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Errors inherent to the graphic analysis of CFD solutions are discussed. Consideration is given to contouring, plotting of vector fields, particle tracing, and the computation of flow functions involving integration or differentiation. Many of the problems addressed are the direct result of knowing the function values only at grid points, not in the interior of the grid cells.
A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.
A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.
The present use of locally refined Cartesian grids to solve transonic flow problems about three-dimensional aircraft configurations obviates surface-conforming grid generation through an embedding of surface-geometry paneling in the grid. Accurate resolution of flow close to the boundary, and in regions with strong velocity gradients, is achieved via hierarchical local refinement which subdivides a given grid cell into eight cells. Fast and reliable convergence is obtained by combining several preconditioners and damping strategies. Methods are suggested for preclusion of global convergence problems.
The sensitivity of passive microwave sea-ice concentration (SIC) algorithms to the selection of tie points was analyzed. SICs were derived with the NASA Team ice algorithm for global tie points and for locally and seasonally adjusted tie points. The SSM/I SIC was then compared to Landsat-MSS-derived SICs. Preliminary results show a mean difference of SSM/I- and Landsat-derived SICs for 50 x 50 km grid cells of 2.7 percent along the ice edge of the Beaufort Sea during fall with local tie points. The accuracy decreased to 9.7 percent when global tie points were used. During freeze-up in the Beaufort Sea, with grey ice and nilas as dominant ice cover, the mean difference was 4.3 percent for local tie points and 13.9 percent for global tie points. For the spring ice cover in the Bering Sea a mean difference of 4.4 percent for local tie points and 15.7 percent for global tie points was found. This large difference reveals some limitations of the NASA-Team algorithm under freeze-up and spring conditions (thin ice areas).
A computer program, ISOLEV, allows interactive visualization of CFD scalar and vector functions by means of user-specified sections of the data. The application is based on table lookups which govern both isosurface generation on hexahedral grid cells and recursive subdivision of the cells. The program supports Gouraud-shaded color maps of the data, surface-on-surface maps, and deformation surfaces of vector fields. The execution of the code for animated sweeps is improved by resorting to the cells in the database and maintaining an active set of cells to be rendered.
The Reynolds averaged Navier-Stokes equations have been applied to Stratospheric Observatory For Infrared Astronomy (SOFIA) configurations. Comparisons between numerical and experimental results are made in two-dimensions for free shear layers and a rectangular cavity, and in three-dimensions for simplified SOFIA geometries. Dominant acoustic behaviour of the cavity flows compare well with experiment. The sensitivity of the solutions to changes in grid cell size and artificial dissipation levels are shown. Furthermore, optical path distortion due to the flow field is modelled using geometrical constructs. The results demonstrate the viability and usefulness of the present computational methods for this class unsteady applications.
We model the annual incoming solar radiation topoclimatology for the Rio Grande River basin in Colorado, U.S.A. Hourly pyranometer measurements are combined with satellite reflectance data and 30-m digital elevation models within a topographic solar radiation algorithm. Our results show that there is large spatial variability within the basin, even at an annual integration length, but the annual, basin-wide mean is close to that measured by the pyranometers. The variance within 16 sq km and 100 sq km regions is a linear function of the average slope in the region, suggesting a possible parameterization for sub-grid-cell variability.
The fraction of the grid cell area covered by rainfall, mu, is an essential parameter in descriptions of land surface hydrology in climate models. A simple procedure is presented for estimating this fraction, based on extensive observations of storm areas and rainfall volumes. Storm area and rainfall volume are often linearly related; this relation can be used to compute the storm area from the volume of rainfall simulated by a climate model. A formula is developed for computing mu, which describes the dependence of the fractional coverage of rainfall on the season of the year, the geographical region, rainfall volume, and the spatial and temporal resolution of the model. The new formula is applied in computing mu over the Amazon region. Significant temporal variability in the fractional coverage of rainfall is demonstrated. The implications of this variability for the modeling of land surface hydrology in climate models are discussed.
The global biogeochemical model presented has two primary objectives. First, it characterizes natural elemental cycles and their linkages for the four elements significant to Earth's biota: C, N, S, and P. Second, it describes changes in these cycles due to human activity. Global nutrient cycles were studied within the drainage basins of several major world rivers on each continent. The initial study region was the Mississippi drainage basin, concentrating on carbon and nitrogen. The model first establishes the nutrient budgets of the undisturbed ecosystems in a study region. It then uses a data set of land use histories for that region to document the changes in these budgets due to land uses. Nutrient movement was followed over time (1800 to 1980) for 30 ecosystems and 10 land use categories. A geographically referenced ecological information system (GREIS) was developed to manage the digital global data bases of 0.5 x 0.5 grid cells needed to run the model: potential vegetation, drainage basins, precipitation, runoff, contemporary land cover, and FAO soil maps of the world. The results show the contributions of land use categories to river nutrient loads on a continental scale; shifts in nutrient cycling patterns from closed, steady state systems to mobile transient or open, steady state systems; soil organic matter depletion patterns in U.S. agricultural lands; changing nutrient ratios due to land use changes; and the effect of using heavy fertilizer on aquatic systems.
The commercial application of Indium Phosphide solar cells in practical space missions is crucially dependent upon achieving a major cost reduction which could be offered by heteroepitaxy on cheaper, more rugged substrates. Furthermore, significant mass reduction, compatibility with mechanically stacked multijunction cells, and elimination of the current loss through glue discoloration, is possible in III-V solar cells by the development of ultrathin, directly glassed cells. The progress of a UK collaborative program to develop high efficiency, homojunction InP solar cells, grown by MOCVD on Si substrates, is described. Results of homoepitaxial cells (is greater than 17 percent 1 Sun AM0) are presented, together with progress in achieving low dislocation density heteroepitaxy. Also, progress in a UK program to develop ultrathin directly-glassed GaAs cells is described. Ultrathin (5 micron) GaAs cells, with 1 Sun AM0 efficiencies up to 19.1 percent, are presented, together with progress in achieving a direct (adhesive-less) bond between the cell and coverglass. Consequential development to, for example, cell grids, are also discussed.
A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated.
Combustion processes in rocket propulsion systems are characterized by the existence of multiple, vastly differing time and length scales, as well as flow-speeds at wide variation of Mach numbers. The chemical kinetics processes in the highly active reaction zone are characterized by much smaller scales compared to fluid convective and diffusive time scales. An operator splitting procedure for transient finite rate chemistry problems has been developed using a pressure based method, which can be applied to all speed flows without difficulties. The splitting of chemical kinetics terms formed the fluid-mechanical terms of the species equation ameliorated the difficulties associated with the disparate time scales and stiffness in the set of equations which describes highly exothermic combustion. A combined efficient ordinary differential equations (ODE) solver was used to integrate the effective chemical source terms over the residence time at each grid cell. One and two dimensional reacting flow situations were carried out to demonstrate and verify the current procedure. Different chemical kinetics with different degrees of nonlinearity have also been incorporated to test the robustness and generality of the proposed method.
Two completely different simulation algorithms are compared by applying them to the same stellar dynamical problems: one is a self-consistent field (SCF) method for solving Poisson's equation and the other is a phase-space method for integrating the collisionless Boltzmann equation. We consider simulations of spherical stellar systems which are initially far from equilibrium and relax to their final states by gravitational collapse. The initial conditions consist of either uniform-density spheres or nonequilibrium models having Plummer density profiles, in which velocity dispersions are assigned according to given virial ratios. If a few tens of radial expansion terms with hundreds of thousands of particles are used in the SCF code, excellent agreement is found between the results it generates and those obtained with the phase-space solver, provided that a sufficiently large number of grid cells are employed with the latter. These findings imply that for simulating collisionless systmes over many dynamical times, the SCF approach based on sampling phase space is competitive with the approach treating phase space as a continuous fluid. The results of our tests make it possible to estimate the number of particles and basis functions required in situations like those modeled. Limitations of the SCF method and the choice of an optimal set of basis functions are also discussed.
A generalization of the single soil layer variable infiltration capacity (VIC) land surface hydrological model previously implemented in the Geophysical Fluid Dynamics Laboratory (GFDL) general circulation model (GCM) is described. The new model is comprised of a two-layer characterization of the soil column, and uses an aerodynamic representation of the latent and sensible heat fluxes at the land surface. The infiltration algorithm for the upper layer is essentially the same as for the single layer VIC model, while the lower layer drainage formulation is of the form previously implemented in the Max-Planck-Institut GCM. The model partitions the area of interest (e.g., grid cell) into multiple land surface cover types; for each land cover type the fraction of roots in the upper and lower zone is specified. Evapotranspiration consists of three components: canopy evaporation, evaporation from bare soils, and transpiration, which is represented using a canopy and architectural resistance formulation. Once the latent heat flux has been computed, the surface energy balance is iterated to solve for the land surface temperature at each time step. The model was tested using long-term hydrologic and climatological data for Kings Creek, Kansas to estimate and validate the hydrological parameters, and surface flux data from three First International Satellite Land Surface Climatology Project Field Experiment (FIFE) intensive field campaigns in the summer-fall of 1987 to validate the surface energy fluxes.
Global sets of surface radiation budget (SRB) have been obtained from satellite programs. These satellite-based estimates need validation with ground-truth observations. This study validates the estimates of monthly mean surface insolation contained in two satellite-based SRB datasets with the surface measurements made at worldwide radiation stations from the Global Energy Balance Archive (GEBA). One dataset was developed from the Earth Radiation Budget Experiment (ERBE) using the algorithm of Li et al. (ERBE/SRB), and the other from the International Satellite Cloud Climatology Project (ISCCP) using the algorithm of Pinker and Laszlo and that of Staylor (GEWEX/SRB). Since the ERBE/SRB data contain the surface net solar radiation only, the values of surface insolation were derived by making use of the surface albedo data contained GEWEX/SRB product. The resulting surface insolation has a bias error near zero and a root-mean-square error (RMSE) between 8 and 28 W/sq m. The RMSE is mainly associated with poor representation of surface observations within a grid cell. When the number of surface observations are sufficient, the random error is estimated to be about 5 W/sq m with present satellite-based estimates. In addition to demonstrating the strength of the retrieving method, the small random error demonstrates how well the ERBE derives from the monthly mean fluxes at the top of the atmosphere (TOA). A larger scatter is found for the comparison of transmissivity than for that of insolation. Month to month comparison of insolation reveals a weak seasonal trend in bias error with an amplitude of about 3 W/sq m. As for the insolation data from the GEWEX/SRB, larger bias errors of 5-10 W/sq m are evident with stronger seasonal trends and almost identical RMSEs.
A binary Coulomb collision algorithm is developed for weighted particle simulations employing Monte Carlo techniques. Charged particles within a given spatial grid cell are pair-wise scattered, explicitly conserving momentum and implicitly conserving energy. A similar algorithm developed by Takizuka and Abe (1977) conserves momentum and energy provided the particles are unweighted (each particle representing equal fractions of the total particle density). If applied as is to simulations incorporating weighted particles, the plasma temperatures equilibrate to an incorrect temperature, as compared to theory. Using the appropriate pairing statistics, a Coulomb collision algorithm is developed for weighted particles. The algorithm conserves energy and momentum and produces the appropriate relaxation time scales as compared to theoretical predictions. Such an algorithm is necessary for future work studying self-consistent multi-species kinetic transport.
Estimating terrestrial net primary production (NPP) using remote-sensing tools and ecosystem models requires adequate ground-based measurements for calibration, parameterization, and validation. These data needs were strongly endorsed at a recent meeting of ecosystem modelers organized by the International Geosphere-Biosphere Program's (IGBP's) Data and Information System (DIS) and its Global Analysis, Interpretation, and Modelling (GAIM) Task Force. To meet these needs, a multinational, multiagency project is being coordinated by the IGBP DIS to compile existing NPP data from field sites and to regionalize NPP point estimates to various-sized grid cells. Progress at Oak Ridge National Laboratory (ORNL) on compiling NPP data for grasslands as part of the IGBP DIS data initiative is described. Site data and associated documentation from diverse field studies are being acquired for selected grasslands and are being reviewed for completeness, consistency, and adequacy of documentation, including a description of sampling methods. Data are being compiled in a database with spatial, temporal, and thematic characteristics relevant to remote sensing and global modeling. NPP data are available from the ORNL Distributed Active Archive Center (DAAC) for biogeochemical dynamics. The ORNL DAAC is part of the Earth Observing System Data and Information System, of the US National Aeronautics and Space Administration.