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NASA NTRS2011

Visual SLAM Using Variance Grid Maps

An algorithm denoted Gamma-SLAM performs further processing, in real time, of preprocessed digitized images acquired by a stereoscopic pair of electronic cameras aboard an off-road robotic ground vehicle to build accurate maps of the terrain and determine the location of the vehicle with respect to the maps. Part of the name of the algorithm reflects the fact that the process of building the maps and determining the location with respect to them is denoted simultaneous localization and mapping (SLAM). Most prior real-time SLAM algorithms have been limited in applicability to (1) systems equipped with scanning laser range finders as the primary sensors in (2) indoor environments (or relatively simply structured outdoor environments). The few prior vision-based SLAM algorithms have been feature-based and not suitable for real-time applications and, hence, not suitable for autonomous navigation on irregularly structured terrain. The Gamma-SLAM algorithm incorporates two key innovations: Visual odometry (in contradistinction to wheel odometry) is used to estimate the motion of the vehicle. An elevation variance map (in contradistinction to an occupancy or an elevation map) is used to represent the terrain. The Gamma-SLAM algorithm makes use of a Rao-Blackwellized particle filter (RBPF) from Bayesian estimation theory for maintaining a distribution over poses and maps. The core idea of the RBPF approach is that the SLAM problem can be factored into two parts: (1) finding the distribution over robot trajectories, and (2) finding the map conditioned on any given trajectory. The factorization involves the use of a particle filter in which each particle encodes both a possible trajectory and a map conditioned on that trajectory. The base estimate of the trajectory is derived from visual odometry, and the map conditioned on that trajectory is a Cartesian grid of elevation variances. In comparison with traditional occupancy or elevation grid maps, the grid elevation variance maps are much better for representing the structure of vegetated or rocky terrain.

Howard, Andrew B.↗

NASA NTRS2011

Adaptive refinement tools for tetrahedral unstructured grids

An exemplary embodiment providing one or more improvements includes software which is robust, efficient, and has a very fast run time for user directed grid enrichment and flow solution adaptive grid refinement. All user selectable options (e.g., the choice of functions, the choice of thresholds, etc.), other than a pre-marked cell list, can be entered on the command line. The ease of application is an asset for flow physics research and preliminary design CFD analysis where fast grid modification is often needed to deal with unanticipated development of flow details.

Pao, S. Paul↗

NASA NTRS2004

Tailoring Ion-Thruster Grid Apertures for Greater Efficiency

A report proposes tailoring the diameters of the apertures in the accelerator grid of an ion thruster to reduce the open grid area through which un-ionized propellant gas can escape. The result would be a reduction in the loss of propellant gas and a corresponding increase in propellant efficiency. In a typical ion thruster, the plasma density decreases with radial distance from the centerline, and as a consequence, the diameters of ion beamlets decrease with increasing radial distance. According to the proposal, the apertures, through which the ion beamlets must pass, would be sized to match the diameters (with margin) of the beamlets. The decrease of the aperture diameters with radial distance would result in a significant reduction in the open grid area: In an example based on representative design parameters, the reduction could be as much as 30 percent. In this example, the transparency to un-ionized propellant would decrease from 0.24 to 0.17 and, as a result, the propellant efficiency would increase from 0.91 to 0.96.

Brophy, John↗

NASA NTRS2011

The Grid Density Dependence of the Unsteady Pressures of the J-2X Turbines

The J-2X engine was originally designed for the upper stage of the cancelled Crew Launch Vehicle. Although the Crew Launch Vehicle was cancelled the J-2X engine, which is currently undergoing hot-fire testing, may be used on future programs. The J-2X engine is a direct descendent of the J-2 engine which powered the upper stage during the Apollo program. Many changes including a thrust increase from 230K to 294K lbf have been implemented in this engine. As part of the design requirements, the turbine blades must meet minimum high cycle fatigue factors of safety for various vibrational modes that have resonant frequencies in the engine's operating range. The unsteady blade loading is calculated directly from CFD simulations. A grid density study was performed to understand the sensitivity of the spatial loading and the magnitude of the on blade loading due to changes in grid density. Given that the unsteady blade loading has a first order effect on the high cycle fatigue factors of safety, it is important to understand the level of convergence when applying the unsteady loads. The convergence of the unsteady pressures of several grid densities will be presented for various frequencies in the engine's operating range.

Schmauch, Preston B.↗

NASA NTRS2012

TRMM Version 7 Level 3 Gridded Monthly Accumulations of GPROF Precipitation Retrievals

In July 2011, improved versions of the retrieval algorithms were approved for TRMM. All data starting with June 2011 are produced only with the version 7 code. At the same time, version 7 reprocessing of all TRMM mission data was started. By the end of August 2011, the 14+ years of the reprocessed mission data became available online to users. This reprocessing provided the opportunity to redo and enhance upon an analysis of V7 impacts on L3 data accumulations that was presented at the 2010 EGU General Assembly. This paper will discuss the impact of algorithm changes made in th GPROF retrieval on the Level 2 swath products. Perhaps the most important change in that retrieval was to replacement of a model based a priori database with one created from Precipitation Radar (PR) and TMI brightness temperature (Tb) data. The radar pays a major role in the V7 GPROF (GPROF2010) in determining existence of rain. The level 2 retrieval algorithm also introduced a field providing the probability of rain. This combined use of the PR has some impact on the retrievals and created areas, particularly over ocean, where many areas of low-probability precipitation are retrieved whereas in version 6, these areas contained zero rain rates. This paper will discuss how these impacts get translated to the space/time averaged monthly products that use the GPROF retrievals. The level 3 products discussed are the gridded text product 3G68 and the standard 3A12 and 3B31 products. The paper provides an overview of the changes and explanation of how the level 3 products dealt with the change in the retrieval approach. Using the .25 deg x .25 degree grid, the paper will show that agreement between the swath product and the level 3 remains very high. It will also present comparisons of V6 and V7 GPROF retrievals as seen both at the swath level and the level 3 time/space gridded accumulations. It will show that the various L3 products based on GPROF level 2 retrievals are in close agreement. The paper concludes by outlining some of the challenges of the TRMM version 7 level 3 products.

Stocker, E. F.↗

NASA NTRS2012

Boundary-Layer Stability Analysis of the Mean Flows Obtained Using Unstructured Grids

Boundary-layer stability analyses of mean flows extracted from unstructured-grid Navier- Stokes solutions have been performed. A procedure has been developed to extract mean flow profiles from the FUN3D unstructured-grid solutions. Extensive code-to-code validations have been performed by comparing the extracted mean ows as well as the corresponding stability characteristics to the predictions based on structured-grid solutions. Comparisons are made on a range of problems from a simple at plate to a full aircraft configuration-a modified Gulfstream-III with a natural laminar flow glove. The future aim of the project is to extend the adjoint-based design capability in FUN3D to include natural laminar flow and laminar flow control by integrating it with boundary-layer stability analysis codes, such as LASTRAC.

Liao, Wei↗

NASA NTRS2013

Toward Verification of USM3D Extensions for Mixed Element Grids

The unstructured tetrahedral grid cell-centered finite volume flow solver USM3D has been recently extended to handle mixed element grids composed of hexahedral, prismatic, pyramidal, and tetrahedral cells. Presently, two turbulence models, namely, baseline Spalart-Allmaras (SA) and Menter Shear Stress Transport (SST), support mixed element grids. This paper provides an overview of the various numerical discretization options available in the newly enhanced USM3D. Using the SA model, the flow solver extensions are verified on three two-dimensional test cases available on the Turbulence Modeling Resource website at the NASA Langley Research Center. The test cases are zero pressure gradient flat plate, planar shear, and bump-inchannel. The effect of cell topologies on the flow solution is also investigated using the planar shear case. Finally, the assessment of various cell and face gradient options is performed on the zero pressure gradient flat plate case.

Pandya, Mohagna J.↗

NASA NTRS2014

Angular and Polarization Response of Multimode Sensors with Resistive-Grid Absorbers

High sensitivity receiver systems with near ideal polarization sensitivity are highly desirable for development of millimeter and sub-millimeter radio astronomy. Multimoded bolometers provide a unique solution to achieve such sensitivity, for which hundreds of single-mode sensors would otherwise be required. The primary concern in employing such multimoded sensors for polarimetery is the control of the polarization systematics. In this paper, we examine the angular- and polarization- dependent absorption pattern of a thin resistive grid or membrane, which models an absorber used for a multimoded bolometer. The result shows that a freestanding thin resistive absorber with a surface resistivity of eta/2, where eta is the impedance of free space, attains a beam pattern with equal E- and H-plane responses, leading to zero cross polarization. For a resistive-grid absorber, the condition is met when a pair of grids is positioned orthogonal to each other and both have a resistivity of eta/2. When a reflective backshort termination is employed to improve absorption efficiency, the cross-polar level can be suppressed below −30 dB if acceptance angle of the sensor is limited to < or approx. 60deg. The small cross-polar systematics have even-parity patterns and do not contaminate the measurements of odd-parity polarization patterns, for which many of recent instruments for cosmic microwave background are designed. Underlying symmetry that suppresses these cross-polar systematics is discussed in detail. The estimates and formalism provided in this paper offer key tools in the design consideration of the instruments using the multimoded polarimeters.

High sensitivity receiver systems↗

NASA NTRS2016

Overview of the NASA Glenn Flux Reconstruction Based High-Order Unstructured Grid Code

A computational fluid dynamics code based on the flux reconstruction (FR) method is currently being developed at NASA Glenn Research Center to ultimately provide a large- eddy simulation capability that is both accurate and efficient for complex aeropropulsion flows. The FR approach offers a simple and efficient method that is easy to implement and accurate to an arbitrary order on common grid cell geometries. The governing compressible Navier-Stokes equations are discretized in time using various explicit Runge-Kutta schemes, with the default being the 3-stage/3rd-order strong stability preserving scheme. The code is written in modern Fortran (i.e., Fortran 2008) and parallelization is attained through MPI for execution on distributed-memory high-performance computing systems. An h- refinement study of the isentropic Euler vortex problem is able to empirically demonstrate the capability of the FR method to achieve super-accuracy for inviscid flows. Additionally, the code is applied to the Taylor-Green vortex problem, performing numerous implicit large-eddy simulations across a range of grid resolutions and solution orders. The solution found by a pseudo-spectral code is commonly used as a reference solution to this problem, and the FR code is able to reproduce this solution using approximately the same grid resolution. Finally, an examination of the code's performance demonstrates good parallel scaling, as well as an implementation of the FR method with a computational cost/degree- of-freedom/time-step that is essentially independent of the solution order of accuracy for structured geometries.

High-Order Methods↗

NASA NTRS2015

Development of a Grid-Independent Geos-Chem Chemical Transport Model (v9-02) as an Atmospheric Chemistry Module for Earth System Models

The GEOS-Chem global chemical transport model (CTM), used by a large atmospheric chemistry research community, has been re-engineered to also serve as an atmospheric chemistry module for Earth system models (ESMs). This was done using an Earth System Modeling Framework (ESMF) interface that operates independently of the GEOSChem scientific code, permitting the exact same GEOSChem code to be used as an ESM module or as a standalone CTM. In this manner, the continual stream of updates contributed by the CTM user community is automatically passed on to the ESM module, which remains state of science and referenced to the latest version of the standard GEOS-Chem CTM. A major step in this re-engineering was to make GEOS-Chem grid independent, i.e., capable of using any geophysical grid specified at run time. GEOS-Chem data sockets were also created for communication between modules and with external ESM code. The grid-independent, ESMF-compatible GEOS-Chem is now the standard version of the GEOS-Chem CTM. It has been implemented as an atmospheric chemistry module into the NASA GEOS- 5 ESM. The coupled GEOS-5-GEOS-Chem system was tested for scalability and performance with a tropospheric oxidant-aerosol simulation (120 coupled species, 66 transported tracers) using 48-240 cores and message-passing interface (MPI) distributed-memory parallelization. Numerical experiments demonstrate that the GEOS-Chem chemistry module scales efficiently for the number of cores tested, with no degradation as the number of cores increases. Although inclusion of atmospheric chemistry in ESMs is computationally expensive, the excellent scalability of the chemistry module means that the relative cost goes down with increasing number of cores in a massively parallel environment.

CTM↗

NASA NTRS2018

Using Adaptive Mesh Refinement to Study Grid Resolution Effects for Shock-Boundary Layer Interactions

Adaptive Mesh Refinement (AMR) promises a much more computationally efficient means to obtain a discrete approximation to a continuous boundary value problem of a specified accuracy than classic isotropic grid refinement. The AMR capability of OVERFLOW (a computational fluid dynamics (CFD) code) is utilized to provide estimates of the exact analytical solutions to problems of interest to turbulence modeling. Predictions of surface pressure and skin friction, essentially the state of stress at the surface, shows little difference with grids believed to be "grid resolved." Velocity profiles, on the other hand, show marked differences in flows with shocks. The AMR method, as implemented in OVERFLOW 2.2k, appears to provide the ability to produce arbitrarily accurate solutions at a predictable cost much smaller than classic uniform mesh refinement.

Turbulence Modeling↗

NASA NTRS2016

On the Synergy Between Numerics and Subgrid Scale Modeling in LES of Stratified Flows: Grid Convergence of a Stratocumulus-Topped Boundary Layer

The effectiveness of a linear upwinding scalar advection scheme to suppress numerical dispersion errors near sharp inversions in large-eddy simulations of a nocturnal stratocumulus-topped boundary layer is assessed. Linear upwinding is a trade-off between non-dissipative and non-linear positive definite advection schemes. It is shown that linear upwinding does not negatively impact the model's grid convergence properties and a sharp inversion free of numerical artifacts is maintained. Even though mean profiles and turbulence fluxes show good grid convergence characteristics the liquid water amount varies significantly with grid resolution. The entrainment rate is identical for all resolutions and independent of the liquid water amount. For the present stratocumulus case, the impact of cloud-top radiative cooling is negligible and turbulence is largely driven by convection emanating from the surface.

Matheou, Georgios↗

NASA NTRS2018

Using Adaptive Mesh Refinement to Study Grid Resolution Effects for Shock/Boundary-Layer Interactions

Adaptive Mesh Refinement (AMR) promises a much more computationally efficient meansto obtain a discrete approximation to a continuous boundary value problem of a specifiedaccuracy than classic isotropic grid refinement. The AMR capability of OVERFLOW is utilizedto provide estimates of the exact analytical solutions to problems of interest to turbulencemodeling. Predictions of surface pressure and skin friction, essentially the state of stress at thesurface, shows little difference with grids believed to be "grid resolved." Velocity profiles, on theother hand, show marked differences in flows with shocks. The AMR method, as implementedin OVERFLOW2.2k, appears to provide the ability to produce arbitrarily accurate solutionsat a predictable cost much smaller than classic uniform mesh refinement.

Adaptive Mesh Refinement↗

NASA NTRS2019

Parameterization-Induced Uncertainties and Impacts of Crop Management Harmonization in a Global Gridded Crop Model Ensemble

Global gridded crop models (GGCMs) combine agronomic or plant growth models with gridded spatial input data to estimate spatially explicit crop yields and agricultural externalities at the global scale. Differences in GGCM outputs arise from the use of different biophysical models, setups, and input data. GGCM ensembles are frequently employed to bracket uncertainties in impact studies without investigating the causes of divergence in outputs. This study explores differences in maize yield estimates from five GGCMs based on the public domain field-scale model Environmental Policy Integrated Climate (EPIC) that participate in the AgMIP Global Gridded Crop Model Intercomparison initiative. Albeit using the same crop model, the GGCMs differ in model version, input data, management assumptions, parameterization, and selection of subroutines affecting crop yield estimates via cultivar distributions, soil attributes, and hydrology among others. The analyses reveal inter-annual yield variability and absolute yield levels in the EPIC-based GGCMs to be highly sensitive to soil parameterization and crop management. All GGCMs show an intermediate performance in reproducing reported yields with a higher skill if a static soil profile is assumed or sufficient plant nutrients are supplied. An in-depth comparison of setup domains for two EPIC-based GGCMs shows that GGCM performance and plant stress responses depend substantially on soil parameters and soil process parameterization, i.e. hydrology and nutrient turnover, indicating that these often neglected domains deserve more scrutiny. For agricultural impact assessments, employing a GGCM ensemble with its widely varying assumptions in setups appears the best solution for coping with uncertainties from lack of comprehensive global data on crop management, cultivar distributions and coefficients for agro-environmental processes. However, the underlying assumptions require systematic specifications to cover representative agricultural systems and environmental conditions. Furthermore, the interlinkage of parameter sensitivity from various domains such as soil parameters, nutrient turnover coefficients, and cultivar specifications highlights that global sensitivity analyses and calibration need to be performed in an integrated manner to avoid bias resulting from disregarded core model domains. Finally, relating evaluations of the EPIC-based GGCMs to a wider ensemble based on individual core models shows that structural differences outweigh in general differences in configurations of GGCMs based on the same model, and that the ensemble mean gains higher skill from the inclusion of structurally different GGCMs. Although the members of the wider ensemble herein do not consider crop-soil-management interactions, their sensitivity to nutrient supply indicates that findings for the EPIC-based sub-ensemble will likely become relevant for other GGCMs with the progressing inclusion of such processes.

Folberth, Christian↗

NASA NTRS2019

Parallel Anisotropic Unstructured Grid Adaptation

Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation.

Tsolakis, Christos↗

NASA NTRSDate not supplied

A 3-D Nodal-Averaged Gradient Approach for Unstructured-Grid Cell-Centered Finite-Volume Methods for Application to Turbulent Hypersonic Flow

A 2-D nodal weighted least-squares gradient method and a related face-averaged nodal gradient approach that were developed for use with triangular grids are extended to 3-D for use with tetrahedral grids. In addition, a method, developed in 2-D, to stabilize the iterative convergence of these methods on quadrilateral cells is described and extended to 3-D and remedies are investigated to determine the nodal gradient averaging approach most suitable for use with grids made up of hexahedral, prismatic, pyramidal and tetrahedral cells. Moreover, due to an interest in hypersonic flow, a robust multidimensional gradient limiter procedure that is consistent with the stencil used to construct the nodal gradients is described. Finally, we demonstrate that the resulting 3-D methods are sufficiently robust for use in scramjet computations through the solution of three canonical turbulent hypersonic flow problems as well as a physically realistic 3-D scramjet inlet geometry.

Jeffery A White↗

NASA NTRS2017

Development of a 50,000-s, Lithium-fueled, Gridded Ion Thruster

The ion propulsion system on NASA’s Dawn mission provided over 11 km/s delta-V to the spacecraft. There is potential interest in missions that have delta-V’s an order of magnitude greater than this, i.e., 100 km/s to 200 km/s. To perform such missions would require a thruster that can produce a specific impulse roughly an order of magnitude greater than the 3100 s of the Dawn ion propulsion system. A 50-kW gridded ion thruster is being developed for operation with lithium propellant to produce a specific impulse of 50,000 s. The resulting thruster design requires a net accelerating voltage of 9 kV and a beam current of 5.5 A. Discharge chamber modeling is used to design a 35-cm diameter ring-cusp discharge chamber with six magnet rings. The discharge chamber is masked down to produce an active grid area that is ~25 cm diameter. Modeling suggests that the unique ionization characteristics of lithium may enable discharge chamber operation at a propellant efficiency of 99%. Operation at such a high propellant efficiency could significantly reduce the production of charge-exchange ions and thereby significantly reduce erosion of the accelerator grid.

Goebel, Dan M.↗

NASA NTRSDate not supplied

Towards an Automated Unstructured Grid Adaptation Workflow with VULCAN

Early work is presented for an unstructured grid adaptation workflow with VULCAN and refine. Anisotropic simplex grids are iteratively adapted to match a Riemannian metric tensor field describing desired mesh spacing. The Riemannian metric tensor field is obtained from Hessians of CFD solution output scalar sensor fields; both Mach number and static temperature sensor fields are explored. In addition, we describe a Newton-method-based solver recently implemented in VULCAN utilizing Jacobian-Free-Newton-Krylov that can be used to increase flow solver automation on early grids in the adadptation process. Hypersonic flow solutions are presented on a high Reynolds number flat plate and wall heat flux is compared against a highly resolved structured solution. Additionally, complex shock boundary-layer interaction is explored in a high Mach number compression corner and complex 3D flow phenomena are evaluated on the Boundary Layer Transition (BOLT) vehicle.

Matthew O'Connell↗