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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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NASA NTRS1992

A comparison of the impact of two time-differencing schemes on the NASA-GLAS climate model

Evidence is presented of the sensitivity of a GCM to the time-differencing scheme employed when the physical parameterizations and space discretization are not changed. Two-time marching schemes, the leapfrog and the Matsuno schemes, are analyzed and tested on the NASA-Goddard Laboratory for Atmospheric Studies fourth-order GCM in terms of the behavior and stability of two-month-averaged fields. Linear analysis indicates that Rossby waves are slightly accelerated and slightly damped when the Matsuno scheme is utilized and that these effects are scale selective, being smallest for the longest waves.

Pfeffer, Richard L.↗
NASA NTRS1992

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

An investigation of the Runge-Kutta time-stepping, combined with compact difference schemes to solve the unsteady Euler equations, is presented. Initially, a generalized form of a N-step Runge-Kutta technique is derived. By comparing this generalized form with its Taylor's series counterpart, the criteria for the three-step and four-step schemes to be of third- and fourth-order accurate are obtained.

Yu, S. T.↗
NASA NTRS1992

An approach for increasing aeroelastic divergence dynamic pressure of wind-tunnel models

An approach for increasing the aeroelastic divergence dynamic pressure of wind-tunnel model support systems is presented. A study has been conducted to investigate the effect of increased flexibility of the forward portion of balances on the divergence pressure of wind-tunnel models. The study utilized prior divergence analyses completed for various models to be tested in NASA Langley Research Center's National Transonic Facility, the Engineering Analysis Language finite-element analysis code, and an in-house computer program which solves for divergence dynamic pressure utilizing a transfer-matrix method based on fourth-order Runge-Kutta integration. Analytical results for balance flexibility changes versus changes in divergence pressure were obtained and demonstrate that a significant increase in divergence pressure can be obtained from the increased flexibility of the balance's forward portion for many models and their support systems.

Edwards, R. W.↗
NASA NTRS1992

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Yu, Sheng-Tao↗
NASA NTRS1993

Thermodynamic data for fifty reference elements

This report is a compilation of thermodynamic functions of 50 elements in their standard reference state. The functions are C(sub p)(sup 0), (H(sup 0)(T) - H(sup 0)(0)), S(sup 0)(T), and -(G(sup 0)(T) - H(sup 0)(O)) for the elements Ag, Al, Ar, B, Ba, Be, Br2, C, Ca, Cd, Cl2, Co, Cr, Cs, Cu, F2, Fe, Ge, H2, He, Hg, I2, K, Kr, Li, Mg, Mn, Mo, N2, Na, Nb, Ne, Ni, O2, P, Pb, Rb, S, Si, Sn, Sr, Ta, Th, Ti, U, V, W, Xe, Zn, and Zr. Deuterium D2 and electron gas e(sup -) are also included. The data are tabulated as functions of temperature as well as given in the form of least-squares coefficients for two functional forms for C(sub p)(sup 0) with integration constants for enthalpy and entropy. One functional form for C(sub p)(sup 0) is a fourth-order polynomial and the other has two additional terms, one with T(exp -1) and the other with T(exp -2). The gases Ar, D2, e(sup -), H2, He, Kr, N2, Ne, O2, and Xe are tabulated for temperatures from 100 to 20,000 K. The remaining gases Cl2 and F2 are tabulated from 100 to 6000 K and 1000 to 6000 K. The second functional form for C(sub p)(sup 0) has an additional interval from 6000 to 20,000 K for the gases tabulated to 20,000 K. The fits are constrained so that the match at the common temperature endpoints. The temperature ranges for the condensed species vary with range of the data, phase changes, and shapes of the C(sub p)(sup 0) curves.

Mcbride, Bonnie J.↗
NASA NTRS1993

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

Carpenter, Mark H.↗
NASA NTRS1993

Computational solution of the defect stream-function equation for nonequilibrium turbulent boundary layers

The derivation of the accurate, second-order, almost linear, approximate equation governing the defect stream function for nonequilibrium compressible turbulent boundary layers is reviewed. The similarity of this equation to the heat conduction equation is exploited in the development of an unconditionally stable, tridiagonal computational method which is second-order accurate in the marching direction and fourth-order accurate in the surface-normal direction. Results compare well with experimental data. Nonlinear effects are shown to be small. This two-dimensional method is simple and has been implemented on a programmable calculator.

Barnwell, Richard W.↗
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 NTRS1991

Current status of conformal Weyl gravity

The status of fourth-order conformal Weyl gravity theory as an alternative theory of gravity to standard second-order Einstein theory is briefly reviewed. The questions remaining open are addressed.

Mannheim, Philip D.↗
NASA NTRS1993

Direct calculations of waves in fluid flows using a high-order compact difference scheme

The solution of the unsteady Euler equations by a sixth-order compact difference scheme combined with a fourth-order Runge-Kutta method is investigated. Closed-form expressions for the amplification factors and their corresponding dispersion correlations are obtained by Fourier analysis of the fully discretized, two-dimensional Euler equations, and the numerical dissipation, dispersion, and anisotropic effects are assessed. It is found that the CFL limit for stable calculations is about 0.8. For a CFL number equal to 0.6, the smallest wavelength which is resolved without numerical damping is about 6 to 8 grid nodes. For phase speeds corresponding to acoustic waves, the corresponding time period is resolved by about 200 to 300 time steps. Three numerical examples of waves in compressible flow are included.

Yu, Sheng-Tao↗
NASA NTRS1993

High order finite difference and multigrid methods for spatially evolving instability in a planar channel

The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.

Liu, C.↗
NASA NTRS1993

Sensitivity derivatives for advanced CFD algorithm and viscous modelling parameters via automatic differentiation

The computational technique of automatic differentiation (AD) is applied to a three-dimensional thin-layer Navier-Stokes multigrid flow solver to assess the feasibility and computational impact of obtaining exact sensitivity derivatives typical of those needed for sensitivity analyses. Calculations are performed for an ONERA M6 wing in transonic flow with both the Baldwin-Lomax and Johnson-King turbulence models. The wing lift, drag, and pitching moment coefficients are differentiated with respect to two different groups of input parameters. The first group consists of the second- and fourth-order damping coefficients of the computational algorithm, whereas the second group consists of two parameters in the viscous turbulent flow physics modelling. Results obtained via AD are compared, for both accuracy and computational efficiency with the results obtained with divided differences (DD). The AD results are accurate, extremely simple to obtain, and show significant computational advantage over those obtained by DD for some cases.

Green, Lawrence L.↗
NASA NTRS1993

Modeling of spray droplets deformation and breakup

A droplet deformation and breakup (DDB) model is proposed to study shear-type mechanism of spray droplets in pure extentional flows. A numerical solution of the DDB model equation is obtained using a fourth-order Runge-Kutta initial-value solver. The predictions of the DDB model as well as semianalytical and the Taylor analogy models are compared with the experimental data (Krzeczkowski, 1980) for shear breakup, which depict the dimensionless deformation of the drop vs dimensionless time.

Ibrahim, E. A.↗
NASA NTRS1993

A comparison of two formulations for high-order accurate essentially non-oscillatory schemes

The finite-volume and finite-difference implementations of high-order accurate essentially nonoscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

Casper, J.↗
NASA NTRS1993

Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements

The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.

Liu, C.↗
NASA NTRS1993

Effects of spatial order of accuracy on the computation of vortical flowfields

The effect of the order-of-accuracy, used for the spatial discretization, on the resolution of the leading edge vortices over sharp-edged delta wings is investigated. The flowfield is computed using a viscous/inviscid zonal approach. The viscous flow in the vicinity of the wing is computed using the conservative formulation of the compressible, thin-layer Navier-Stokes equations. The leeward-side vortical flowfield and the other flow regions away from the surface are computed as inviscid. The time integration is performed with both an explicit fourth-order Runge-Kutta scheme and an implicit, factorized, iterative scheme. High-order-accurate inviscid fluxes are computed using both a conservative and a non-conservative (primitive variable) formulation. The nonlinear, inviscid terms of the primitive variable form of the governing equations are evaluated with a finite-difference numerical scheme based on the sign of the eigenvalues. High-order, upwind-biased, finite difference formulas are used to evaluate the derivatives of the nonlinear convective terms. Computed results are compared with available experimental data, and comparisons of the flowfield in the vicinity of the vortex cores are presented.

Ekaterinaris, J. A.↗
NASA NTRS1993

Some aspects of high-order numerical solutions of the linear convection equation with forced boundary conditions

A six-stage low-storage Runge-Kutta time-marching method is presented and shown to be an efficient method for use with high-accuracy spatial difference operators for wave propagation problems. The accuracy of the method for inhomogeneous ordinary differential equations is demonstrated through numerical solutions of the linear convection equation with forced boundary conditions. Numerical experiments are presented simulating a sine wave and a Gaussian pulse propagating into and through the domain. For practical levels of mesh refinement corresponding to roughly ten points per wavelength, the six-stage Runge-Kutta method is more accurate than the popular fourth-order Runge-Kutta method. Further numerical experiments are presented which show that the numerical boundary scheme at an inflow boundary can be a significant source of error when high-accuracy spatial discretizations are used.

Zingg, D. W.↗
NASA NTRS1991

Observational and modeling study of the maintenance of short-term subtropical wind maxima in the Southern Hemisphere during SOP-1, FGGE

The findings of the earlier observational work of Hurrel and Vincent (1990) are substantiated using a recent version of the Goddard Laboratory for Atmospheres fourth-order general circulation model. The observed heating and subtropical zonal flow structure over the South Pacific is reproduced by a control integration with full model physics, for the period of 6-20 January 1979. A subtropical westerly maximum observed over the central South Pacific is found to be highly correlated to enhancements of poleward-moving divergent outflow from tropical heat sources. The divergent meridional flow accounted for much of the total ageostrophic meridional wind in the Southern Hemisphere subtropics, and, consequently, resulted in strong Coriolis accelerations in the entrance regions westerly maxima.

Hurrell, James W.↗