famiglietti et al. found a similar situation in California's Central Valley. Zaitchik et al. and Lo et al. described approaches to use GRACE to constrain hydrological models, enabling integration of GRACE data with other observations and achieving much higher spatial and temporal resolutions than GRACE alone. Such approaches are now supporting applications including drought and water resources monitoring. Oceanography has likewise benefitted from the independent nature of GRACE observations. One application is measurement of the mass component of sea level rise, which complements radar altimetry and in situ measurements. GRACE also measures ocean bottom pressures (OBP), which help to refine understanding and modeling of ocean circulation and the ocean's fresh water budget, among other things. For example, Hayakawa et al. showed that GRACE observes OBP patterns absent from the background models of oceanic variability. Morison et al. used GRACE to describe important decadal scale shifts in circulation and an ongoing trend of freshening of the western Arctic, important indicators of climate variability. The research of Song and Zlotnicki and Chambers and Willis on GRACE-derived ocean bottom pressures in the sub-polar gyre led to the discovery of an ENSO teleconnection and a long-term change in OBP in the North Pacific sub-polar gyre that was not predicted by an ocean model. Further, Chambers and Willis were able to identify an internal redistribution of mass between Atlantic and Pacific Oceans lasting at least six years, which was not predicted by ocean models and was the first direct evidence of sustained mass transport from one ocean basin to another on periods longer than a year. Boening et al. observed a record increase in OBP over part of the southeastern Pacific in late 2009 and early 2010, primarily caused by wind stress curl associated with a strong and persistent anticyclone and likely related to the concurrent Central Pacific El Nino. GRACE has far surpassed its 5-year design lifetime, but it will likely succumb to the aging of batteries and instrument systems sometime in the next few years. NASA has begun initial development of a follow-on to GRACE with very similar design, which could launch as soon as 2016 and would provide continuity in the data record while improving resolution slightly. Higher resolution time variable gravity missions are also on the drawing board .

Rodell, Matthew↗
NASA NTRS2012

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Leffell, Joshua Isaac↗