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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

FEM/SINDA: Combining the strengths of NASTRAN, SINDA, I-DEAS, and PATRAN for thermal and structural analysis

This paper describes the interface/integration between FEM/SINDA, a general purpose geometry driven thermal analysis code, and the FEM software: I-DEAS, PATRAN, and NASTRAN. FEM/SINDA brings together the advantages of the finite element method to model arbitrary geometry and anisotropic materials and SINDA's finite difference capability to model thermal properties, loads, and boundary conditions that vary with time or temperature. I-DEAS and PATRAN thermal entities are directly supported since FEM/SINDA uses the nodes of the FEM model as the point at which the temperature is determined. Output from FEM/SINDA (as well as the FEM/SINDA input deck) can be used directly by NASTRAN for structural analysis.

Zarda, P. Richard↗
NASA NTRS1994

Pseudospectral collocation methods for fourth order differential equations

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Malek, Alaeddin↗
NASA NTRS1993

Tension fracture of laminates for transport fuselage. Part 2: Large notches

Tests were conducted on over 200 center-crack specimens to evaluate: (a) the tension-fracture performance of candidate materials and laminates for commercial fuselage applications; and (b) the accuracy of several failure criteria in predicting response. Crack lengths of up to 12 inches were considered. Other variables included fiber/matrix combination, layup, lamination manufacturing process, and intraply hybridization. Laminates fabricated using the automated tow-placement process provided significantly higher tension-fracture strengths than nominally identical tape laminates. This confirmed earlier findings for other layups, and possibly relates to a reduced stress concentration resulting from a larger scale of repeatable material inhomogeneity in the tow-placed laminates. Changes in material and layup result in a trade-off between small-notch and large-notch strengths. Toughened resins and 0 deg-dominate layups result in higher small-notch strengths but lower large-notch strengths than brittle resins, 90 deg and 45 deg dominated layups, and intraply S2-glass hybrid material forms. Test results indicate that strength-prediction methods that allow for a reduced order singularity of the crack-tip stress field are more successful at predicting failure over a range of notch sizes than those relying on the classical square-root singularity. The order of singularity required to accurately predict large-notch strength from small-notch data was affected by both material and layup. Measured crack-tip strain distributions were generally higher than those predicted using classical methods. Traditional methods of correcting for finite specimen width were found to be lacking, confirming earlier findings with other specimen geometries. Fracture tests of two stiffened panels, identical except for differing materials, with severed central stiffeners resulted in nearly identical damage progression and failure sequences. Strain-softening laws implemented within finite element models appear attractive to account for load redistribution in configured structure due to damage-induced crack tip softening

Walker, Tom H.↗
NASA NTRS2005

Coupled fvGCM-GCE Modeling System, 3D Cloud-Resolving Model and Cloud Library

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud- resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. A seed fund is available at NASA Goddard to build a MMF based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM). A prototype MMF in being developed and production runs will be conducted at the beginning of 2005. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes, ( 2 ) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), (3) A cloud library generated by Goddard MMF, and 3D GCE model, and (4) A brief discussion on the GCE model on developing a global cloud simulator.

Tao, Wei-Kuo↗
NASA NTRS2006

A Coupled GCM-Cloud Resolving Modeling System, and a Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CFWs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1 998 and 1999). In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗
NASA NTRSDate not supplied

High-Order Shock Fitting with Finite Element Methods

A moving-grid, shock-tracking, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, element edges in the computational mesh are fitted to the shock front and moved with the shock throughout the simulation. The Euler equations are solved on the moving mesh in an arbitrary Lagrangian-Eulerian framework. Three different methods for specifying the shock motion have been tested,and the order of accuracy of the resulting solutions was verified. It was found that one of the methods is applicable only for problems with a constant upstream flow state, whereas the other two methods converge to the expected solution for general shock problems. When using a finite element method with polynomial degree p, the two general shock motion methods converged with the expected order of accuracy of (p+1). Finally, accurate solutions are obtained for supersonic nozzle and blunt body bow shock problems. Based on the results, it is concluded that the shock tracking method can preserve high-order solution accuracy in the vicinity of a shock wave.

Luke D'Aquila↗
DOE OSTI2024

Difference equations and integral families for Witten diagrams

We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as “summation-by-parts relations”, in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

AdS-CFT Correspondence↗
NASA NTRS1991

Phase retrieval for the Hubble Space Telescope using iterative propagation algorithms

Phase retrieval algorithms, including the iterative transform algorithm and gradient search algorithms, were generalized to include the effects of propagation through a complicated optical system and to discount the effects of bad CCD pixels. For the gradient search algorithms, analytic gradients were derived that greatly speed up the computation over finite difference methods. For the Hubble Space Telescope (HST), the aperture function was reconstructed and the phase errors were retrieved. This information is useful to design correction optics for the telescope and for the deconvolution of blurred images from the HST.

Fienup, J. R.↗
NASA NTRS2003

Influence of Ice-phase of Hydrometeors on Moist-Convection

Climate models often ignore the influence of ice-phase physics (IPP) of hydrometeors as a second order effect. This has also been true for McRAS (Microphysics of clouds with Relaxed Arakawa Schubert Scheme) developed by the authors. Recognizing that the temperature sounding is critical for moist-convection, and, that IPP would modify it, we investigated the influence of introducing IPP into McRAS coupled to FvGCM (finite volume General Circulation Model with NCAR physics). We analyzed three 3-yr long simulations; the first called Control Case, CC and had no IPP; the other two called Experiments El and E2 had IPP introduced with two different in-cloud freezing assumptions. Simulation El assumed that all hydrometeors remain liquid in the updraft and freeze upon detrainment. Simulation E2 invoked the in-cloud freezing of new condensate generated at subfreezing temperatures in the updraft while old cloud water continued to ascend as liquid. Upon detrainment, this cloud water also froze like in E1. With these assumptions, about 50% of hydrometeors froze in the tower and the rest froze in the anvil. However, in both El and E2, the frozen hydrometeors melted during fall at the first encounter of above freezing ambient temperature. Comparative analysis revealed that El simulated far more mid-level and far less deep clouds while E2 had modified deep and more mid-level clouds as compared to CC along with some major changes around the melt-level. We infer that IPP produced a more realistic response in E2. At the basic level, the results show that ice-phase processes influence convective detrainment at mid- and deep levels in accord with TOGAGOARE observations. The results suggest that IPP can help to mitigate less-than-observed mid-level and over-abundance of deep convective clouds in McRAS.

Sud, Y. C.↗
NASA NTRS2003

The Effect of the Density Ratio on the Nonlinear Dynamics of the Unstable Fluid Interface

Here we report multiple harmonic theoretical solutions for a complete system of conservation laws, which describe the large-scale coherent dynamics in RTI and RMI for fluids with a finite density ratio in the general three-dimensional case. The analysis yields new properties of the bubble front dynamics. In either RTI or RMI, the obtained dependencies of the bubble velocity and curvature on the density ratio differ qualitatively and quantitatively from those suggested by the models of Sharp (1984), Oron et al. (2001), and Goncharov (2002). We show explicitly that these models violate the conservation laws. For the first time, our theory reveals an important qualitative distinction between the dynamics of the RT and RM bubbles.

Abarzhi, S. I.↗
DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

A mixed pseudospectral/finite difference method for a thermally driven fluid in a nonuniform gravitational field

A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later Shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modeled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.

Macaraeg, M. G.↗
DOE OSTI2019

Compatible meshfree discretization of surface PDEs

Meshfree discretization of surface partial differential equations is appealing, due to their ability to naturally adapt to deforming motion of the underlying manifold. In this work, we consider an existing scheme proposed by Liang et al. reinterpreted in the context of generalized moving least squares (GMLS), showing that existing numerical analysis from the GMLS literature applies to their scheme. With this interpretation, their approach may then be unified with recent work developing compatible meshfree discretizations for the div-grad problem in R d . Informally, this is analogous to an extension of collocated finite differences to staggered finite difference methods, but in the manifold setting and with unstructured nodal data. In this way, we obtain a compatible meshfree discretization of elliptic problems on manifolds which is naturally stable for problems with material interfaces, without the need to introduce numerical dissipation or local enrichment near the interface. As a result, we provide convergence studies illustrating the high-order convergence and stability of the approach for manufactured solutions and for an adaptation of the classical five-strip benchmark to a cylindrical manifold.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1986

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗
NASA NTRS1989

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗
DOE OSTI2019

HALO: A full-orbit model of nonlinear interaction of fast particles with eigenmodes

HALO (HAgis LOcust) solves the initial value Vlasov-Maxwell problem perturbatively for application to certain nonlinear wave-particle problems in tokamak plasmas. It uses the same basic approach as the HAGIS code for wave evolution but is built on the LOCUST-GPU full-orbit code for the solution of the Hamiltonian fast particle motion in cylindrical coordinates. The wave amplitude and particle evolution include all finite Larmour radius effects. We describe and benchmark the currently implemented Alfvén eigenmode workflow, demonstrating correct particle motion, linear and nonlinear power transfer. Here, the formulation and numerical scheme are sufficiently general as to allow easy future implementation of different kinds of eigenmodes, such as modes close to the ion-cyclotron frequency. The code can model multiple eigenmodes and multiple fast ion species simultaneously, and supports the general form of the equilibrium distribution in constants of motion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

A higher order approximate static condensation method for multi-material diffusion problems

The paper studies an approximate static condensation method for the diffusion problem with discontinuous diffusion coefficients. The method allows for a general polygonal mesh which is unfitted to the material interfaces. Moreover, the interfaces can be discontinuous across the mesh edges as typical for numerical reconstructions using the volume or moment-of-fluid methods. We apply a mimetic finite difference method to solve local diffusion problems and use P 1 (mortar) edge elements to couple local problems into the global system. The condensation process and the properties of the resulting algebraic system are discussed. It is demonstrated that the method is second order accurate on smooth solutions and performs well for problems with high contrast in diffusion coefficients. Experiments also show the robustness with respect to position of the material interfaces against the underlying mesh.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

On steady alternate bars forced by a localized asymmetric drag distribution in erodible channels

Studying the effect of different in-stream fluvial turbines siting on river morphodynamics allowed us to witness the onset of a time-averaged, large-scale, alternate distortion of bed elevations, which could not be exclusively related to the turbine rotor blockage. The longitudinal profiles of this two-dimensional bathymetric perturbation resemble those of steady fluvial bars. In this contribution we generalize the problem addressing a spatially impulsive, asymmetric distribution of drag force in the channel cross-section. Furthermore, this is experimentally investigated through the deployment of differently sized grids perpendicular to the flow, and analytically explored as a finite perturbation of an open channel flow over an erodible sediment layer, as described by a coupled flow–sediment shallow water equation. The steady solutions of this fluvial morphodynamic problem, physically represented by alternate bars scaling with the channel width, highlight the importance of the resonant conditions in defining the spatial extent of the bed deformation. The equations further suggest that in very shallow flows any asymmetric obstruction may lead to an upstream propagation of the steady bars, consistent with previous studies on the effects of channel curvature. In broad terms, this study provides the preliminary framework to control the onset of river meandering through imposed finite perturbations of the cross-section. In a more applied sense, it provides a tool to predict non-local scour–deposition patterns associated with the deployment of energy converters or other flow obstructions.

42 ENGINEERING↗