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The purpose of this investigation was to study methods and ways for rapid inversion programs involving the correlated k-method, and to study the infrared observations of Saturn from the Cassini orbiter.
The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended.
A virtual presentation for NASA Sounder Science Team Meeting
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One of the most promising approaches for the reduction of convection during the crystal growth of conductive melts (semiconductor crystals) is the application of magnetic fields. Current technology allows the experimentation with very intense static fields (up to 80 KGauss) for which nearly convection free results are expected from simple scaling analysis in stabilized systems (vertical Bridgman method with axial magnetic field). However, controversial experimental results were obtained. The computational methods are, therefore, a fundamental tool in the understanding of the phenomena accounting during the solidification of semiconductor materials. Moreover, effects like the bending of the isomagnetic lines, different aspect ratios and misalignments between the direction of the gravity and magnetic field vectors can not be analyzed with analytical methods. The earliest numerical results showed controversial conclusions and are not able to explain the experimental results. Although the generated flows are extremely low, the computational task is a complicated because of the thin boundary layers. That is one of the reasons for the discrepancy in the results that numerical studies reported. Modeling of these magnetically damped crystal growth experiments requires advanced numerical methods. We used, for comparison, three different approaches to obtain the solution of the problem of thermal convection flows: (1) Spectral method in spectral superelement implementation, (2) Finite element method with regularization for boundary layers, (3) Multiquadric method, a novel method with global radial basis functions, that is proven to have exponential convergence. The results obtained by these three methods are presented for a wide region of Rayleigh and Hartman numbers. Comparison and discussion of accuracy, efficiency, reliability and agreement with experimental results will be presented as well.
As Voyager 2 approached Jupiter's bow shock, large-amplitude fluctuations were seen in both the magnetic field and plasma fluid velocity. These fluctuations generally coincided with the occurrence of long-lived energetic particle events similar to the upstream waves often observed near the earth's bow shock. In this paper an analysis of the magnetic field and plasma observations using spectral methods is presented. The characteristic spectral features related to the upstream waves are generally seen near 1 mHz. The measured correlation lengths of these fluctuations suggest that they are coherent over only a few wavelengths. The analysis is consistent with the hypothesis that these fluctuations are driven by streaming ions, possibly protons. No evidence for the existence of whistler waves is found. It is argued that some of the observed spectral features suggest that dynamical turbulent processes are occurring in the uptream wave region, including a possible observation of an inverse cascade of magnetic helicity to large spatial scales.
Observations of magnetic field fluctuations near Comet Halley have revealed a rapid development of a Kolmogoroff-like turbulence spectrum extending from below 0.01 Hz to above 0.1 Hz. Spectra obtained far from the comet have a strong peak in power near the Doppler-shifted ion-cyclotron frequency of singly ionized water. Closer to the comet, the spectrum at higher frequencies is enhanced in power level over the background solar wind spectrum by approximately an order of magnitude. The equations of incompressible MHD are solved using a two-dimensional 256 x 256 mode spectral method code to simulate this spectral evolution as an inertial range turbulent cascade. The initial conditions contained a constant magnetic field and a single coherent wave mode at a low wave number. The solar wind turbulence was modeled by a background noise spectrum having a Kolmogoroff spectral index. The coherent mode decayed into an inertial range spectrum with Kolmogoroff slope within a few eddy-turnover times. Both the time scale and the increase in power level of the turbulence seen in the simulation are in accord with the Giotto observations.
The purpose here is to assess the state of the art in the areas of numerical analysis that are particularly relevant to computational fluid dynamics (CFD), to identify promising new developments in various areas of numerical analysis that will impact CFD, and to establish a long-term perspective focusing on opportunities and needs. Overviews are given of discretization schemes, computational fluid dynamics, algorithmic trends in CFD for aerospace flow field calculations, simulation of compressible viscous flow, and massively parallel computation. Also discussed are accerelation methods, spectral and high-order methods, multi-resolution and subcell resolution schemes, and inherently multidimensional schemes.
Although the primary focus of the Jupiter Icy Moons Orbiter (JIMO) mission will be the characterization and study of Jupiter's icy moons, there will be opportunities throughout the mission for unprecendented observations of Jupiter. With an adaptable suite of payload instruments, the atmospheric data collected by JIMO can help to answer fundamental questions about the largest planet in our solar system that remain after (or were generated by) previous spacecraft reconnaissance (e.g. Voyager, Galileo, and Cassini). Near-IR (0.7-4 micron) spectral imaging will most likely be used to identify mineralogies and ices on the Jovian satellites by virtue of their spectral signatures. This same capability is very well tailored for studies of Jovian atmospheric dynamics and structure. Near-IR methane absorption bands allow 2-D mapping of the horizontal wind field at size scales to tens of kms, as well as the height dependence of this field above the ammonia cloud deck (700 to a few mbar), constraining current models of atmospheric vertical structure. Likewise, atmospheric ice aerosols with unique spectroscopic signatures (ammonia ice near 1.5, 2.0, and 2.8 microns and water ice between 3.0 - 3.5 microns) can be detected and mapped using spectral difference imaging or spectrally inclusive principal-component methods. Spectral imaging of the Jovian aurora via (3)H(+) emission lines between 3 - 4 microns can be used to spatially map the interplay between the satellites) Jupiter's magnetosphere, and Jupiter's atmosphere. Each of these measurements addresses one or more fundamental questions related to the energy balance in Jupiter's atmosphere. All of these tunable imaging objectives can be achieved using acousto-optic tunable filters (AOTF's), which have been used for years in ground-based observing instruments and which have been proposed for numerous planetary missions. The application of this technology to the science objectives of both the icy satellites and Jovian atmospheric components of the JIMO mission will be discussed.
In this report we compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a dimensionless parameter. We begin with the simple and widely used finite difference time domain (FDTD) methods, and establish rigorous error bounds of them, which are valid up to the time at $O(1/\varepsilon)$. In the error estimates, we pay particular attention to how the errors depend explicitly on the mesh size $h$ and time step $\tau$ as well as the small parameter $\varepsilon$. Based on the results, in order to obtain "correct" numerical solutions up to the time at $O(1/\varepsilon)$, the $\varepsilon$-scalability (or meshing strategy requirement) of the FDTD methods should be taken as $h = O(\varepsilon^{1/2})$ and $\tau = O(\varepsilon^{1/2})$. To improve the spatial resolution capacity, we apply the Fourier spectral method to discretize the Dirac equation in space. Error bounds of the resulting finite difference Fourier pseudospectral (FDFP) methods show that they exhibit uniform spatial errors in the long-time regime, which are optimal in space as suggested by the Shannon's sampling theorem. Extensive numerical results are reported to confirm the error bounds and demonstrate that they are sharp.
The convergence of the spectral vanishing method for both the spectral and pseudospectral discretizations of the inviscid Burgers' equation is analyzed. It is proven that this kind of vanishing viscosity is responsible for a spectral decay of those Fourier coefficients located toward the end of the computed spectrum; consequently, the discretization error is shown to be spectrally small independent of whether the underlying solution is smooth or not. This in turn implies that the numerical solution remains uniformly bounded and convergence follows by compensated compactness arguments.
The study deals with a method of calibrating the spectral irradiance of an unknown radiation source based on an existing standard source of spectral radiance. The method is applied to several sources that are being applied as irradiance sources in various experimental situations, e.g., on board the Space Shuttle.
The results of a NASA investigation of a claimed Overlap between two gust response analysis methods: the Statistical Discrete Gust (SDG) Method and the Power Spectral Density (PSD) Method are presented. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented for several different airplanes at several different flight conditions indicate that such an Overlap does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.
This paper presents the results of a NASA investigation of a claimed 'Overlap' between two gust response analysis methods: the Statistical Discrete Gust (SDG) method and the Power Spectral Density (PSD) method. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented in this paper for several different airplanes at several different flight conditions indicate that such an 'Overlap' does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.
In this paper we describe some classes of multigrid methods for solving large linear systems arising in the solution by finite difference methods of certain boundary value problems involving Poisson's equation on rectangular regions. If parallel computing systems are used, then with standard multigrid methods many of the processors will be idle when one is working at the coarsest grid levels. We describe the use of Multiple Coarse Grid MultiGrid (MCGMG) methods. Here one first constructs a periodic set of equations corresponding to the given system. One then constructs a set of coarse grids such that for each grid corresponding to the grid size h there are four grids corresponding to the grid size 2*h. Multigrid operations such as restriction of residuals and interpolation of corrections are done in parallel at each grid level. For suitable choices of the multigrid operators the MCGMG method is equivalent to the Parallel Superconvergent MultiGrid (PSMG) method of Frederickson and McBryan. The convergence properties of MCGMG methods can be accurately analyzed using spectral methods.
We present two efficient methods for simulating real-time behavior of a dynamically deformable 3D object modeled by finite element equations. The first method is based on modal analysis, which uses the most significant vibration modes of the object to compute the deformations in real-time for applied forces. The second method uses the spectral Lanczos decomposition to obtain the explicit solutions of the finite element equations.
The CLARREO Pathfinder (CPF) mission will implement a state-of-the-art intercalibration method for transferring CPF’s in-orbit Système Internationale (SI)-traceable reference to the shortwave channel of the Clouds and the Earth’s Radiance Energy System (CERES) and the reflective solar bands of the Visible Infrared Imaging Radiometer Suite (VIIRS) aboard the NOAA-20 satellite platform with a targeted intercalibration methodology uncertainty of 0.3% (k=1). In order to achieve such a high intercalibration accuracy, the CPF intercalibration measurements to be scheduled need to closely match those from CERES and VIIRS in time, space, angles, and wavelength. Despite’s CPF’s two-axis pointing capability to match its boresight line of sight to that of a target sensor, there will be finite residual differences in angular samplings of the two instruments. The potential angular mismatch between CPF and the target sensors can introduce systematic errors in the intercalibration results, and therefore needs to be corrected using a rigorously designed algorithm. The CPF intercalibration team has been developing a correction method for mitigating the impact of these angular anisotropic effects in the CPF-VIIRS and CPF-CERES intercalibration. The method explores the spectral correlation relationship between the reflected solar radiances from the same surface target that would be measured by CPF at two adjacent angles. Our studies have shown that the spectral information based on CPF measurements can be used to accurately predict the spectral radiance or reflectance difference due to a given mismatch in the viewing and solar geometry. The hyper-spectral information can also be used to provide scene stratification without using any auxiliary data, which is critical to reduce the angular correction uncertainty. The angular correction relationship can be well established using simulated CPF-like top-of-atmosphere spectral radiances observed at all sorts of viewing geometry and solar angles and for different scenes. Intensive radiative transfer simulations have been completed using a state-of-art radiative transfer model developed by the CPF team members. The implementation of the algorithm on high-fidelity event simulation data and the characterization for the angular adjustment uncertainty will be presented.
Multidomain spectral methods are presently used to numerically simulate a strut-wall intersection's laminar horseshoe vortex flow through direct solution of the three-dimensional, incompressible, time-dependent Navier-Stokes equations. Direct expansion in Chebyshev polynomials and spectral element method spatial discretization of flow dependence are used to achieve high-order accuracy, and minimal dispersion errors. Low and moderate Reynolds number results are presented to illustrate the method application.