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NASA NTRS1992

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Tsang, Leung↗

NASA NTRS1992

Second order closure modeling of turbulent buoyant wall plumes

Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.

Zhu, Gang↗

NASA NTRS1990

Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1

A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.

Haminh, Hieu↗

NASA NTRS1992

Protostellar hydrodynamics: Constructing and testing a spatially and temporally second-order-accurate method. I - Spherical coordinates

Two related numerical schemes for calculating the 3D collapse of protostellar clouds are defined, developed, and checked on a wide variety of test problems in spherical symmetry and multiple dimensions. One scheme is first-order accurate in time (code S), and the other second-order accurate in time (code ST). Through convergence testing, the codes are shown to be second-order accurate in spatial differences. Compared with the previous 3D code, the combination of reduced numerical dissipation through second-order accuracy and of removing the systematic bias toward central concentrations implies that the tendency for fragmentation into binary or multiple protostars should increase. A reinvestigation of fragmentation as a mechanism for forming binary stars is expected to yield an even more favorable evaluation.

Boss, Alan P.↗

NASA NTRS1993

A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems

The finite-volume approach is presently used to obtain a 2D, high-order accurate and basically nonoscillatory shock-capture method whose high-order spatial accuracy is obtained by means of a piecewise polynomial approximation of the solution from cell averages. Attention is given to a high-order spatial operator that is able to both retain high-order accuracy in smooth regions and avoid the oscillations that are associated with interpolations across steep gradients. The operator is extended to hyperbolic systems of equations and curvilinear meshes.

Casper, Jay↗

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 NTRS1990

A high-order compact numerical algorithm for supersonic flows

A dissipative compact two-four scheme (second-order time, fourth-order space) similar to the original MacCormack scheme has been developed, that exhibits greater accuracy than conventional fourth-order schemes. The dissipative nature of the scheme allows it to resolve weak discontinuities without artificial damping. A derivation of the scheme is presented, as well as the theoretical stability characteristics. The temporal scheme is then generalized into a steady-state formulation which achieves fourth-order spatial accuracy at steady-state. Several test problems are used to show that the scheme is more accurate than the traditional MacCormack scheme, and is nearly as efficient.

Carpenter, M. H.↗

NASA NTRS1993

High order accurate solutions of viscous problems

We consider a fourth order extension to MacCormack's scheme. The original extension was fourth order only for the inviscid terms but was second order for the viscous terms. We show how to modify the viscous terms so that the scheme is uniformly fourth order in the spatial derivatives. Applications are given to some boundary layer flows. In addition, for applications to shear flows the effect of the outflow boundary conditions are very important. We compare the accuracy of several of these different boundary conditions for both boundary layer and shear flows. Stretching at the outflow usually increases the oscillations in the numerical solution but the addition of a filtered sponge layer (with or without stretching) reduces such oscillations. The oscillations are generated by insufficient resolution of the shear layer. When the shear layer is sufficiently resolved then oscillations are not generated and there is less of a need for a nonreflecting boundary condition.

Hayder, M. E.↗

NASA NTRS1992

First-order inflation

I discuss the most recent model of inflation. In first-order inflation the inflationary epoch is associated with a first-order phase transition, with the most likely candidate being GUT symmetry breaking. The transition from the false-vacuum inflationary phase to the true-vacuum radiation-dominated phase proceeds through the nucleation and percolation of true-vacuum bubbles. The first successful and simplest model of first-order inflation, extended inflation, is discussed in some detail: evolution of the cosmic-scale factor, reheating, density perturbations, and the production of gravitational waves both from quantum fluctuations and bubble collisions. Particular attention is paid to the most critical issue in any model of first-order inflation: the requirements on the nucleation rate to ensure a graceful transition from the inflationary phase to the radiation-dominated phase.

Turner, Michael S.↗

NASA NTRS1993

Order-sorting filter transmittance measured with an array detector

The simultaneous measurement of the spectrally and spatially variant transmittance of a linear variable order-sorting filter in a manner that closely resembles its conditions of actual use is described. The transmittance of a prototype order-sorting filter was measured in the 400- to 880-nm wavelength region by illuminating it with the output beam of a spectrophotometer while the filter was attached to the front of a 30 x 32 pixel silicon array detector. The filter was designed to be used in the output beam of a grating spectrometer to prevent the dispersal of higher diffracted orders onto an array detector. Areas of the filter that were spatially matched to the corresponding detector pixel column had measured peak transmittances of about 90 percent that were uniform to within +/- 1.5 percent along a given column. Transmittances for incident wavelengths shorter than the desired bandpass, corresponding to the order overlap region, were measured in the 0.003 range. Line spread function measurements made with the array detector indicated no significant beam spreading caused by inserting the filter into the beam.

Heaney, James B.↗

NASA NTRS1993

High order accurate solutions of viscous problems

Hayder, M. Ehtesham↗

NASA NTRS1993

Ordered organic thin films self-assembled from the vapor phase

Organic films self-assembled from a liquid phase, as in Langmuir-Blodgett or adsorption from solution, have received much attention in the past decade as techniques to achieve highly oriented-ordered polymeric thin films. Many organic compounds including some of the same fatty acids have been vapor deposited as well. However, organic pigments and dyes comprise a major class of important materials which have very low solubilities yet excellent thermal stabilities, making them ideally suited for film deposition from the vapor phase. Surprisingly, such molecular systems exhibit a significant propensity to self order, a high sensitivity to deposition parameters, and a range of microstructural forms that cannot be duplicated by the less energetic mechanisms associated with solution adsorption processes. Molecular solids such as heterocyclic polynuclear aromatics are excellent candidates for film formation by vacuum deposition means. Over the past decade, our work and that of others investigating a wide variety of perylene and phthalocyanine derivatives identified five deposition parameters that can significantly affect film morphology, physical microstructure, and type and extent of ordering developed in vacuum and vapor transport grown films. These parameters are substrate temperature, deposition rate, substrate chemistry and epitaxy, ambient gas convective flows, and post deposition annealing. Examples of how each of these conditions manifest themselves in the film structure and ordering, most frequently revealed by scanning electron microscopy, reflection absorption infrared spectroscopy (RAIR), and grazing incidence x-ray diffraction (GIX), are presented.

Debe, M. K.↗

NASA NTRS1994

Weighted graph based ordering techniques for preconditioned conjugate gradient methods

We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.

Clift, Simon S.↗

NASA NTRS1994

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth-order central differences through fast Fourier transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large scale features, such as the total circulation around the roll-up region, are adequately resolved.

Weinan, E.↗

NASA NTRS1994

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

The objective of the present investigation is to assess the effect of the spatial order of accuracy used for the evaluation of the inviscid fluxes on the resolution of higher order quantitites, such as velocity gradients. The viscous terms are computed as second-order accurate with central difference formulas, even though for the explicit part of the algorithm higher order approximations may be used. A viscous/inviscid method is used, and the outer part of the flowfield is computed with the inviscid flow equations. The viscous boundary-layer type flow region close to the body surface is computed with an algebraic eddy viscosity model. Results obtained with the conservative and nonconservative formulations and the viscous/inviscid approach are compared with available experimental data. The effect of grid refinement on the accuracy of the solution is also presented.

Ekaterinaris, J. A.↗

NASA NTRS1996

Chaos in a Fractional Order Chua System

This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.

Lorenzo, Carl F.↗

NASA NTRS1998

Algorithms for Efficient Computation of Transfer Functions for Large Order Flexible Systems

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, still-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open- and closed-loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, the present method was up to two orders of magnitude faster than a traditional method. The present method generally showed good to excellent accuracy throughout the range of test frequencies, while traditional methods gave adequate accuracy for lower frequencies, but generally deteriorated in performance at higher frequencies with worst case errors being many orders of magnitude times the correct values.

Maghami, Peiman G.↗

NASA NTRS1998

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

Sandham, N. D.↗