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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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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Finite difference analysis of torsional vibrations of pretwisted, rotating, cantilever beams with effects of warping

Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.

Subrahmanyam, K. B.↗
DOE OSTI2021

Seismic waves in medium with poroelastic/elastic interfaces: a two-dimensional P-SV finite-difference modelling

SUMMARY We present a new methodology of the finite-difference (FD) modelling of seismic wave propagation in a strongly heterogeneous medium composed of poroelastic (P) and (strictly) elastic (E) parts. The medium can include P/P, P/E and E/E material interfaces of arbitrary shapes. The poroelastic part can be with (i) zero resistive friction, (ii) non-zero constant resistive friction or (iii) JKD model of the frequency-dependent permeability and resistive friction. Our FD scheme is capable of subcell resolution: a material interface can have an arbitrary position in the spatial grid. The scheme keeps computational efficiency of the scheme for a smoothly and weakly heterogeneous medium (medium without material interfaces). Numerical tests against independent analytical, semi-analytical and spectral-element methods prove the efficiency and accuracy of our FD modelling. In numerical examples, we indicate effect of the P/E interfaces for the poroelastic medium with a constant resistive friction and medium with the JKD model of the frequency-dependent permeability and resistive friction. We address the 2-D P-SV problem. The approach can be readily extended to the 3-D problem.

58 GEOSCIENCES↗
NASA NTRS1980

An implicit finite-difference code for inviscid and viscous cascade flow

An implicit finite-difference code is developed to solve either inviscid or viscous flow about two-dimensional cascade blade elements. General coordinate transformations are used so that boundaries can coincide with coordinate lines, and an automatic grid generation routine based on elliptic partial differential equations is employed to mesh arbitrary cascade elements. Characteristic combinations of the differential equations are used at inflow and outflow boundaries. Computed results for both inviscid and viscous flow are compared with other existing cascade solutions and experimental data.

Steger, J. L.↗
NASA NTRS1980

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

Steger, J. L.↗
NASA NTRS1981

Some modifications to, and operational experiences with, the two-dimensional, finite-difference, boundary-layer code, STAN5

The two-dimensional, finite-difference boundary-layer code, STAN5, is the primary tool used at the NASA-Lewis Research Center for predicting turbine blade gas-side heat-transfer coefficients. A number of modifications have been made to the program to enhance its usefulness for these calculations. Experience in using STAN5 has identified some problems in the program that can be treated through program input, without modifying the program. These include the presence of a small separation bubble near the leading edge, and the effect of full-coverage film cooling on transition to turbulence. Some of the techniques used to treat these problems are described.

Gaugler, R. E.↗
NASA NTRS1987

A finite difference scheme for three-dimensional steady laminar incompressible flow

A finite difference scheme for three-dimensional steady laminar incompressible flows is presented. The Navier-Stokes equations are expressed conservatively in terms of velocity and pressure increments (delta form). First order upwind differences are used for first order partial derivatives of velocity increments resulting in a diagonally dominant matrix system. Central differences are applied to all other terms for second order accuracy. The SIMPLE pressure correction algorithm is used to satisfy the continuity equation. Numerical results are presented for cubic cavity flow problems for Reynolds numbers up to 2000 and are in good agreement with other numerical results.

Hwang, Danny P.↗
NASA NTRS1987

A finite difference scheme for three-dimensional steady laminar incompressible flow

A finite difference scheme for three-dimensional steady laminar incompressible flows is presented. The Navier-Stokes equations are expressed conservatively in terms of velocity and pressure increments (delta form). First order upwind differences are used for first order partial derivatives of velocity increments resulting in a diagonally dominant matrix system. Central differences are applied to all other terms for second order accuracy. The SIMPLE pressure correction algorithm is used to satisfy the continuity equation. Numerical results are presented for cubic cavity flow problems for Reynolds numbers up to 2000 and are in good agreement with other numerical results.

Hwang, Danny P.↗
NASA NTRS1988

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

Abramopoulos, Frank↗
NASA NTRS1993

An optimized finite-difference scheme for wave propagation problems

Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.

Zingg, D. W.↗
NASA NTRS1993

Conservative high-order-accurate finite-difference methods for curvilinear grids

Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.

Rai, Man M.↗
NASA NTRS1980

Implicit Finite-Difference Simulations of Three-Dimensional Compressible Flow

An implicit finite-difference procedure for unsteady three-dimensional flow capable of handling arbitrary geometry through the use of general coordinate transformations is described. Viscous effects are optionally incorporated with a "thin-layer" approximation of the Navier-Stokes equations. An implicit approximate factorization technique is employed so that the small grid sizes required for spatial accuracy and viscous resolution do not impose stringent stability limitations. Results obtained from the program include transonic inviscid or viscous solutions about simple body configurations. Comparisons with existing theories and experiments are made. Numerical accuracy and the effect of three-dimensional coordinate singularities are also discussed.

Pulliam, Thomas H.↗
NASA NTRS1978

The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings

Separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances was performed. The steady velocity potential was obtained first from the well known nonlinear equation for steady transonic flow. The unsteady velocity potential was then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. The results of an investigation into the relaxation-solution-instability problem was discussed. Concepts examined include variations in outer boundary conditions, a coordinate transformation so that the boundary condition at infinity may be applied to the outer boundaries of the finite difference region, and overlapping subregions. The general conclusion was that only a full direct solution in which all unknowns are obtained at the same time will avoid the solution instabilities of relaxation. An analysis of the one-dimensional form of the unsteady transonic equation was studied to evaluate errors between exact and finite difference solutions. Pressure distributions were presented for a low-aspect-ratio clipped delta wing at Mach number of 0.9 and for a moderate-aspect-ratio rectangular wing at a Mach number of 0.875.

Weatherill, W. H.↗
DOE OSTI2026

A variational mimetic finite difference method for elliptic interface problems on non-matching polytopal meshes with geometric interface inconsistencies

A new variational mimetic finite difference method for elliptic interface problems with perfect and imperfect thermal contacts on non-matching polytopal meshes with geometric interface inconsistencies is developed and analyzed theoretically and numerically. The method is defined on multiple non-matching submeshes with gaps and overlaps along their interfaces. The discrete equations are derived from a minimization problem for the augmented Dirichlet functional. For a perfect thermal contact, the functional uses a modified mimetic gradient with extended stencil which couples unknowns from both sides of an interface, as well as penalty terms to enforce weak continuity of temperature across the interface. The method leads to a symmetric positive definite matrix for any scaling of the penalty terms. For an imperfect thermal contact, the Dirichlet functional is supplemented with a quadratic jump term along the interface related to the interface thermal resistance. We prove that the method conserves the total heat flux across each interface. In conclusion, the obtained results are verified with numerical experiments showing convergence in the discrete L 2 and L ∞ norms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Rank-Limiting Strategies for Optimizing Tensor-Train Finite-Difference Time-Domain Simulations

We introduce rank-limiting strategies to optimize tensor-train decompositions for three-dimensional finite-difference time-domain simulations using the relationship between the tensors and their specific dimensionality. These include the use of hard caps on the inner ranks of the tensor train decomposition and the use of a group rounding algorithm taking into account all field components simultaneously. Here, several numerical examples are considered to verify the efficacy of the proposed optimization strategies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗