Search NASA⌕ Search

SEARCH · Search NASA

Results for “Variational discretization”

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 127 records · Page 7

A Pressure Based Multigrid Procedure for the Navier-Stokes Equations on Unstructured Grids

We present details and performance of a pressure based multigrid solution procedure for the Navier-Stokes equations discretized on triangular grids. The discretization uses a control volume methodology, with linear inter-nodal variation of the flow variables. The use of the multigrid technique provides rapid and grid-independent rates of convergence. Three model driven cavity flows are computed, and the performance of the method at several grid densities and Reynolds numbers is reported. Representative flow fields characterizing the viscous eddies are also presented.

Jyotsna, R.↗

Fast Multigrid Techniques in Total Variation-Based Image Reconstruction

Existing multigrid techniques are used to effect an efficient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-differential equation which, when discretized using cell-centered finite differences, yields a full matrix equation. A fixed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the differential operator. With effective preconditioning, the method presented seems to require Omicron(n) operations. Numerical results are given for a two-dimensional example.

Oman, Mary Ellen↗

An Assessment of Five Modeling Approaches for Thermo-Mechanical Stress Analysis of Laminated Composite Panels

A study is made of the effects of variation in the lamination and geometric parameters, and boundary conditions of multi-layered composite panels on the accuracy of the detailed response characteristics obtained by five different modeling approaches. The modeling approaches considered include four two-dimensional models, each with five parameters to characterize the deformation in the thickness direction, and a predictor-corrector approach with twelve displacement parameters. The two-dimensional models are first-order shear deformation theory, third-order theory; a theory based on trigonometric variation of the transverse shear stresses through the thickness, and a discrete layer theory. The combination of the following four key elements distinguishes the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the solutions obtained by using three-dimensional continuum models for each of the individual layers; (2) both mechanical and thermal loadings are considered; (3) boundary conditions other than simply supported edges are considered; and (4) quantities compared include detailed through-the-thickness distributions of transverse shear and transverse normal stresses. Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective technique for obtaining accurate transverse stresses, and for thermal loading, none of the two-dimensional models is adequate for calculating transverse normal stresses, even when used in conjunction with three-dimensional equilibrium equations.

Noor, A. K.↗

On the Dynamics of Some Discretizations of Convection-Diffusion Equations

Numerical discretizations of differential equations which model physical processes can possess dynamics quite different from that of the equations themselves. Recently the emphasis has been on the the dynamics of numerical discretizations for Ordinary Differential Equations (ODEs). For Partial Differential Equations (PDEs) using a method of lines approach the situation is more complex. First, the spatial discretisation may introduce dynamics not present in the original equations; second, the solution of the resulting system of ODEs is open to the modified dynamics of the ODE solver used. These two effects may interact in a complex manner. In this talk we present some results of our recent work on the dynamics of discretizations of convection-diffusion equations, including those produced using Total Variation Diminishing (TVD) schemes and adaptive grid techniques. A more general overview of the area may be found on our accompanying poster presentation.

Sweby, Peter K.↗

Computational Icing Risk Analysis of the D8 "Double Bubble" Aircraft

A computational icing risk analysis utilizing LEWICE3D was performed for the D8 Double Bubble aircraft. A variety of discrete drop sizes spanning the Appendix C and O regimes were simulated. For computational efficiency a 50-bin global discretization was produced and projected onto the distributions of interest, eliminating redundant simulations. The trajectory and impingement characteristics for discrete drop diameters were analyzed to help understand the behavior of the water drops in the presence of a complex flow field. The collection efficiency results for the discrete drop diameters were then weighted by their contributions to the total water content of six different continuous distributions and subsequently superposed to approximate these curves. Results indicate that significant variation in impingement exists as a function of drop diameter for complex wing body geometries, and that current discretization practices may be insufficient to accurately predict water collection on certain regions of the aircraft. Results also indicate that the Appendix O distributions, specifically those with considerable water content at large drops, generates water collection patterns that are markedly different from distributions representative of Appendix C.

icing↗

Computational Icing Risk Analysis of the D8 "Double Bubble" Aircraft

A computational icing risk analysis utilizing LEWICE3D was performed for the D8 Double Bubble aircraft. A variety of discrete drop sizes spanning the Appendix C and O regimes were simulated. For computational efficiency a 50-bin global discretization was produced and projected onto the distributions of interest, eliminating redundant simulations. The trajectory and impingement characteristics for discrete drop diameters were analyzed to help understand the behavior of the water drops in the presence of a complex flow field. The collection efficiency results for the discrete drop diameters were then weighted by their contributions to the total water content of six different continuous distributions and subsequently superposed to approximate these curves. Results indicate that significant variation in impingement exists as a function of drop diameter for complex wing body geometries, and that current discretization practices may be insufficient to accurately predict water collection on certain regions of the aircraft. Results also indicate that the Appendix O distributions, specifically those with considerable water content at large drops, generates water collection patterns that are markedly different from distributions representative of Appendix C.

Porter, Christopher E.↗

On the Relationship Between Sub-Daily Instantaneous and Daily Total Gross Primary Production: Implications for Interpreting Satellite-Based SIF Retrievals

Spatially and temporally continuous estimation of plant photosynthetic carbon fixation (or gross primary production, GPP) is crucial to our understanding of the global carbon cycle and the impact of climate change. Besides spatial, seasonal and interannual variations, GPP also exhibits strong diurnal variations. Satellite retrieved solar-induced chlorophyll fluorescence (SIF) provides a spatially continuous, but temporally discrete measurement of plant photosynthesis, and has the potential to be used to estimate GPP at global scale. However, it remains unclear whether the seasonal time series of SIF snapshots taken at a fixed time of the day can be used to infer daily total GPP variation at spatial and seasonal scales. In this study, we first used GPP estimates from 135 eddy covariance flux sites, covering a wide range of geographic locations and biome types, to investigate the relationship between the instantaneous GPP (GPP(sub inst)) and daily GPP (GPP(sub daily)) on the seasonal course for different times of the day. Latitudinal and diurnal patterns were found to correspond to variations in photosynthetically active radiation (PAR) and light use efficiency (LUE), respectively. We then used the Soil-Canopy Observation Photosynthesis and Energy Balance (SCOPE) model and the FluxCom GPP product to investigate the instantaneous and daily SIF-GPP relationships at five flux tower sites along a latitudinal gradient and at a global scale for different biome types. The results showed that daily SIF had a stronger linear correlation with daily GPP than instantaneous SIF at the seasonal scale, with an instantaneous to daily SIF conversion factor following the latitudinal and seasonal pattern driven by PAR. Our study highlights the necessity to take the latitudinal and diurnal factors into consideration for SIF-GPP relationship analyses or for physiological phenology analyses based on SIF.

photosynthesis model↗

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Ahmad, Shahid↗

Making Ceramic Parts by Laminating and Sintering Thin Sheets

Chemical composition varies as function of depth. Technique developed to fabricate monolithic ceramic component by sintering laminated body made from thin sheets of green ceramic. Method allows discrete changes in chemistry effected across monolith. Component having one-dimensional variation in material composition fabricated in this manner.

Cawley, J. D.↗

Development of an integrated BEM approach for hot fluid structure interaction

Significant progress was made toward the goal of developing a general purpose boundary element method for hot fluid-structure interaction. For the solid phase, a boundary-only formulation was developed and implemented for uncoupled transient thermoelasticity in two dimensions. The elimination of volume discretization not only drastically reduces required modeling effort, but also permits unconstrained variation of the through-the-thickness temperature distribution. Meanwhile, for the fluids, fundamental solutions were derived for transient incompressible and compressible flow in the absence of the convective terms. Boundary element formulations were developed and described. For the incompressible case, the necessary kernal functions, under transient and steady-state conditions, were derived and fully implemented into a general purpose, multi-region boundary element code. Several examples were examined to study the suitability and convergence characteristics of the various algorithms.

Dargush, Gary F.↗

Recurrent episodic mass loss in a B2e star - 66 Ophiuchi, 1982-1985

The results of three intensive ultraviolet monitoring campaigns for 66 Oph in September-October 1982, September 1983, and September 1984, supplemented by the available IUE archival data from April, 1982 to June, 1985 are reported. The stellar wind went through at least two and probably three episodes of weak-wind absorption. At wind minimum, the resonance profiles and equivalent widths of C IV, Si IV, Si III, and Al III are similar to those observed in normal B stars of comparable luminosity, effective temperature, and v sin i. The strong-wind absorption profiles show one or more shortward-shifted discrete components superposed upon the weak-wind absorption profiles. Significant profile variations are seen on time scales spanning over two orders of magnitude, ranging from small-amplitude changes detected on time scales of hours to the transitions from wind minimum to maximum, which take months.

Grady, C. A.↗

Variational modal identification of gyroscopic distributed-parameter systems

Variational modal identification of gyroscopic distribution parameter systems is discussed. Topics covered include: equation of motion for gyroscopic distributed-parameter systems; a variational formulation for the eigenvalue problem; a variational formulation for the modal identification of gyroscopic distributed-parameter systems; discretization; and numerical example.

Silverberg, Larry M.↗

Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. The two-equation turbulence models are discretized in space with an upwind-biased, second order accurate total variation diminishing scheme. One and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered. The more recently developed field-equation turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are obtained. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading edge transitional flow region in order to capture the correct physical mechanism that leads to dynamic stall.

Ekaterinaris, John A.↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

Neoproterozoic variations in the C-isotopic composition of seawater: stratigraphic and biogeochemical implications

The recent proliferation of stratigraphic studies of delta 13C variation in carbonates and organic C in later Neoproterozoic and basal Cambrian successions (approximately 850-530 Ma) indicates a strong oscillating trend in the C-isotopic composition of surface seawater. Alone, this trend does not adequately characterize discrete intervals in Neoproterozoic time. However, integrated with the vectorial signals provided by fossils and Sr-isotopic variations, C isotope chemostratigraphy facilitates the interbasinal correlation of later Neoproterozoic successions. Results of these studies are evaluated in terms of four stratigraphic intervals: (1) the Precambrian/Cambrian boundary, (2) the post-Varanger terminal Proterozoic, (3) the late Cryogenian, and (4) the early Cryogenian. Where biostratigraphic or radiometric data constrain the age of Neoproterozoic sedimentary sequences, secular variations in C and Sr isotopes can provide a level of stratigraphic resolution exceeding that provided by fossils alone. Isotopic data place strong constraints on the chemical evolution of seawater, linking it to major tectonic and paleoclimatic events. They also provide a biogeochemical framework for the understanding of the initial radiation of macroscopic metazoans, which is associated stratigraphically, and perhaps causally, with a global increase in the burial of organic C and a concomitant rise of atmospheric O2.

NASA Discipline Exobiology↗

Total pressure averaging in pulsating flows

A number of total-pressure tubes were tested in a non-steady flow generator in which the fraction of period that pressure is a maximum is approximately 0.8, thereby simulating turbomachine-type flow conditions. Most of the tubes indicated a pressure which was higher than the true average. Organ-pipe resonance which further increased the indicated pressure was encountered within the tubes at discrete frequencies. There was no obvious combination of tube diameter, length, and/or geometry variation used in the tests which resulted in negligible averaging error. A pneumatic-type probe was found to measure true average pressure, and is suggested as a comparison instrument to determine whether nonlinear averaging effects are serious in unknown pulsation profiles. The experiments were performed at a pressure level of 1 bar, for Mach number up to near 1, and frequencies up to 3 kHz.

Krause, L. N.↗

Total-pressure averaging in pulsating flows.

A number of total-pressure tubes were tested in a nonsteady flow generator in which the fraction of period that pressure is a maximum is approximately 0.8, thereby simulating turbomachine-type flow conditions. Most of the tubes indicated a pressure which was higher than the true average. Organ-pipe resonance which further increased the indicated pressure was encountered with the tubes at discrete frequencies. There was no obvious combination of tube diameter, length, and/or geometry variation used in the tests which resulted in negligible averaging error. A pneumatic-type probe was found to measure true average pressure and is suggested as a comparison instrument to determine whether nonlinear averaging effects are serious in unknown pulsation profiles.

Krause, L. N.↗

Total-pressure-tube averaging in pulsating flows.

A number of total-pressure tubes were tested in a nonsteady flow generator in which the fraction of period that pressure is a maximum is approximately 0.8, thereby simulating turbomachine-type flow conditions. The tests were performed at a pressure level of 1 bar, for Mach numbers up to near 1, and frequencies up to 3 kHz. Most of the tubes indicated a pressure which was higher than the true average. Organ-pipe resonances which further increased the indicated pressure were encountered within the tubes at discrete frequencies. There was no obvious combination of tube diameter, length, and/or geometry variation used in the tests which resulted in negligible averaging error. A pneumatic-type probe was found to measure true average pressure, and is suggested as a comparison instrument to determine whether nonlinear averaging effects are serious in unknown pulsation profiles.

Krause, L. N.↗