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At least 379 records · Page 21

Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media

A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

Campbell, W.↗

Simplified clustering of nonorthogonal grids generated by elliptic partial differential equations

A simple clustering transformation is combined with the Thompson, Thames, and Mastin (TTM) method of generating computational grids to produce controlled mesh spacings. For various practical grids, the resulting hybrid scheme is easier to apply than the inhomogeneous clustering terms included in the TTM method for this purpose. The technique is illustrated in application to airfoil problems, and listings of a FORTRAN computer code for this usage are included.

Sorenson, R. L.↗

Establishing a Lunar Surface Power Grid

The National Aeronautics and Space Administration (NASA) is seeking to develop a lunar surface power system for its Artemis missions as well as for planned future commercial lunar surface activities. This power system is composed of a number of assets which contain electrical loads and many of these contain energy resources. These assets can be connected to form a grid, which allows power to be shared between the system’s distributed energy resources. This grid can provide backup power to existing assets as well as primary power to future assets. A trade study was conducted for an Artemis scale grid, which has identified 3 kV AC as an ideal transmission voltage. Development work has also begun for a universal modular interface converter (UMIC) which connects assets and microgrids operating at 120 V DC space power to the grid. Products from this grid definition and UMIC development work will enable highly reliable and available power for Artemis and future planetary surface missions, which is key to achieving NASA’s long term vision of space exploration.

Planetary surface power↗

Near-Body Grid Adaption for Overset Grids

A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.

Buning, Pieter G.↗

Using XR for Improving Scientific Discovery With Numerical Weather Models

Earth science (ES) digital twins will help us understand the complex interactions and interrelationships that make up our Earth system and the impacts of earth science phenomena on it. Our work addresses two underdeveloped areas in current ES digital twin work: improving the understanding and interaction with ES model outputs by using Virtual and Mixed Reality (XR) tools and improving the non-intuitive mapping of continuous ES natural phenomena to gridded reference frames in current numerical models. Traditionally, scientists working on ES view and analyze the results of calculated or measured observables with static 1-dimensional (1D), 2D or 3D plots displayed on flat computer screens or paper. Using such limited mediums, it can be very difficult to identify, track and understand the evolution of key features due to poor viewing angles and the nature of flat computer screens. In addition, numerical models, such as the NASA Goddard Earth Observing System (GEOS) ES model, are almost exclusively formulated, visualized and analyzed in an Eulerian reference frame with fixed grid points in space and time. However, ES phenomena such as convective clouds, hurricanes and wildfire smoke plumes are visualized and analyzed in a Lagrangian reference frame: therefore it is often difficult and unnatural to understand these phenomena in relation to each other, visualized either in an Eulerian or Lagrangian context. In 3D visualizations, data generally takes one of three forms: gridded (e.g., voxelized) data, where space is divided into regions; point clouds, where data is represented as a set of points; and meshes, where objects are rendered as surfaces composed of small polygons (usually triangles). A gridded, Eulerian reference frame has been the default representation for the 2D visual analysis of atmospheric data in part because the numerical methods used to generate atmospheric model data in the first place use a gridded approach, with equations defining the relationships between the physical variables in each of a grid's cells across successive timesteps. In our work, we are particularly interested in data from GEOS. Another reason why gridded representations tend to be used for visualizing data from such models is because trajectories are difficult to interpret from representations on 2D surfaces, due to line-of-sight ambiguity. Instead of a fixed grid from GEOS, we embed a trajectory model to simulate particles' movement throughout a GEOS run. We then ingest these particle trajectories as animated point clouds with a NASA open source XR toolkit, the Mixed Reality Exploration Toolkit (MRET), and merge GEOS data with ES phenomena data onto one combined visualization that the user can intuitively interact with. Efficient rendering of arbitrarily large point clouds is an ongoing challenge being addressed by the computer science community, with the GPU-based optimizations and efficient GPU memory utilization a common theme of recent advances, especially for XR, where sustained high frame rate is mandatory to save the user from suffering due to simulation sickness. In this work, we describe and evaluate our progress in choosing and implementing appropriate methods for rendering arbitrarily large point clouds within MRET for XR. While tracking the XR headset enables the immersion of a user within a 3D scene of a data visualization, tracking of XR handheld controllers or user’s hands enables us to implement intuitive user interactions with the visualized datasets. Conventional tools require a user working with an ES visualization to conduct many interactions to commit their intended selections or manipulations with a visualized dataset; for example to specify a set of points in 3D space. Doing so in a 2D flat screen interface has traditionally required specifying a set of points in three distinct 2D coordinate systems (XY, XZ, and YZ), which is cumbersome. In other scientific domains, it has been shown that specifying or selecting a location or volume in XR using handheld controllers or tracked hands allows for greater speed and accuracy. We anticipate the same will hold true for atmospheric data, and we will share initial results of measuring the utility of such an interface. Notably, as the data being visualized is generated by GEOS as a prediction based on initial conditions, an intended application of our tool is to serve as part of an iterative feedback loop. Through XR, a scientist will review and manipulate a GEOS model run, modifying the conditions as needed to do subsequent runs of GEOS. Thereby, XR-based improvements to speed and accuracy of 3D tagging of points minimizes the effort required by both the scientist and the computer cluster conducting the necessary calculations.

Thomas Grubb↗

Conical-Domain Model for Estimating GPS Ionospheric Delays

The conical-domain model is a computational model, now undergoing development, for estimating ionospheric delays of Global Positioning System (GPS) signals. Relative to the standard ionospheric delay model described below, the conical-domain model offers improved accuracy. In the absence of selective availability, the ionosphere is the largest source of error for single-frequency users of GPS. Because ionospheric signal delays contribute to errors in GPS position and time measurements, satellite-based augmentation systems (SBASs) have been designed to estimate these delays and broadcast corrections. Several national and international SBASs are currently in various stages of development to enhance the integrity and accuracy of GPS measurements for airline navigation. In the Wide Area Augmentation System (WAAS) of the United States, slant ionospheric delay errors and confidence bounds are derived from estimates of vertical ionospheric delay modeled on a grid at regularly spaced intervals of latitude and longitude. The estimate of vertical delay at each ionospheric grid point (IGP) is calculated from a planar fit of neighboring slant delay measurements, projected to vertical using a standard, thin-shell model of the ionosphere. Interpolation on the WAAS grid enables estimation of the vertical delay at the ionospheric pierce point (IPP) corresponding to any arbitrary measurement of a user. (The IPP of a given user s measurement is the point where the GPS signal ray path intersects a reference ionospheric height.) The product of the interpolated value and the user s thin-shell obliquity factor provides an estimate of the user s ionospheric slant delay. Two types of error that restrict the accuracy of the thin-shell model are absent in the conical domain model: (1) error due to the implicit assumption that the electron density is independent of the azimuthal angle at the IPP and (2) error arising from the slant-to-vertical conversion. At low latitudes or at mid-latitudes under disturbed conditions, the accuracy of SBAS systems based upon the thin-shell model suffers due to the presence of complex ionospheric structure, high delay values, and large electron density gradients. Interpolation on the vertical delay grid serves as an additional source of delay error. The conical-domain model permits direct computation of the user s slant delay estimate without the intervening use of a vertical delay grid. The key is to restrict each fit of GPS measurements to a spatial domain encompassing signals from only one satellite. The conical domain model is so named because each fit involves a group of GPS receivers that all receive signals from the same GPS satellite (see figure); the receiver and satellite positions define a cone, the satellite position being the vertex. A user within a given cone evaluates the delay to the satellite directly, using (1) the IPP coordinates of the line of sight to the satellite and (2) broadcast fit parameters associated with the cone. The conical-domain model partly resembles the thin-shell model in that both models reduce an inherently four-dimensional problem to two dimensions. However, unlike the thin-shell model, the conical domain model does not involve any potentially erroneous simplifying assumptions about the structure of the ionosphere. In the conical domain model, the initially four-dimensional problem becomes truly two-dimensional in the sense that once a satellite location has been specified, any signal path emanating from a satellite can be identified by only two coordinates; for example, the IPP coordinates. As a consequence, a user s slant-delay estimate converges to the correct value in the limit that the receivers converge to the user s location (or, equivalently, in the limit that the measurement IPPs converge to the user s IPP).

Sparks, Lawrence↗

Utilizing a Database of Simulated Geometric Albedo Spectra for Photometric Characterization of Rocky Exoplanet Atmospheres

In anticipation of future flagship missions focused on the goal of achieving direct imaging of rocky exoplanets, we have developed a database of models to help the community examine the potential spectral characteristics of a broad range of rocky planet atmospheres. Using the publicly available Planetary Spectrum Generator, we have computed a grid of 141,600 rocky exoplanet geometric albedo spectra across a seven-dimensional parameter space. Using this grid, we have performed a color–color analysis seeking to identify the most useful near-UV and red or near-infrared photometric follow-up channels to combine with a green-optical(discovery)spectral channel. We found that a combination of filters at 0.4, 0.58, and∼0.8μm were able to distinguish between atmospheres with moderate-to-high concentrations of four different dominant absorbing constituents, given at least 10 hr of observation on a star at 10 parsec with a 15 m class space telescope; however, more moderate abundances similar to those of solar system rocky bodies would be more challenging to detect. We recommend that future missions seeking to characterize directly imaged rocky exoplanets by colors alone further consider multiband photometry as a first discriminator for planetary characteristics.

Adam J R W Smith↗

Documentation of the Fourth Order Band Model

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Kalnay-Rivas, E.↗

Three-dimensional numerical simulation of near-surface flows over the Martian north polar cap

Measurements made by Viking Lander VL-2 (48 N) have shown that the near-surface wind and temperature regime on Mars displays striking similarities to terrestrial counterparts. The diurnal radiative cycle is responsible for establishment of a well-defined thermal circulation in which downslope (Katabatic) flows prevail during the nighttime hours and weak upslope (anabatic) conditions prevail during the daytime. Previous work has indicated that the slope flows are much like those found on Earth, particularly the Katabatic winds, which show striking similarities to drainage flows observed over Antarctica. The low-level wind regime appears to be an important factor in the scouring of the martian landscape. The north polar cap shows evidence of eolian features such as dunes, frost streaks, and grooves from Viking imagery. The direction of the prevailing wind can in cases be inferred from the eolian features. We examine the thermally induced flows that result from the radiative heating and cooling of the martian north polar region using a comprehensive three-dimensional atmospheric mesoscale numerical model. The same model has been used previously for simulation of Antarctic Katabatic winds. The model equations are written in terrain-following coordinates to allow for irregular terrain; prognostic equations include the flux forms of the horizontal momentum equations, temperature, continuity. A surface energy budget equation is also incorporated in which the surface temperature is determined. Explicit parameterization of both terrestrial (longwave) and solar (shortwave) radiation is included. Turbulent transfer of heat and momentum in the martian atmosphere is assumed to follow the similarity expressions in the surface boundary layer on Earth. The terrain heights for the martian north polar region have been obtained from the U.S. Geological Survey map and digitized onto a 57x57 grid with a spacing of 75 km. The resulting terrain map is shown in Fig. 1. The vertical grid consists of 15 levels (delta equals 0.998, 0.99, 0.98, 0.97, 0.96, 0.94, 0.92, 0.90, 0.85, 0.775, 0.70, 0.60, 0.50, 0.30, 0.10). The high resolution in the lower atmosphere is necessary to capture details of the boundary layer flows. The lowest level corresponds to a height of approximately 20 m above the ground, the seconds level 100 m.

Parish, Thomas R.↗

Numerical generation of two-dimensional grids by the use of Poisson equations with grid control at boundaries

A method for generating boundary-fitted, curvilinear, two dimensional grids by the use of the Poisson equations is presented. Grids of C-type and O-type were made about airfoils and other shapes, with circular, rectangular, cascade-type, and other outer boundary shapes. Both viscous and inviscid spacings were used. In all cases, two important types of grid control can be exercised at both inner and outer boundaries. First is arbitrary control of the distances between the boundaries and the adjacent lines of the same coordinate family, i.e., stand-off distances. Second is arbitrary control of the angles with which lines of the opposite coordinate family intersect the boundaries. Thus, both grid cell size (or aspect ratio) and grid cell skewness are controlled at boundaries. Reasonable cell size and shape are ensured even in cases wherein extreme boundary shapes would tend to cause skewness or poorly controlled grid spacing. An inherent feature of the Poisson equations is that lines in the interior of the grid smoothly connect the boundary points (the grid mapping functions are second order differentiable).

Sorenson, R. L.↗

Unstructured grid generation using the distance function

A new class of methods for obtaining level sets to generate unstructured grids is presented. The consecutive grid levels are computed using the distance functions, which corresponds to solving the Hamilton-Jacobi equations representing the equations of motion of fronts propagating with curvature-dependent speed. The relationship between the distance function and the governing equations will be discussed as well as its application to generating grids. Multi-ply connected domains and complex geometries are handled naturally, with a straightforward generalization to several space dimensions. The grid points for the unstructured grid are obtained simultaneously with the grid levels. The search involved in checking for overlapping triangles is minimized by triangulating the entire domain one level at a time.

Bihari, Barna L.↗

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Douglas, C. C.↗

FIRAS wire grid characterization techniques

Characterization techniques used to verify the quality and spectral performance of the large freestanding wire grid polarizing beamsplitters and input/output polarizers used in the Far Infrared Absolute Spectrophotometer (FIRAS) are presented. The clear aperture of these grids is lined with 20.8 micron diameter gold coated tungsten wire, spaced 33 microns apart. The grid characteristics measured throughout fabrication and space flight qualification are the center to center wire spacing and wire plane flatness. Ideally, the wire grids should produce coherent wavefronts with equal reflectance and transmittance properties. When the spacing is inconsistent, these wavefront intensities are unequal, thus decreasing the efficiency of the grids and reducing the output signal of the FIRAS. The magnitude of the output interferogram is also reduced by incoherence in the interfering wave fronts caused by uneven flatness.

Barney, Richard D.↗

Interactive algebraic grid-generation technique

An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth-cubic-spline functions is presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.

Smith, R. E.↗

Structured background grids for generation of unstructured grids by advancing front method

A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.

Pirzadeh, Shahyar↗

Spaceflight Operations Services Grid Prototype

NASA over the years has developed many types of technologies and conducted various types of science resulting in numerous variations of operations, data and applications. For example, operations range from deep space projects managed by JPL, Saturn and Shuttle operations managed from JSC and KSC, ISS science operations managed from MSFC and numerous low earth orbit satellites managed from GSFC that are varied and intrinsically different but require many of the same types of services to fulfill their missions. Also, large data sets (databases) of Shuttle flight data, solar system projects and earth observing data exist which because of their varied and sometimes outdated technologies are not and have not been fully examined for additional information and knowledge. Many of the applications/systems supporting operational services e.g. voice, video, telemetry and commanding, are outdated and obsolete. The vast amounts of data are located in various formats, at various locations and range over many years. The ability to conduct unified space operations, access disparate data sets and to develop systems and services that can provide operational services does not currently exist in any useful form. In addition, adding new services to existing operations is generally expensive and with the current budget constraints not feasible on any broad level of implementation. To understand these services a discussion of each one follows. The Spaceflight User-based Services are those services required to conduct space flight operations. Grid Services are those Grid services that will be used to overcome, through middleware software, some or all the problems that currently exists. In addition, Network Services will be discussed briefly. Network Services are crucial to any type of remedy and are evolving adequately to support any technology currently in development.

Bradford, Robert N.↗

Two dimensional vernier

A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.

Juday, Richard D.↗