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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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Finite element thermal analysis of convectively-cooled aircraft structures

The design complexity and size of convectively-cooled engine and airframe structures for hypersonic transports necessitate the use of large general purpose computer programs for both thermal and structural analyses. Generally thermal analyses are based on the lumped-parameter finite difference technique, and structural analyses are based on the finite element technique. Differences in these techniques make it difficult to achieve an efficient interface. It appears, therefore, desirable to conduct an integrated analysis based on a common technique. A summary is provided of efforts by NASA concerned with the development of an integrated thermal structural analysis capability using the finite element method. Particular attention is given to the development of conduction/forced-convection finite element methodology and applications which illustrate the capabilities of the developed concepts.

Wieting, A. R.↗
NASA NTRS1983

A fully vectorized numerical solution of the incompressible Navier-Stokes equations

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Patel, N.↗
NASA NTRS1987

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗
NASA NTRS1991

Parallelized solvers for heat conduction formulations

Based on multilevel partitioning, this paper develops a structural parallelizable solution methodology that enables a significant reduction in computational effort and memory requirements for very large scale linear and nonlinear steady and transient thermal (heat conduction) models. Due to the generality of the formulation of the scheme, both finite element and finite difference simulations can be treated. Diverse model topologies can thus be handled, including both simply and multiply connected (branched/perforated) geometries. To verify the methodology, analytical and numerical benchmark trends are verified in both sequential and parallel computer environments.

Padovan, Joe↗
NASA NTRS2004

Sensitivity of the FVGCM to Changes in Ozone

We have carried out an experiment with the finite volume general circulation model (FVGCM). This experiment consisted of two different imposed changes in the climatological ozone fields assumed in the radiation code. for conditions with no significant ozone hole. This distribution was obtained from a 50-year simulation of the full stratospheric ozone chemistry, with a time-dependent chlorine loading, done with our off-line chemical transport model (CTM). Three years (1978-1980) of this simulation were averaged to form a monthly, zonal-mean ozone distribution that was used in the 20-year integration of the FVGCM for "unperturbed" conditions. The second 20-year GCM integration included a fully-developed ozone hole. This ozone distribution was from three years, 1998-2000, from the same CTM simulation. The goal of this work is to determine the coupled response of the chemistry and dynamics of the stratosphere. These experiments are the first step in understanding the coupled response. An important initial question concerns the significance of the signals: if 20-year integrations turn out to be too short, the runs will be extended.

Stolarski↗
NASA NTRS2019

Efficient Entropy Stable Gauss Collocation Methods

The construction of high-order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize the construction of semidiscrete, entropy stable schemes on tensor product elements to Gauss points and generalized SBP operators. Numerical experiments suggest 8 that the use of Gauss points significantly improves accuracy on curved meshes.

Jesse Chan↗
DOE OSTI2016

Optical NOR logic gate design on square lattice photonic crystal platform

We numerically demonstrate a new configuration of all-optical NOR logic gate with square lattice photonic crystal (PhC) waveguide using finite difference time domain (FDTD) method. The logic operations are based on interference effect of optical waves. We have determined the operating frequency range by calculating the band structure for a perfectly periodic PhC using plane wave expansion (PWE) method. Response time of this logic gate is 1.98 ps and it can be operated with speed about 513 GB/s. The proposed device consists of four linear waveguides and a square ring resonator waveguides on PhC platform.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1996

Spectral Ambiguity of Allan Variance

We study the extent to which knowledge of Allan variance and other finite-difference variances determines the spectrum of a random process. The variance of first differences is known to determine the spectrum. We show that, in general, the Allan variance does not. A complete description of the ambiguity is given.

Allan Variance variances finite-difference varianc↗
NASA NTRS1979

A computational fluid dynamic technique valid at the centerline for non-axisymmetric problems in cylindrical coordinates

A technique is described for the numerical solution of non-axisymmetric flow problems posed in cylindrical coordinates when the z-axis is included in the flowfield. The highlight of the technique is the manner in which the singularities at the centerline are handled. Specifically, the governing flowfield equations at r = 0 are put in a special form by applying L'Hospital's Rule. The required radial derivatives are evaluated using a one-sided, second-order accurate, first-difference. This leads to a smooth, convergent calculation of the flowfield at the centerline. This appears to be the first generally applicable numerical method for avoiding coordinate system singularities in the context of a finite-difference scheme, and could have application to many nonaxisymmetric flows. The technique is illustrated by specific results for the time-dependent flowfield inside an internal combustion engine.

Griffin, M. D.↗
DOE OSTI2016

Mimetic Finite Differences and Algebraic Multilevel Methods for Reservoir Performance Predictions: CRADA Final Report

The need to better predict and control reservoir performance is driving the development of increasingly sophisticated reservoir models that use unstructured general polyhedral grids to capture highly detailed stratigraphy. However, both discretization methods and scalable iterative solution algorithms for these situations are an active area of research. In this work we compared the performance of a new Mimetic Finite Difference (MFD) method with two new Mixed Finite Element methods, and LANL and the CRADA Participant investigated the performance of Los Alamos National Laboratory’s algebraic multigrid code on realistic flow problems. Furthermore, uncertainty quantification requires rapid evaluations of reservoir models. To do this, fine-scale reservoir models need to be coarsened and yet important fine-scale features and processes that have a significant impact on flows need to be preserved. To this end, we investigated the use of multi-resolution methods, such as the Multilevel Multiscale Mimetic (M3) method, to coarsen reservoir models.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Mixing and non-equilibrium chemical reaction in a compressible mixing layer

The effects of compressibility, chemical reaction exothermicity, and non-equilibrium chemical modeling in a reacting plane mixing layer were investigated by means of two dimensional direct numerical simulations. The chemical reaction was irreversible and second order of the type A + B yields Products + Heat. The general governing fluid equations of a compressible reacting flow field were solved by means of high order finite difference methods. Physical effects were then determined by examining the response of the mixing layer to variation of the relevant non-dimensionalized parameters. The simulations show that increased compressibility generally results in a suppressed mixing, and consequently a reduced chemical reaction conversion rate. Reaction heat release was found to enhance mixing at the initial stages of the layer growth, but had a stabilizing effect at later times. The increased stability manifested itself in the suppression or delay of the formation of large coherent structures within the flow. Calculations were performed for a constant rate chemical kinetics model and an Arrhenius type kinetic prototype. The choice of the model was shown to have an effect on the development of the flow. The Arrhenius model caused a greater temperature increase due to reaction than the constant kinetic model. This had the same effect as increasing the exothermicity of the reaction. Localized flame quenching was also observed when the Zeldovich number was relatively large.

Steinberger, Craig J.↗
NASA NTRS1969

Finite element formulation for linear thermoviscoelastic materials

Report presents the finite difference equations in time and finite element matrix equations in space for general linear thermovisoelastic problems. The equations are derived for a general three-dimensional body but are applicable to one- and two-dimensional configurations with minor changes.

Chen, J. C.↗
NASA NTRS1975

Numerical solution of the Navier-Stokes equations with topography

A finite difference scheme for solving the equations of fluid motion in a generalized coordinate system has been constructed. The scheme conserves mass and all the first integral moments of the motion. The scheme also advectively 'almost conserves' second moments, in that the magnitude of implicit numerical smoothing is typically about an order smaller than explicit viscosity and diffusion. Calculations with the model support the theoretical conjecture that the difference scheme is stable whenever the analogous Cartesian scheme is stable. The scheme has been used to calculate dry atmospheric convection due to differential heating between top and bottom of mountainous terrain. The general small-scale characteristics of mountain up-slope winds have been simulated. In addition, the results have demonstrated the crucial role played by the eddy diffusivities and the environmental stability, in determining both the quantitative and the qualitative features of the circulation.

Gal-Chen, T.↗
NASA NTRS1976

Flux-corrected transport techniques for transient calculations of strongly shocked flows

New flux-corrected transport algorithms are described for solving generalized continuity equations. These techniques were developed by requiring that the finite difference formulas used ensure positivity for an initially positive convected quantity. Thus FCT is particularly valuable for fluid-like problems with strong gradients or shocks. Repeated application of the same subroutine to mass, momentum, and energy conservation equations gives a simple solution of the coupled time-dependent equations of ideal compressible fluid dynamics without introducing an artificial viscosity. FCT algorithms span Eulerian, sliding-rezone, and Lagrangian finite difference grids in several coordinate systems. The latest FCT techniques are fully vectorized for parallel/pipeline processing.

Boris, J. P.↗
NASA NTRS1982

Transonic perturbation analysis of wing-fuselage-nacelle-pylon configurations with powered jet exhausts

A transonic small perturbation method has been developed for the analysis of general wing-fuselage-nacelle-pylon configurations with powered jet exhausts. Finite difference successive line relaxation algorithm is used to solve the small disturbance potential equation in conservative form. The nacelle tangency condition and the jet exhaust plume contact conditions are fulfilled in a quasi-cylindrical fashion on a surface fitting the Cartesian grid. The pylon tangency condition is treated in a quasi-planar manner as for the wing. Viscous displacement effects on the wing are modeled by suitable shape changes including the placement of a viscous ramp at the base of the shock. Computed results of a transport configuration show satisfactory correlation with test data.

Wai, J. C.↗
NASA NTRS1981

Mesh generation by conformal and quasiconformal mappings

It is pointed out that many recent advances in the finite-difference solution of elliptic equations have been limited to regions whose boundary contours coincide with coordinate lines of the Cartesian coordinate system. The reason for this is related to the fact that in the case of an arbitrary curvilinear coordinate system the original equation becomes much more complex. However, there is no added complexity if an orthogonal coordinate system is generated from a conformal mapping. In the present investigation, a finite difference method developed for the construction of conformal mappings has been generalized to construct quasi-conformal mappings. It is expected that the use of more sophisticated numerical algorithms could lead to improvements in both speed and accuracy. Quasi-conformal mappings have applications not only in the solution of elliptic equations but also in other areas such as orthogonal mesh generation on surfaces and the solution of certain fluid flow problems.

Mastin, C. W.↗
NASA NTRS1985

Numerical studies of 2-dimensional flows

A formulation of the lambda scheme for the analysis of two dimensional inviscid, compressible, unsteady transonic flows is presented. The scheme uses generalized Riemann variables to determine the appropriate two point, one sided finite difference approximation for each derivative in the unsteady Euler equations. These finite differences are applied at the predictor and corrector levels with shock updating at each level. The weaker oblique shocks are captured, but strong near normal shocks are fitted into the flow using the Rankine-Hugoniot relations. This code is demonstrated with a numerical example of a duct flow problem with developing normal and oblique shock waves. The technique is implemented in a code which has been made efficient by streamlining to a minimal number of operations and by eliminating branch statements. The scheme is shown to provide an accurate analysis of the flow, including formation, motions, and interactions of shocks; the results obtained on a relatively coarse mesh are comparable to those obtained by other methods on much finer meshes.

Moretti, G.↗