Search NASA⌕ Search

SEARCH · Search NASA

Results for “Collocation scheme”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Investigation of Liquid Cloud Microphysical Properties of Deep Convective Systems: 2. Parameterization of Raindrop Size Distribution and its Application for Convective Rain Estimation

The liquid cloud microphysical properties for stratiform rain (SR) have been investigated in Part 1 of this series. Since convective rain (CR) has characteristics in raindrop size distribution (DSD) and precipitation that are distinct from SR, we investigate the CR properties in this study by using 20 hr of CR samples collected by 17 Automatic Parsivel Units disdrometers during the Midlatitude Continental Convective Clouds Experiment over the Atmospheric Radiation Measurement Southern Great Plains site. A full spectrum of DSD is constructed based on a total of 23 size channels (0.321 to 9.785 mm), and both Gamma and Exponential fitted functions are applied to extract the DSD shape parameters. Compared to SR properties, CR has distinct features including broader size range and narrower exponential slope parameter (λ E ). These results indicate that the assumption of constant exponential intercept parameter ( N 0E ) is inappropriate for CR rain rate estimates. Additionally, the subsetting scheme of the CR DSD spectra also has a strong impact on the Gamma/Exponential functions. Therefore, a new CR DSD parameterization scheme is developed by choosing the appropriate spectra subset with the constraint of rain rate and using the constant λ E instead of constant N 0E . With the input of the radar reflectivity at the lowest observed height, the newly calculated CR rain rates match well with the collocated surface rain gauge measurements (127 Mesonet stations and 17 Automatic Parsivel Units), while the rain rates calculated using traditional Z-R relationship are 3–4 times larger, indicating that constant λ E is a better assumption for CR DSD.

58 GEOSCIENCES↗
NASA NTRS2015

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Parsani, Matteo↗
DOE OSTI2018

A semi-discrete scheme for solving fourth-order partial integro-differential equation with a weakly singular kernel using Legendre wavelets method

In this paper, a semi-discrete scheme is presented for solving fourth-order partial integro-differential equations with a weakly singular kernel. The second-order backward difference formula is used to discretize the temporal derivatives. After discretizing the temporal derivatives, the considered problems are converted into a set of ordinary differential equations which are solved by using Legendre wavelets collocation method. The stability and convergence properties related to the time discretization are discussed and theoretically proven. Several numerical examples are included to demonstrate the accuracy and efficiency of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilized linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2008

Spectrally Resolved Flux Derived from Collocated AIRS and CERES Observations and its Application in Model Validation: Clear-Sky Over the Tropic Oceans - Part I

Spectrally resolved outgoing IR flux, the integrand of the outgoing longwave radiation (OLR), has its unique value in evaluating model simulations. Here we describe an algorithm of deriving such clear-sky outgoing spectral flux through the whole IR region from the collocated Atmospheric Infrared Sounder (AIRS) and the Clouds & the Earth's Radiant Energy System (CERES) measurements over the tropical oceans. Based on the scene types and corresponding angular distribution models (ADMs) used in the CERES Single Satellite Footprint (SSF) dataset, spectrally-dependent ADMs are developed and used to estimate the spectral flux at each AIRS channel. A multivariate linear prediction scheme is then used to estimate spectral fluxes at frequencies not covered by the AIRS instrument. The whole algorithm is validated using synthetic spectra as well as the CERES OLR measurements. Using the GFDL AM2 model simulation as a case study, the application of the derived clear-sky outgoing spectral flux in model evaluation is illustrated. By comparing the observed and simulated spectral flux in 2004, compensating errors in the simulated OLR from different absorption bands can be revealed, so does the errors from frequencies within a given absorption band. Discrepancies between the simulated and observed spatial distributions and seasonal evolutions of the spectral fluxes at different spectral ranges are further discussed. The methodology described in this study can be applied to other surface types as well as cloudy-sky observations and corresponding model evaluations.

Huang, Xianglei↗
DOE OSTI2016

The GEWEX LandFlux project: Evaluation of model evaporation using tower-based and globally gridded forcing data

Determining the spatial distribution and temporal development of evaporation at regional and global scales is required to improve our understanding of the coupled water and energy cycles and to better monitor any changes in observed trends and variability of linked hydrological processes. With recent international efforts guiding the development of long-term and globally distributed flux estimates, continued product assessments are required to inform upon the selection of suitable model structures and also to establish the appropriateness of these multi-model simulations for global application. In support of the objectives of the Global Energy and Water Cycle Exchanges (GEWEX) LandFlux project, four commonly used evaporation models are evaluated against data from tower-based eddy-covariance observations, distributed across a range of biomes and climate zones. The selected schemes include the Surface Energy Balance System (SEBS) approach, the Priestley–Taylor Jet Propulsion Laboratory (PT-JPL) model, the Penman–Monteith-based Mu model (PM-Mu) and the Global Land Evaporation Amsterdam Model (GLEAM). Here we seek to examine the fidelity of global evaporation simulations by examining the multi-model response to varying sources of forcing data. To do this, we perform parallel and collocated model simulations using tower-based data together with a global-scale grid-based forcing product. Through quantifying the multi-model response to high-quality tower data, a better understanding of the subsequent model response to the coarse-scale globally gridded data that underlies the LandFlux product can be obtained, while also providing a relative evaluation and assessment of model performance. Using surface flux observations from 45 globally distributed eddy-covariance stations as independent metrics of performance, the tower-based analysis indicated that PT-JPL provided the highest overall statistical performance (0.72; 61 W m –2 ; 0.65), followed closely by GLEAM (0.68; 64 W m –2 ; 0.62), with values in parentheses representing the R 2 , RMSD and Nash–Sutcliffe efficiency (NSE), respectively. PM-Mu (0.51; 78 W m –2 ; 0.45) tended to underestimate fluxes, while SEBS (0.72; 101 W m –2 ; 0.24) overestimated values relative to observations. A focused analysis across specific biome types and climate zones showed considerable variability in the performance of all models, with no single model consistently able to outperform any other. Results also indicated that the global gridded data tended to reduce the performance for all of the studied models when compared to the tower data, likely a response to scale mismatch and issues related to forcing quality. Rather than relying on any single model simulation, the spatial and temporal variability at both the tower- and grid-scale highlighted the potential benefits of developing an ensemble or blended evaporation product for global-scale LandFlux applications. Hence, challenges related to the robust assessment of the LandFlux product are also discussed.

58 GEOSCIENCES↗
NASA NTRS1977

The separated turbulent boundary layer over a wavy wall

A study and application of the fourth order spline collocation procedure, numerical solution of boundary layer like differential equations, is presented. A simple inversion algorithm for the simultaneous solution of the resulting difference equations is given. Particular attention is focused on the boundary condition representation for the spline second derivative approximations. Solutions using the spline procedure, as well as the three point finite difference method, are presented for several model problems in order to assess and improve the spline numerical scheme. Application of the resulting algorithm to the incompressible laminar self similar boundary layer equations is presented.

Polak, A.↗
NASA NTRS2001

Vertical Profiles of Latent Heating in TRMM: Validation and Assimilation in the GEOS Data Assimilation System

I have derived the vertical profiles of apparent heating Q and Q2 by using 3-hourly balloon sounding data from the ARM SGP sounding array for three IOPs in 2000. These IOPs cover the periods from 3/1 to 3/22, from 9/25 to 10/8, and from 11/27 to 12/22. These heating profiles will be collocated with the TRMM heating profiles for validation studies once the TRMM profiles become available to the investigators. I have also produced the objective analyses of Q1, Q2 and forcing fields for the international GCSS Case 3 Intercomparison project. The GSFC CRM participated in study, based on which TRMM heating profiles are derived. I have also studied to assimilate the vertical heating profile by constraining the cloud-base mass flux in the cumulus convection scheme using the CCM3. I first derive the vertical heating profile for each convective plume of unit cloud-base mass flux. The observed heating profile form ARM is then de-convoluted to derive the cloud base mass fluxes of all individual plumes. These fluxes are compared with those derived from the quasi-equilibrium hypothesis. They are shown to improve many other aspects of the model behavior.

Zhang, Ming-Hua↗
NASA NTRS1986

A spectral multidomain method for the solution of hyperbolic systems

A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations were developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several domains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one dimensional linear models and one and two dimensional nonlinear gas dynamics problems are presented.

Kopriva, D.↗
NASA NTRS1991

A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0

The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.

Chen, C. P.↗
NASA NTRS2014

A Multisensor Investigation of Convection During HyMeX SOP1 IOP13

A multisensor analysis of the convective precipitation event occurred over Rome during the IOP13 (October 15th, 2012) of the HyMeX (Hydrological cycle in the Mediterranean eXperiment) Special Observation Period (SOP) 1 is presented. Thanks to the cooperation among Italian meteorological services and scientific community and a specific agreement with NASA-GSFC, different types of devices for meteorological measurements were made available during the HyMeX SOP.1. For investigating this event, used are the 3-D lightning data provided by the LINET, the CNR ISAC dual-pol C-band radar (Polar 55C), located in Rome, the Drop Size Distributions (DSD) collected by the 2D Video Disdrometer (2DVD) and the collocated Micro Rain Radar (MRR) installed at the Radio Meteorology Lab. of "Sapienza" University of Rome, located 14 km from the Polar 55C radar. The relation between microphysical structure and electrical activity during the convective phase of the event was investigated using LINET lightning data and Polar 55C (working both in PPI and RHI scanning mode) observations. Location of regions of high horizontal reflectivity (Zh) values ( > 50 dBz), indicating convective precipitation, were found to be associated to a high number of LINET strokes. In addition, an hydrometeor classification scheme applied to the Polar 55C scans was used to detect graupel and to identify a relation between number of LINET strokes and integrated IWC of graupel along the event. Properties of DSDs measured by the 2DVD and vertical DSD profiles estimated by MRR and their relation with the lighting activity registered by LINET were investigated with specific focus on the transition from convective to stratiform regimes. A good agreement was found between convection detected by these instruments and the number of strokes detected by LINET.

Roberto, N.↗
DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Dynamic earthquake rupture simulations on nonplanar faults embedded in 3D geometrically complex, heterogeneous elastic solids

Dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes. The conditions relating discontinuities in particle velocities across fault zones and tractions acting on the fault are often expressed as nonlinear friction laws. The corresponding initial boundary value problems are both numerically and computationally challenging. In addition, seismic waves generated by earthquake ruptures must be propagated for many wavelengths away from the fault. Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods. We present a high order accurate finite difference method for: a) enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration; b) dynamic propagation of earthquake ruptures along nonplanar faults; and c) accurate propagation of seismic waves in heterogeneous media with free surface topography. We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts (SBP) finite difference operators in space. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. The finite difference stencils used in this paper are sixth order accurate in the interior and third order accurate close to the boundaries. However, the method is applicable to any spatial operator with a diagonal norm satisfying the SBP property. Time stepping is performed with a 4th order accurate explicit low storage Runge–Kutta scheme, thus yielding a globally fourth order accurate method in both space and time. We show numerical simulations on band limited self-similar fractal faults revealing the complexity of rupture dynamics on rough faults.

58 GEOSCIENCES↗
NASA NTRS2012

Evaluations of Thin Cirrus Contamination and Screening in Ground Aerosol Observations Using Collocated Lidar Systems

Cirrus clouds, particularly sub visual high thin cirrus with low optical thickness, are difficult to be screened in operational aerosol retrieval algorithms. Collocated aerosol and cirrus observations from ground measurements, such as the Aerosol Robotic Network (AERONET) and the Micro-Pulse Lidar Network (MPLNET), provide us with an unprecedented opportunity to examine the susceptibility of operational aerosol products to thin cirrus contamination. Quality assured aerosol optical thickness (AOT) measurements were also tested against the CALIPSO vertical feature mask (VFM) and the MODIS-derived thin cirrus screening parameters for the purpose of evaluating thin cirrus contamination. Key results of this study include: (1) Quantitative evaluations of data uncertainties in AERONET AOT retrievals are conducted. Although AERONET cirrus screening schemes are successful in removing most cirrus contamination, strong residuals displaying strong spatial and seasonal variability still exist, particularly over thin cirrus prevalent regions during cirrus peak seasons, (2) Challenges in matching up different data for analysis are highlighted and corresponding solutions proposed, and (3) Estimation of the relative contributions from cirrus contamination to aerosol retrievals are discussed. The results are valuable for better understanding and further improving ground aerosol measurements that are critical for aerosol-related climate research.

Huang, Jingfeng↗
NASA NTRS2021

Applications of Dynamic Land Surface Information for Passive Microwave Precipitation Retrieval

Accurate, physically based precipitation retrieval over global land surfaces is an important goal of the NASA/JAXA Global Precipitation Measurement Mission (GPM). This is a difficult problem for the passive microwave constellation, as the signal over radiometrically warm land surfaces in the microwave frequencies means that the measurements used are indirect and typically require inferring some type of relationship between an observed scattering signal and precipitation at the surface. GPM, with collocated radiometer and dual-frequency radar, is an excellent tool for tackling this problem and improving global retrievals. In the years following the launch of the GPM Core Observatory satellite, physically based passive microwave retrieval of precipitation over land continues to be challenging. Validation efforts suggest that the operational GPM passive microwave algorithm, the Goddard profiling algorithm (GPROF), tends to overestimate precipitation at the low (<5 mm h−1) end of the distribution over land. In this work, retrieval sensitivities to dynamic surface conditions are explored through enhancement of the algorithm with dynamic, retrieved information from a GPM-derived optimal estimation scheme. The retrieved parameters describing surface and background characteristics replace current static or ancillary GPROF information including emissivity, water vapor, and snow cover. Results show that adding this information decreases probability of false detection by 50% and, most importantly, the enhancements with retrieved parameters move the retrieval away from dependence on ancillary datasets and lead to improved physical consistency.

Sarah Ringerud↗
NASA NTRS1991

Estimation of geopotential differences over intercontinental locations using satellite and terrestrial measurements

An error analysis study was conducted in order to assess the current accuracies and the future anticipated improvements in the estimation of geopotential differences over intercontinental locations. An observation/estimation scheme was proposed and studied, whereby gravity disturbance measurements on the Earth's surface, in caps surrounding the estimation points, are combined with corresponding data in caps directly over these points at the altitude of a low orbiting satellite, for the estimation of the geopotential difference between the terrestrial stations. The mathematical modeling required to relate the primary observables to the parameters to be estimated, was studied for the terrestrial data and the data at altitude. Emphasis was placed on the examination of systematic effects and on the corresponding reductions that need to be applied to the measurements to avoid systematic errors. The error estimation for the geopotential differences was performed using both truncation theory and least squares collocation with ring averages, in case observations on the Earth's surface only are used. The error analysis indicated that with the currently available global geopotential model OSU89B and with gravity disturbance data in 2 deg caps surrounding the estimation points, the error of the geopotential difference arising from errors in the reference model and the cap data is about 23 kgal cm, for 30 deg station separation.

Pavlis, Nikolaos K.↗
NASA NTRS2002

Decoupling the Role of Particle Inertia and Gravity on Particle Dispersion

Particle dispersion and the influence that particle momentum exchange has on the properties of a turbulent carrier flow in micro-gravity environments challenge present understanding and predictive schemes. The objective of this effort has been to develop and assess high-fidelity simulation tools for predicting particle transport within micro-gravity environments suspended in turbulent flows. The computational technique is based on Direct Numerical Simulation (DNS) of the incompressible Navier-Stokes equations. The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian timescale of the turbulence and particle mass loadings up to one. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 96(exp 3) collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier-Stokes equations using the point-force approximation in which 96(exp 3) particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviors. The spectrum of the fluid-particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid-particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of others.

Squires, Kyle D.↗
NASA NTRS1998

Sensor/Actuator Selection for Gust and Turbulence Control

From aircraft fuselages and space stations to vacuum cleaners and automobiles, active control of noise and/or vibration has come of age. Determining the number of active control devices (e.g. actuators) to be placed and where they are to be placed is the prototypical location problem. However, unlike typical location problems, where the customer is readily identified and is actively engaged in the assessment of the performance of the chosen locations, the customers that active control devices serve are not so easily identified and their impact on system performance issues may be unclear. For example, consider the problem of where to locate actuators to attenuate cabin noise in a propeller driven aircraft. Clearly, the ultimate customers are the passengers who will travel in these aircraft. But to decide whether one set of actuator locations is better than another it is unlikely we will ask passengers to fly in the aircraft and fill out a questionnaire about noise levels. Instead a set of sensors (pseudo-customers) are placed and the system performance of the actuators, as measured by these sensors, is recorded. Hence, we have yet another location problem. How many sensors should there be and where should they be located? In many instances collocation of sensors and actuators is the answer but in other instances it is not. A variety of approaches have been taken to address these sensor/actuator location problems. With regard to damping vibrations in truss structures (space station prototypes) it was formulated a new noxious location problem and generated high-quality solutions with a combination of LP-relaxations and heuristic search procedures. Other related efforts are summarized the actuator location problem for a single frequency interior noise control problem was examined for an idealized aircraft cabin. A tabu search procedure was shown to generate better locations for the actuators than a modal decomposition approach. The model was extended to include multi-frequency information. The sensor location problem is addressed. In the latter article a reactive tabu search scheme was shown to dominate a static tabu search approach. Our focus here is to determine locations to control and/or sense vibrations on a truss structure. However, instead of using one of the earlier optimization models referenced in the above paragraph we adopt an experimental design approach.

Kincaid, Rex K.↗