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NASA NTRS1981

Multigrid method with weighted mean scheme

Multigrid algorithms based on the weighted mean scheme are developed for the solution of the two dimensional incompressible Navier-Stokes equations. They are applied to two typical problems encountered in engineering applications, namely, the convection diffusion problem of the Benard convection cell, and the driven cavity problem. An analysis of the smoothing rates and stability is given. The efficiency of the multigrid method is investigated.

Lustman, L. R.↗

NASA NTRS1989

Adaptive implicit-explicit methods for flow problems

Studies on the adaptive implicit-explicit (AIE) method for large-scale problems are presented. The AIE method is based on dynamic grouping of the elements into the implicit and explicit subsets as dictated by the element level stability and accuracy considerations. The method has been applied to various flow problems including the incompressible flow and convection-diffusion problems, and it has been demonstrated that substantial savings in CPU time and memory can be achieved.

Liou, J.↗

NASA NTRS1992

The appliation of potential CFD methods to helicopter hover flows

Fixed-wing code development is now aimed primarily at the solution of problems dominated by separation--based on the assumptions that the ability to solve such problems implies the ability to solve all other problems and that present inviscid method are already adequate for most other problems. Neither of the above assumptions are correct for rotary wing problems. This is because of the unique and overriding importance of wake modeling to rotor problems and also due to the well-known numerical diffusion problems which convectional Eulerian Computational fluid dynamics (CFD) method encounter when called on to convect strong vortical regions for long distances. The need for accurate wake analyses is probably the most fundamental difference between rotory and fixed-wing aerodynamics. In addition, rotary wing complexity requires a much more intimate relationship between test and analysis than is common in fixed-wing work. With these issues in mind, this paper will review some of our recent experience in using a unique-Eulerian-Lagrangian Computational fluid dynamics (CFC) method for the solution of a critical rotor-wake problem--the prediction of hover performance.

Caradonna, F. X.↗

NASA NTRS1996

MGLab: An Interactive Multigrid Environment

MGLab is a set of Matlab functions that defines an interactive environment for experimenting with multigrid algorithms. The package solves two-dimensional elliptic partial differential equations discretized using either finite differences or finite volumes, depending on the problem. Built-in problems include the Poisson equation, the Helmholtz equation, a convection-diffusion problem, and a discontinuous coefficient problem. A number of parameters controlling the multigrid V-cycle can be set using a point-and-click mechanism. The menu-based user interface also allows a choice of several Krylov subspace methods, including CG, GMRES(k), and Bi-CGSTAB, which can be used either as stand-alone solvers or as multigrid acceleration schemes. The package exploits Matlab's visualization and sparse matrix features and has been structured to be easily extensible.

Bordner, James↗

NASA NTRS1980

Iterative solutions for one-dimensional diffusion with time varying surface composition and composition-dependent diffusion coefficient

Solutions are given for one-dimensional diffusion problems with a time varying surface composition and also a composition dependent diffusion coefficient. The most general solution does not require special mathematical functions to fit the variation in surface composition or D(C). In another solution, a series expansion may be used to fit the time dependent surface concentration. These solutions make use of iterative calculations that converge rapidly and are highly stable. Computer times are much shorter than that required for finite difference calculations and can efficiently make use of interactive graphics terminals. Existing gas carburization data were used to provide an illustration of an iterative approach with a time varying carbon composition at the free surface.

Chow, M.↗

NASA NTRS1980

Single-, two-, and three-phase binary-alloy systems

Series of three computer programs solves one-dimensional transient diffusion problems in single-and multiphase binary-alloy systems. Accurate understanding of diffusion process in binary-alloy system is important for development of metal matrix composites, some protective coatings, and thin-film technology.

Tenney, D. R.↗

NASA NTRS2017

The Diffuse Interstellar Bands: Solving a Century Old Problem

The Diffuse Interstellar Bands (DIBs) are a set of apporoximately 500 absorption bands that are seen in the spectra of reddened stars (i.e., stars obscured by the presence of interstellar clouds in their line of sight). The first DIBs were detected in the visible over a century ago. Diffuse Interstellar Bands are now detected from the near ultraviolet to the near infrared in the spectra of reddened stars spanning a variety of interstellar environments in our local, and in other galaxies. Although DIB carriers are a significant part of the interstellar chemical inventory as they account for a noticeable fraction of the interstellar extinction, the nature of their carriers is still unknown over a century after the detection of the first bands. DIB carriers are stable and ubiquitous in a broad variety of interstellar environments and play a unique role in interstellar physics and chemistry. It has long been realized that the solving of the DIB problem requires a strong synergy between astronomical observations, laboratory astrophysics and astrochemistry, quantum chemistry calculations and astrophysical modeling of line-of-sights. In this review, we'll present and discuss the current state of this perplexing problem. We'll review the progress and the failures that have been encountered in the long quest for the identification of the carriers of these ubiquitous interstellar bands.

Molecules in Space↗

NASA NTRS1975

On upstream blocking in a viscous diffusive stratified flow

The effect of diffusion of specie upon the flow about a transverse flat plate moving horizontally in a viscous stratified medium is considered. Asymptotic expansions are used to define a parameter regime where a viscous-diffusive-buoyancy balance is dominant. The solution, expressed in terms of an inverse Fourier transform, is numerically integrated. The results show that, as in the non-diffusive problem, a region of closed streamlines exists ahead of the body. However, unlike the case where diffusion is neglected, the density field within this recirculating region is uniquely determined and found to be statically stable. It is also found that varying the relative amount of diffusion affects not only the density distribution, but the velocity profile as well, indicating a strong coupling between the vorticity and specie equation.

Koop, C. G.↗

NASA NTRS1991

Domain-decomposed preconditionings for transport operators

The performance was tested of five different interface preconditionings for domain decomposed convection diffusion problems, including a novel one known as the spectral probe, while varying mesh parameters, Reynolds number, ratio of subdomain diffusion coefficients, and domain aspect ratio. The preconditioners are representative of the range of practically computable possibilities that have appeared in the domain decomposition literature for the treatment of nonoverlapping subdomains. It is shown that through a large number of numerical examples that no single preconditioner can be considered uniformly superior or uniformly inferior to the rest, but that knowledge of particulars, including the shape and strength of the convection, is important in selecting among them in a given problem.

Chan, Tony F.↗

NASA NTRS1972

Variance reduction in Monte Carlo analysis of rarefied gas diffusion.

The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.

Perlmutter, M.↗

NASA NTRS1977

The crack-contact and the free-end problem for a strip under residual stress

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact where the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual-stress profiles. In the limiting case of the crack's crossing the entire plate thickness, the problem becomes a stressfree end problem for a semiinfinite strip under a given residual-stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semiinfinite strip are of special interest. For two typical residual-stress states the solution is obtained, and some numerical results are given.

Bakioglu, M.↗

NASA NTRS1976

The Crack-contact and the Free End Problem for a Strip Under Residual Stress

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact problem in which the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual stress profiles. In the limiting case of the crack crossing the entire plate thickness, the problem becomes a stress-free end problem for a semi-infinite strip under a given residual stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semi-infinite strip are of special interest. For two typical residual stress states the solution is obtained, and some numerical results are given.

Bakioglu, M.↗

NASA NTRS1988

On the application of pseudo-spectral FFT technique to non-periodic problems

The reduction-to-periodicity method using the pseudo-spectral Fast Fourier Transform (FFT) technique is applied to the solution of nonperiodic problems including the two-dimensional Navier-Stokes equations. The accuracy of the method is demonstrated by calculating derivatives of given functions, one- and two-dimensional convective-diffusive problems, and by comparing the relative errors due to the FFT method with seocnd order Finite Difference Methods (FDM). Finally, the two-dimensional Navier-Stokes equations are solved by a fractional step procedure using both the FFT and the FDM methods for the driven cavity flow and the backward facing step problems. Comparisons of these solutions provide a realistic assessment of the FFT method indicating its range of applicability.

Biringen, S.↗

NASA NTRS1991

Comptonization of gamma rays by cold electrons

An analytic method is developed for calculating the emergent spectrum of gamma-rays and X-rays scattered in a homogeneous medium with low-temperature electrons. The Klein-Nishina corrections of the scattering cross section and absorption processes are taken in account. The wavelength relaxation and the spatial diffusion problems are solved separately, and the emergent spectrum is calculated by convolving the evolution function of the spectrum in an infinite medium with the photon luminosity resulting from the spatial diffusion in a finite sphere. The analytic results are compared with that of Monte Carlo calculations and it is concluded that the analytic result is quite accurate.

Xu, Yueming↗

NASA NTRS1978

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 X 10 to the minus 7th power squared cm per sec + or - 30 percent in 45 percent potassium hydroxide and 1.4 x 10 to the minus 7 squared cm per sec + or - 25 percent in 40 percent sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite size chambers. Details and discussion of the experimental method are also given.

May, C. E.↗

NASA NTRS1978

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 x 10 to the -7th power sq cm/sec + or - 30% in 45% potassium hydroxide and 1.4 x 10 to the -7th power sq cm/sec + or - 25% in 40% sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half-cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite-size chambers. Details and discussion of the experimental method are also given.

May, C. E.↗

NASA NTRS1995

Spectral ordering techniques for incomplete LU preconditoners for CG methods

The effectiveness of an incomplete LU (ILU) factorization as a preconditioner for the conjugate gradient method can be highly dependent on the ordering of the matrix rows during its creation. Detailed justification for two heuristics commonly used in matrix ordering for anisotropic problems is given. The bandwidth reduction and weak connection following heuristics are implemented through an ordering method based on eigenvector computations. This spectral ordering is shown to be a good representation of the heuristics. Analysis and test cases in two and three dimensional diffusion problems demonstrate when ordering is important, and when an ILU decomposition will be ordering insensitive. The applicability of the heuristics is thus evaluated and placed on a more rigorous footing.

Clift, Simon S.↗

NASA NTRS1987

Magnetic braking in weakly ionized media

The combined magnetic braking-ambipolar diffusion problem in weakly ionized, rigidly rotating disks is studied. An analytical solution is presented for a disk whose angular velocity and magnetic yield vectors are aligned with the symmetry axis, illustrating the effects of the relative azimuthal drift of neutrals and ions. The effects of radial drift are added, commenting on the ratio of the characteristic ambipolar diffusion and magnetic braking time scales in high-mass and low-mass disks. A numerical calculation is used to show the combined action of these two processes.

Konigl, Arieh↗