Low thrust orbit determination program

Logical flow and guidelines are provided for the construction of a low thrust orbit determination computer program. The program, tentatively called FRACAS (filter response analysis for continuously accelerating spacecraft), is capable of generating a reference low thrust trajectory, performing a linear covariance analysis of guidance and navigation processes, and analyzing trajectory nonlinearities in Monte Carlo fashion. The choice of trajectory, guidance and navigation models has been made after extensive literature surveys and investigation of previous software. A key part of program design relied upon experience gained in developing and using Martin Marietta Aerospace programs: TOPSEP (Targeting/Optimization for Solar Electric Propulsion), GODSEP (Guidance and Orbit Determination for SEP) and SIMSEP (Simulation of SEP)

3D velocity-depth model building using surface seismic and well data

The objective of this work was to develop techniques that could be used to rapidly build a three-dimensional velocity-depth model of the subsurface, using the widest possible variety of data available from conventional seismic processing and allowing for moderate structural complexity. The result is a fully implemented inversion methodology that has been applied successfully to a large number of diverse case studies. A model-based inversion technique is presented and shown to be significantly more accurate than the analytical methods of velocity determination that dominate industrial practice. The inversion itself is based around two stages of ray-tracing. The first takes picked interpretations in migrated-time and maps them into depth using a hypothetical interval velocity field; the second checks the validity of this field by simulating fully the kinematics of seismic acquisition and processing as accurately as possible. Inconsistencies between the actual and the modelled data can then be used to update the interval velocity field using a conventional linear scheme. In order to produce a velocity-depth model that ties the wells, the inversion must include anisotropy. Moreover, a strong correlation between anisotropy and lithology is found. Unfortunately, surface seismic and well-tie data are not usually sufficient to uniquely resolve all the anisotropy parameters; however, the degree of non-uniqueness can be measured quantitatively by a resolution matrix which demonstrates that the model parameter trade-offs are highly dependent on the model and the seismic acquisition. The model parameters are further constrained by introducing well seismic traveltimes into the inversion. These introduce a greater range of propagation angles and reduce the non- uniqueness

Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation

Improved estimation of hydrometeorological states from down-sampled observations and background model forecasts in a noisy environment, has been a subject of growing research in the past decades. Here, we introduce a unified framework that ties together the problems of downscaling, data fusion and data assimilation as ill-posed inverse problems. This framework seeks solutions beyond the classic least squares estimation paradigms by imposing proper regularization, which are constraints consistent with the degree of smoothness and probabilistic structure of the underlying state. We review relevant regularization methods in derivative space and extend classic formulations of the aforementioned problems with particular emphasis on hydrologic and atmospheric applications. Informed by the statistical characteristics of the state variable of interest, the central results of the paper suggest that proper regularization can lead to a more accurate and stable recovery of the true state and hence more skillful forecasts. In particular, using the Tikhonov and Huber regularization in the derivative space, the promise of the proposed framework is demonstrated in static downscaling and fusion of synthetic multi-sensor precipitation data, while a data assimilation numerical experiment is presented using the heat equation in a variational setting

Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals

We demonstrate that the global fields of temperature, humidity and geopotential heights admit a nearly sparse representation in the wavelet domain, offering a viable path forward to explore new paradigms of sparsity-promoting data assimilation and compressive recovery of land surface-atmospheric states from space. We illustrate this idea using retrieval products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave Sounding Unit (AMSU) on board the Aqua satellite. The results reveal that the sparsity of the fields of temperature is relatively pressure-independent while atmospheric humidity and geopotential heights are typically sparser at lower and higher pressure levels, respectively. We provide evidence that these land-atmospheric states can be accurately estimated using a small set of measurements by taking advantage of their sparsity prior.Comment: 12 pages, 8 figures, 1 tabl

ESTIMATION OF DISCRETIZATION ERROR FOR THREE DIMENSIONAL CFD SIMULATIONS USING A TAYLOR SERIES MODIFIED EQUATION ANALYSIS

The Consortium for Advanced Simulation of LightWater Reactors (CASL) is working towards developing a virtual reactor called the Virtual Environment for Reactor Application (VERA). As part of this work, computational fluid dynamics (CFD) simulations are being made to inform lower fidelity models to predict heat transfer and fluid flow through a light water reactor core. A 5x5 fuel rod assembly with mixing vanes was chosen to represent a 17x17 fuel rod assembly. Even with this simplified geometry, it is estimated that hundreds of millions of cells are needed for a solution to be close to the asymptotic region. The large number of cells is an issue when completing solution verification studies because of computational cost. Solution verification studies traditionally involve the use of Roache’s grid convergence index (GCI) to estimate the error, but require the solution to be in the asymptotic region. This is a severely limiting restriction for simulations with large range of length scales as is the case with the 5x5 fuel rod assembly with mixing vanes. Unfortunately, GCI does not perform well when the solution is outside the asymptotic region. However, a new method called the robust multi-regression (RMR) solution verification method has the potential to produce good results, even when the solution is outside the asymptotic region. This study builds a software framework that improves the RMR solution verification analysis by improving the error model used to estimate the discretization error. Previous RMR work used a power function to model the error, which was the same function used in the Richardson extrapolation. The power function form is a result of a Taylor series expansion on a uniform grid for simple numerical schemes and physics. It can be improved by completing a Taylor series expansion for the numerical scheme, boundary conditions, and physics that are being employed in the simulation of interest. This framework was shown to improve the ability for the error model to estimate the discretization error and uncertainty. The improved error model was able to predict error on a refined grid within the uncertainty bounds, while the standard error model did not. In addition, the method of manufactured modified equation analysis solutions (MMMEAS) was developed and applied to justify the use of a down selection method for terms in the error model

Comparison of Subgrid-scale Viscosity Models and Selective Filtering Strategy for Large-eddy Simulations

Explicitly filtered large-eddy simulations (LES), combining high-accuracy schemes with the use of a selective filtering without adding an explicit subgrid-scales (SGS) model, are carried out for the Taylor-Green-vortex and the supersonic-boundary-layer cases. First, the present approach is validated against direct numerical simulation (DNS) results. Subsequently, several SGS models are implemented in order to investigate if they can improve the initial filter-based methodology. It is shown that the most accurate results are obtained when the filtering is used alone as an implicit model, and for a minimal cost. Moreover, the tests for the Taylor-Green vortex indicate that the discretization error from the numerical methods, notably the dissipation error from the high-order filtering, can have a greater influence than the SGS models