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NASA NTRS1971

Application of conservative finite-difference methods to advection problems

The possibility of applying the most recent conservative and widely applied numerical techniques in gas dynamics to problems encountered in meteorological computations is investigated. Solutions of the advection equation are obtained using conservative differencing methods. These results are compared to those obtained by differencing the advection equation directly. The comparison shows that better results are obtained when the conservative form of governing equation is used. In addition, better results are obtained with lower order conservative methods as compared with higher order differencing applied to the advection equation.

Fattahi, B.↗

NASA NTRS1975

ECASTAR: Energy conservation. An assessment of systems, technologies and requirements

A methodology was presented for a systems approach to energy conservation actions and their potentials and impacts in the United States. Constraints affecting the approach were ranked, and the most important ones are the present economic and technical conditions. The following unresolved issues were identified: consumptive lifestyles vs. conservation ethic, environmental standards vs. energy conservation, capital availability, decentralization and vertical integration vs. centralization, fuel rich regions vs. fuel poor regions, supply vs. end use conservation, life cycle costing vs. initial cost, mandatory savings vs. voluntary savings, labor intensive vs. capital intensive, price control vs. free market. The following recommendations were made: provide action/impact assessment, establish regional energy centers, improve technology articulation with government, design total energy systems, utilize existing systems approach expertise.

Source record↗

NASA NTRS1975

Energy conservation and the residential and commercial sector

A detailed analysis of energy conservation actions relevant to the residential and commercial sector has led to the conclusion that the potential for savings is great. The task will not be easy, however, since many of the actions require significant life style changes that are difficult to accomplish. Furthermore, many of the conservation actions cited as instant solutions to the energy crisis are those with only mid to long term potential, such as solar energy or heat pumps. Three significant conservation approaches are viable: adjusting price structure, mandating actions, and educating consumers. The first two appear to be the most feasible. But they are not without a price. Higher utility bills adversely affect the poor and the elderly on fixed incomes. Likewise, strict mandatory measures can be quite distasteful. But the effect of alternatives, such as voluntary savings accomplished through education processes, is minimal in a nation without a true conservation ethic.

Source record↗

NASA NTRS1976

Frequency modulation at a moving material interface and a conservation law for wave number

An integral conservation law for wave numbers is considered. In order to test the validity of the proposed conservation law, a complete solution for the reflection and transmission of an acoustic wave impinging normally on a material interface moving at a constant speed is derived. The agreement between the frequency condition thus deduced from the dynamic equations of motion and the frequency condition derived from the jump condition associated with the integral equation supports the proposed law as a true conservation law. Additional comparisons such as amplitude discontinuities and Snells' law in a moving media further confirm the stated proposition. Results are stated concerning frequency and wave number relations across a shock front as predicted by the proposed conservation law.

Kleinstein, G. G.↗

NASA NTRS1977

The NASA Energy Conservation Program

Large energy-intensive research and test equipment at NASA installations is identified, and methods for reducing energy consumption outlined. However, some of the research facilities are involved in developing more efficient, fuel-conserving aircraft, and tradeoffs between immediate and long-term conservation may be necessary. Major programs for conservation include: computer-based systems to automatically monitor and control utility consumption; a steam-producing solid waste incinerator; and a computer-based cost analysis technique to engineer more efficient heating and cooling of buildings. Alternate energy sources in operation or under evaluation include: solar collectors; electric vehicles; and ultrasonically emulsified fuel to attain higher combustion efficiency. Management support, cooperative participation by employees, and effective reporting systems for conservation programs, are also discussed.

Gaffney, G. P.↗

NASA NTRS1981

On the conservation of the first adiabatic invariant in perpendicular shocks

The conservation of the first adiabatic invariant of particle motion, the particle magnetic moment, at the front of perpendicular magnetosonic fast-mode shock waves is considered. Results of numerical simulations are presented which show that preshock and postshock values of the magnetic moment are on the average equal for particles transmitted by infinitesimally thin perpendicular magnetosonic fast-mode shocks, in contrast to extrapolations from adiabatic theory, which suggest that the first invariant is least likely to be conserved in this situation. The observed conservation is thus attributed to the continuity of the flux of total particle and field angular momentum across the shock front as a result of angular momentum conservation.

Pesses, M. E.↗

NASA NTRS1982

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics for real and perfect gases

A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.

Lombard, C. K.↗

NASA NTRS1983

On the symmetric form of systems of conservation laws with entropy

The present investigation has the objective to review the general structure of system of conservation laws with entropy, giving particular attention to a presentation of symmetric formulations of the equations of gas dynamics. Systems of hyperbolic conservation laws are considered, taking into account the case in which a system of equations is symmetric hyperbolic, questions of symmetrization, and entropy functions. The Euler equations for a polytropic gas in conservation form are considered. The symmetric form retains the conservation properties of the equations. Weak solutions remain, therefore, unchanged. Of particular computational interest is the possibility of using the symmetric form.

Harten, A.↗

NASA NTRS1986

Entropy conservative finite element schemes

The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.

Tadmor, E.↗

NASA NTRS1994

A new flux-conserving numerical scheme for the steady, incompressible Navier-Stokes equations

This paper is concerned with the continued development of a new numerical method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific scheme is then constructed for the solution of the thin airfoil boundary layer problem. Numerical results are presented which demonstrate the ability of the scheme to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other numerical methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.

Scott, James R.↗

NASA NTRS1995

On the Conservative Interface Treatment for Multi-Block Viscous Flow Computations

A pressure-based multi-block computational method is developed for solving the incompressible Navier-Stokes equations in general curvilinear grid systems. The scheme is based on the semi-implicit type flow solver with the staggered grid. Issues concerning the mass and momentum flux treatments at the discontinuous grid interface are addressed. Systematic numerical experiments for different interface treatments involving (1) straightforward interpolation, (2) globally conservative scheme, and (3) locally conservative scheme have been conducted. It is demonstrated that mass conservation has to be maintained locally, at the grid interface, with accuracy compatible with that of the scheme used in interior domain. Direct interpolation or globally conservative interface treatment of mass flux can not yield solutions with desirable accuracy.

Liu, J.↗

NASA NTRS1992

Conservative-coordinate transformations for atmospheric measurements

This lecture describes a technique by which atmospheric measurements of trace species with medium to long lifetimes can be 'coincidentally' compared and validated even though measurements are taken at different locations and different times In other words, the method, under suitable counditions, can remove a large amount of the natural meteorological variability. The technique involves the use of quasi-Lagrangian or conservative coordinates - air parcel tags which are invariant or nearly invariant under the motion of the parcel. The technique is called 'reconstruction', since measurements taken at one location can be reconstructed at different locations. In order to do this, the data are transformed into the conservative coordinates and accumulated. Within the conservative reference frame, much of the meteorological variability is removed. Once enough data are obtained within the system, the observations can be tranformed back into physical space at any location and compared with other measurements. The method by which the trace species data are obtained makes no difference; satellite, balloon, rocket, aircraft and ground-based data all become equivalent and can be intercompared. The conservative-coordinate system not only allows for intercomparison of data, but shows how data can be taken in such a way as to maximize the physical scope of the information. In other words, the method automatically suggests when conditions might be suitable to obtain information with different environmental situations. It also allows for the forecast of constituent fields using only the meteorological forecasts and limited observational data.

Schoeberl, M. R.↗

NASA NTRS2000

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Barth, Timothy↗

NASA NTRS2001

Distributed Relaxation for Conservative Discretizations

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Diskin, Boris↗

NASA NTRS2000

Developmental evolutionary biology of the vertebrate ear: conserving mechanoelectric transduction and developmental pathways in diverging morphologies

This brief overview shows that a start has been made to molecularly dissect vertebrate ear development and its evolutionary conservation to the development of the insect hearing organ. However, neither the patterning process of the ear nor the patterning process of insect sensory organs is sufficiently known at the moment to provide more than a first glimpse. Moreover, hardly anything is known about otocyst development of the cephalopod molluscs, another triploblast lineage that evolved complex 'ears'. We hope that the apparent conserved functional and cellular components present in the ciliated sensory neurons/hair cells will also be found in the genes required for vertebrate ear and insect sensory organ morphogenesis (Fig. 3). Likewise, we expect that homologous pre-patterning genes will soon be identified for the non-sensory cell development, which is more than a blocking of neuronal development through the Delta/Notch signaling system. Generation of the apparently unique ear could thus represent a multiplication of non-sensory cells by asymmetric and symmetric divisions as well as modification of existing patterning process by implementing novel developmental modules. In the final analysis, the vertebrate ear may come about by increasing the level of gene interactions in an already existing and highly conserved interactive cascade of bHLH genes. Since this was apparently achieved in all three lineages of triploblasts independently (Fig. 3), we now need to understand how much of the morphogenetic cascades are equally conserved across phyla to generate complex ears. The existing mutations in humans and mice may be able to point the direction of future research to understand the development of specific cell types and morphologies in the formation of complex arthropod, cephalopod, and vertebrate 'ears'.

Non-NASA Center↗

NASA NTRS2006

Mapping the Rainforest of the Sea: Global Coral Reef Maps for Global Conservation

Coral reefs are the center of marine biodiversity, yet are under threat with an estimated 60% of coral reef habitats considered at risk by the World Resources Institute. The location and extent of coral reefs in the world are the basic information required for resource management and as a baseline for monitoring change. A NASA sponsored partnership between remote sensing scientists, international agencies and NGOs, has developed a new generation of global reef maps based on data collected by satellites. The effort, dubbed the Millennium Coral Reef Map aims to develop new methods for wide distribution of voluminous satellite data of use to the conservation and management communities. We discuss the tradeoffs between remote sensing data sources, mapping objectives, and the needs for conservation and resource management. SeaWiFS data were used to produce a composite global shallow bathymetry map at 1 km resolution. Landsat 7/ETM+ data acquisition plans were modified to collect global reefs and new operational methods were designed to generate the firstever global coral reef geomorphology map. We discuss the challenges encountered to build these databases and in implementing the geospatial data distribution strategies. Conservation applications include a new assessment of the distribution of the world s marine protected areas (UNEPWCMC), improved spatial resolution in the Reefs at Risk analysis for the Caribbean (WRI), and a global basemap for the Census of Marine Life's OBIS database. The Millennium Coral Reef map and digital image archive will pay significant dividends for local and regional conservation projects around the globe. Complete details of the project are available at http://eol.jsc.nasa.gov/reefs.

Robinson, Julie A.↗

NASA NTRS2005

Conservative Patch Algorithm and Mesh Sequencing for PAB3D

A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.

Pao, S. P.↗

NASA NTRS2011

Improving Simulated Soil Moisture Fields Through Assimilation of AMSR-E Soil Moisture Retrievals with an Ensemble Kalman Filter and a Mass Conservation Constraint

Model simulated soil moisture fields are often biased due to errors in input parameters and deficiencies in model physics. Satellite derived soil moisture estimates, if retrieved appropriately, represent the spatial mean of soil moisture in a footprint area, and can be used to reduce model bias (at locations near the surface) through data assimilation techniques. While assimilating the retrievals can reduce model bias, it can also destroy the mass balance enforced by the model governing equation because water is removed from or added to the soil by the assimilation algorithm. In addition, studies have shown that assimilation of surface observations can adversely impact soil moisture estimates in the lower soil layers due to imperfect model physics, even though the bias near the surface is decreased. In this study, an ensemble Kalman filter (EnKF) with a mass conservation updating scheme was developed to assimilate the actual value of Advanced Microwave Scanning Radiometer (AMSR-E) soil moisture retrievals to improve the mean of simulated soil moisture fields by the Noah land surface model. Assimilation results using the conventional and the mass conservation updating scheme in the Little Washita watershed of Oklahoma showed that, while both updating schemes reduced the bias in the shallow root zone, the mass conservation scheme provided better estimates in the deeper profile. The mass conservation scheme also yielded physically consistent estimates of fluxes and maintained the water budget. Impacts of model physics on the assimilation results are discussed.

Li, Bailing↗