SEARCH · Search NASA

Results for “generalized finite differences”

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.

SourceResearch connectionFrom yearThrough year

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

At least 415 records · Page 23

All sources NASA NTRS DOE OSTI

NASA NTRS1989

Parallel iterative methods for sparse linear and nonlinear equations

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Saad, Youcef↗

NASA NTRS2000

Effect of Elevated Pressure on the Heat Transfer and Power Requirements During Bridgman Growth of PMN-PT Crystals

Performance of the furnace during Bridgman growth of the lead magnesium niobate-lead titanate crystal (PMN-PT) is analyzed. PMN-PT is electrostrictive ceramic that has near ideal strain-voltage function. Furthermore piezoelectric (2000 to 2300 pC/N) and coupling (92 to 95%) constants are exceptionally good. Due to these properties PMN-PT has wide range of applications - from sonars to transducers in a high precision optical systems. In this research first attempt to crystallize PMN-PT in a Mellen type vertical Bridgman furnace was not successful, as melting temperature of precursor materials was not achieved. At this point choice was between building a new more powerful facility or finding ways to enhance performance of the existing furnace. Besides adjusting power supply to the individual heating elements, redesigning ampoule holding cartridge and improving furnace insulation one more radical improvement was proposed. The entire furnace was placed into the high pressure chamber. Further experiments confirmed that temperature inside the furnace was increased sufficiently to melt precursor materials to obtain PMN-PT. Numerical modeling is undertaken to find limitations of this technique and to predict temperature distribution inside the ampoule. It is of interest also to account for main factors contributing to a higher temperatures achieved in the furnace under the higher pressure (up to 10 atm.). Numerical model of the furnace is based on general purpose finite - element code FIDAP and on previous efforts to model Bridgman type furnace with multiply heaters. In order to account for all heat transfer mechanism involved - conduction, convection and radiation - different parts of the furnace are modeled in accordance with expected dominant mode of heat transfer - conduction in the solid parts, conduction and radiation in the ampoule, gas convection and conduction in the furnace openings complemented with wall-to-wall radiation. Because of these complicating factors, dimensional rather than non-dimensional modeling is performed using steady-state 2-D and 3-D models. Particular attention is paid to the modeling of radiation in a semitransparent material of ampoule 7 sapphire. The radiation model is validated by solving realistic test problem - conduction and radiation heat transfer in the fused quartz. Results are in agreement with both experimental and analytical data.

Bune, Andris↗

NASA NTRS2006

A Measure-Theoretic Proof of the Markov Property for Hybrid Systems with Markovian Inputs

The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k+1) = Fk(x(k), theta(k)), where theta(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), theta(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts.

Tejada, Arturo↗

DOE OSTI2016

Developing A Fully Implicit Compressible Flow Valve Model in RELAP-7 and Its Application in Short Term BWR Station Black-Out Analyses

This paper presents a set of dynamical models for SRV simulation and their implementation in the RELAP-7 code, which is a new reactor system analysis code being developed at INL. RELAP-7 is based on the MOOSE (the Multi-Physics Object-Oriented Simulation Environment) framework. The compressible flow SRV model covers three different sets of models: fully closed case, subsonic case, and choking case. The RELAP-7 is a fully implicit code and the preconditioned Jacobian-free Newton-Krylov (JFNK) method is used to solve the discretized nonlinear problem. The JFNK method generally needs a good preconditioning scheme to be effective and efficient. There are different ways to precondition the JFNK method. In RELAP-7, two main options are used to obtain the preconditioning matrix: (1) FDP (Finite Difference Preconditioning) option which uses the default finite differencing method provided in the PETSc package. PETSc is the numerical solver software developed by Argonne National Laboratory and used by MOOSE as the numerical solution engine; (2) SMP (Single Matrix Preconditioning) option which requires code developers to provide approximate analytical Jacobian inputs for the important diagonal and off-diagonal terms. Due to the strong discontinuity in the residual vector space when the compressible flow valve model switches from one set of model to another, FDP option cannot guarantee convergence. Instead, accurate analytical Jacobain terms are provided for the compressible flow valve model. With the SMP option selected, the compressible flow valve model can be solved efficiently under different cases. The developed compressible flow valve model has been used for SRV component simulation in several simplified BWR SBO (Station Black-Out) simulations with RELAP-7. This paper only presents cases for short-term SBO in which all the safety systems fail to start and function properly when SBO occurs. Consequently, only the SRVs automatically open and close periodically to control the primary system pressure and discharge the high temperature and high pressure steam into the suppression pool. Although simplified, this case is quite similar to what happened in Fukushima Daiichi Unit 1. Unit 1 had no RCIC system, while the isolation condenser system was believed to be non-functioning, or only available for a very short period of time during the accident. Therefore, the Unit 1 reactor core reached a fuel failure temperature only a few hours into the accident. Two short-term SBO cases will be compared: one with single SRV discharge line which represents all the SRV lines and another case with multi-group SRVs which represent each group of SRV line with different setting points.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1983

A general perturbation approach for the equations of fluid dynamics

An efficient numerical technique to produce accurate solutions to the equations of fluid dynamics is presented where the governing equations are perturbed about an approximate solution and solved by finite-difference methods on a coarsened grid. The result is a scheme which substantially reduces the number of grid points necessary to accurately resolve the flow. Applications are presented for the two-dimensional Euler equations perturbed about a solution of the transonic full potential equation. However, the concept is applicable to arbitrary equation sets, higher dimensions and for a wide variety of applications.

Chow, L. J.↗

DOE OSTI2020

Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence

A filtering operation, based on B-spline discretizations, is introduced to target weakly growing mesh-scale oscillations that can arise in high-fidelity turbulence simulations. This is a spectral regularization that can be described using the singular values of a banded matrix operator, with the filtering strength set by a scalar- or vector-valued penalty parameter. The penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation (GCV) measure of distance between the pre- and post-filtered solutions. Efficient algorithms are developed to compute both the scalar and vector penalty parameters. The B-spline filter has a sharper localization to high-wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the Burgers' equation, decaying Burgers' turbulence, and compressible Navier–Stokes turbulent channel flow. Furthermore, these simulations confirm the scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions. An advantage over finite-difference filters is that these B-spline filters are stable on bounded domains and even preserve formal order of accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Transformer Leakage Inductance Design Methodology

The leakage inductance exhibited by a transformer depends on its winding geometry, which generally involves the selection of several key design parameters in addition to the winding structure and the interleaving configuration. With few resources explaining the effects of these design choices on the observed leakage inductance, numerous trial-and-error iterations become necessary to realize the desired leakage inductance. This paper explores more than a hundred winding geometries feasible in a 2-winding transformer comprising the same magnetic core, number of turns, and wire gauge, and finds the leakage inductance for each unique design using 2-D finite element method (FEM) simulations in association with the semi-analytical double- 2-D model. These leakage inductances are plotted and further analyzed to understand the effects of different design parameters on the effective leakage inductance. The results presented herein and the conclusions drawn from this research can serve as a valuable resource for future design practitioners from both industry and academia.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Deep Learning-Assisted Real-Time Forward Modeling of Electromagnetic Logging in Complex Formations

Higher dimensional (i.e., 2-D and 3-D) modeling is indispensable to correctly evaluate the responses of electromagnetic logging tools in complex formation environments. However, limited by the high computational cost of rigorous modeling such as finite difference method and the finite element method, the real-time applications in the well logging industry primarily rely on the 1-D forward solver, which would result in erroneous formation evaluation for complex scenarios. As a result, aiming at realizing fast modeling for electromagnetic logging tools in complex formations, this paper proposes a general framework assisted by deep neural networks (DNNs). The framework consists of three modules: earth model classification, parameter extraction, and surrogate construction. Separate DNNs are trained and tested for different modules. The accuracy and efficiency of the DNN assisted fast modeling are validated by several experiments. Here, this study finds that the fast modeling assisted by DNNs is able to calculate the tool responses and reconstruct the subsurface formations in real-time.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A coupled cluster framework for electrons and phonons

Here, we describe a coupled cluster framework for coupled systems of electrons and harmonic phonons. Neutral and charged excitations are accessed via the equation-of-motion version of the theory. Benchmarks on the Hubbard–Holstein model allow us to assess the strengths and weaknesses of different coupled cluster approximations, which generally perform well for weak to moderate coupling. Finally, we report progress toward an implementation for ab initio calculations on solids and present some preliminary results on finite-size models of diamond with a linear electron–phonon coupling. We also report the implementation of electron–phonon coupling matrix elements from crystalline Gaussian type orbitals within the PySCF program package.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1983

Numerical study of the effect of an embedded surface-heat source on the separation bubble of supersonic flow

A numerical study of the conjugated problem of a separated supersonic flow field and a conductive solid wall with an embedded heat source is presented. Implicit finite-difference schemes were used to solve the two-dimensional time-dependent compressible Navier-Stokes equations and the time-dependent heat-conduction equation for the solid in both general coordinate systems. A detailed comparison between the thin-layer and Navier-Stokes models was made for steady and unsteady supersonic flow and showed insignificant differences. Steady-state and transient cases were computed and the results show that a temperature pulse at the solid-fluid interface can be used to detect the flow direction near the wall in the vicinity of separation without significant distortion of the flow field.

Degani, D.↗

NASA NTRS1984

Maximum likelihood algorithm using an efficient scheme for computing sensitivities and parameter confidence intervals

Improved techniques for estimating airplane stability and control derivatives and their standard errors are presented. A maximum likelihood estimation algorithm is developed which relies on an optimization scheme referred to as a modified Newton-Raphson scheme with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared to integrating the analytically-determined sensitivity equations or using a finite difference scheme. An aircraft estimation problem is solved using real flight data to compare MNRES with the commonly used modified Newton-Raphson technique; MNRES is found to be faster and more generally applicable. Parameter standard errors are determined using a random search technique. The confidence intervals obtained are compared with Cramer-Rao lower bounds at the same confidence level. It is observed that the nonlinearity of the cost function is an important factor in the relationship between Cramer-Rao bounds and the error bounds determined by the search technique.

Murphy, P. C.↗

NASA NTRS1993

Source term evaluation for combustion modeling

A modification is developed for application to the source terms used in combustion modeling. The modification accounts for the error of the finite difference scheme in regions where chain-branching chemical reactions produce exponential growth of species densities. The modification is first applied to a one-dimensional scalar model problem. It is then generalized to multiple chemical species, and used in quasi-one-dimensional computations of shock-induced combustion in a channel. Grid refinement studies demonstrate the improved accuracy of the method using this modification. The algorithm is applied in two spatial dimensions and used in simulations of steady and unsteady shock-induced combustion. Comparisons with ballistic range experiments give confidence in the numerical technique and the 9-species hydrogen-air chemistry model.

Sussman, Myles A.↗

NASA NTRS1993

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Moorthi, Shrinivas↗

NASA NTRS2001

The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites

The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident, that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with (1) simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as (2) finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.

Pahr, D. H.↗

NASA NTRS2001

The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites

The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.

Pahr, D. H.↗

NASA NTRS1998

Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.

Prosser, W. H.↗

DOE OSTI2017

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. Here, the numerical scheme is verified on a number of difficult benchmark problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Simulation of the 2003 Foss Barge - Point Wells Oil Spill: A Comparison between BLOSOM and GNOME Oil Spill Models

The Department of Energy’s (DOE’s) National Energy Technology Laboratory’s (NETL’s) Blowout and Spill Occurrence Model (BLOSOM), and the National Oceanic and Atmospheric Administration’s (NOAA’s) General NOAA Operational Modeling Environment (GNOME) are compared. Increasingly complex simulations are used to assess similarities and differences between the two models’ components. The simulations presented here are forced by ocean currents from a Finite Volume Community Ocean Model (FVCOM) implementation that has excellent skill in representing tidal motion, and with observed wind data that compensates for a coarse vertical ocean model resolution. The comprehensive comparison between GNOME and BLOSOM presented here, should aid modelers in interpreting their results. Beyond many similarities, aspects where both models are distinct are highlighted. Some suggestions for improvement are included, e.g., the inclusion of temporal interpolation of the forcing fields (BLOSOM) or the inclusion of a deflection angle option when parameterizing wind-driven processes (GNOME). Overall, GNOME and BLOSOM perform similarly, and are found to be complementary oil spill models. This paper also sheds light on what drove the historical Point Wells spill, and serves the additional purpose of being a learning resource for those interested in oil spill modeling. The increasingly complex approach used for the comparison is also used, in parallel, to illustrate the approach an oil spill modeler would typically follow when trying to hindcast or forecast an oil spill, including detailed technical information on basic aspects, like choosing a computational time step. We discuss our successful hindcast of the 2003 Point Wells oil spill that, to our knowledge, had remained unexplained. The oil spill models’ solutions are compared to the historical Point Wells’ oil trajectory, in time and space, as determined from overflight information. Our hindcast broadly replicates the correct locations at the correct times, using accurate tide and wind forcing. While the choice of wind coefficient we use is unconventional, a simplified analytic model supported by observations, suggests that it is justified under this study’s circumstances. We highlight some of the key oceanographic findings as they may relate to other oil spills, and to the regional oceanography of the Salish Sea, including recommendations for future studies.

42 ENGINEERING↗