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NASA NTRS1991

A comparison of three time-dependent wave packet methods for calculating electron-atom elastic scattering cross sections

Three time-dependent wave packet methods for performing elastic scattering calculations from screened Coulomb potentials are compared. The three methods are the time-dependent amplitude density method (TDADM), a Cayley-transform method (CTM), and the Chebyshev propagation method of Tal-Ezer and Kosloff. Both the TDADM and the CTM are based on a time-dependent integral equation for the wave function. In the first, the time-dependent amplitude density is propagated, while in the other two, the wave function is propagated. As a numerical example, phase shifts and cross sections are calculated using a screened Coulomb, Yukawa type potential over the range 200-1000 eV. It is found that, in most cases, all three methods yield comparable accuracy and are about equally efficient computationally. However for l = 0, where the Coulomb well is not screened by the centrifugal potential, the TDADM requires smaller grid spacings to maintain accuracy.

Judson, Richard S.↗

NASA NTRS1991

Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime

Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.

Malevsky, A. V.↗

NASA NTRS1991

Discussion summary: Fictitious domain methods

Fictitious Domain methods are constructed in the following manner: Suppose a partial differential equation is to be solved on an open bounded set, Omega, in 2-D or 3-D. Let R be a rectangle domain containing the closure of Omega. The partial differential equation is first solved on R. Using the solution on R, the solution of the equation on Omega is then recovered by some procedure. The advantage of the fictitious domain method is that in many cases the solution of a partial differential equation on a rectangular region is easier to compute than on a nonrectangular region. Fictitious domain methods for solving elliptic PDEs on general regions are also very efficient when used on a parallel computer. The reason is that one can use the many domain decomposition methods that are available for solving the PDE on the fictitious rectangular region. The discussion on fictitious domain methods began with a talk by R. Glowinski in which he gave some examples of a variational approach to ficititious domain methods for solving the Helmholtz and Navier-Stokes equations.

Glowinski, Rowland↗

NASA NTRS1991

The research progress on Hodograph Method of aerodynamic design at Tsinghua University

Progress in the use of the Hodograph method of aerodynamic design is discussed. It was found that there are some restricted conditions in the application of Hodograph design to transonic turbine and compressor cascades. The Hodograph method is suitable not only to the transonic turbine cascade but also to the transonic compressor cascade. The three dimensional Hodograph method will be developed after obtaining the basic equation for the three dimensional Hodograph method. As an example of the Hodograph method, the use of the method to design a transonic turbine and compressor cascade is discussed.

Chen, Zuoyi↗

NASA NTRS1991

Optimal least-squares finite element method for elliptic problems

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Jiang, Bo-Nan↗

NASA NTRS1991

Simplified computational methods for elastic and elastic-plastic fracture problems

This paper presents an overview of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fracture: (i) analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids (the crack-plane being at an arbitrary angle to the axis of transverse isotropy), with crack-faces being subjected to arbitrary tractions; (ii) finite-element or boundary-element alternating methods for two- and three-dimensional crack problems; (iii) a "direct-stiffness" method for stiffened panels with flexible fasteners and with multiple cracks, using the alternating method; (iv) multiplesite-damage near a row of fastener holes; (v) analysis of cracks with bonded repair patches; (vi) methods for generation of weight-functions for 2- and 3-D crack problems, and (vii) domain-integral methods for elastic-plastic or inelastic crack mechanics.

Aging Aircraft↗

NASA NTRS1992

A boundary element alternating method for two-dimensional mixed-mode fracture problems

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

Raju, I. S.↗

NASA NTRS1992

Comparison between the PISO algorithm and preconditioning methods for compressible flow

Two widely used family of algorithms, pressure-based and density-based methods, have been developed for computational fluid dynamics (CFD) problems over the years. Pressure-based methods (such as SIMPLE and PISO) use a Poisson-like equation for updating pressure instead of the continuity equation, while density-based methods use the continuity equation to update density (an equation of state is used to provide density in pressure based schemes and pressure in density based schemes). Pressure-based methods were developed originally for incompressible flows at low Reynolds numbers and were then extended to high Reynolds numbers and compressible applications. On the other hand, density based methods were originally developed for transonic flows and have been extended down to low Mach numbers through the use of preconditioning techniques. We compare these two very different approaches to solving the Navier-Stokes equations in order to gain an understanding of their similarities and differences. Specifically, we consider the PISO scheme as a representative pressure-based method and contrast it with a recently developed preconditioning scheme. We also compare the relative performance of the PISO algorithm with a Euler implicit algorithm that is employed to solve the preconditioned equations by means of a vector stability analysis.

Merkle, Charles L.↗

NASA NTRS1992

Application of vector-valued rational approximations to the matrix eigenvalue problem and connections with Krylov subspace methods

Let F(z) be a vectored-valued function F: C approaches C sup N, which is analytic at z=0 and meromorphic in a neighborhood of z=0, and let its Maclaurin series be given. We use vector-valued rational approximation procedures for F(z) that are based on its Maclaurin series in conjunction with power iterations to develop bona fide generalizations of the power method for an arbitrary N X N matrix that may be diagonalizable or not. These generalizations can be used to obtain simultaneously several of the largest distinct eigenvalues and the corresponding invariant subspaces, and present a detailed convergence theory for them. In addition, it is shown that the generalized power methods of this work are equivalent to some Krylov subspace methods, among them the methods of Arnoldi and Lanczos. Thus, the theory provides a set of completely new results and constructions for these Krylov subspace methods. This theory suggests at the same time a new mode of usage for these Krylov subspace methods that were observed to possess computational advantages over their common mode of usage.

Sidi, Avram↗

NASA NTRS1992

A spectral overlay method for dissimilar materials

The spectral overlay method is applied to examine the stress distribution along the interface between the two different materials. The essential feature of the spectral overlay method is that the high resolution of localized steep gradients can be achieved by overlaying a spectral interpolant on a standard finite element mesh. In order to evaluate this method and compare it with conventional finite element method, a test problem with high gradients in Poisson equation has been devised. The results show that this method is very powerful in capturing the shape of the gradient field and its peak value. Solutions for two problems with interfaces between dissimilar materials are then given to illustrate the effectiveness of this method.

Belytschko, T.↗

NASA NTRS1992

Paneling methods with vorticity effects and corrections for nonlinear compressibility

Supersonic panel methods and axisymmetric body-modeling singularity methods are presently combined with corrections for nonlinear flow phenomena to a complete missile, its airbreathing inlets, and wing-body combinations. The computer code LRCDM2 is used as an illustrative example of the methods in question. Attention is given to a preliminary method which employs panels to estimate additive drag and lift acting on supersonic rectangular inlets, as well as to the method used to correct off-body flowfields for the presence of a shock. Examples of missile applications of these methods with the appropriate nonlinear corrections are presented.

Dillenius, Marnix F. E.↗

NASA NTRS1989

A least-squares finite element method for incompressible Navier-Stokes problem

Most finite element schemes for solving the Navier-Stokes equations can be categorized into the Galerkin mixed method and the penalty method. The mixed method leads to a saddle-point problem. In order to guarantee the existence of a solution, the combination of velocity and pressure interpolations requires satisfaction of the Ladyzhenskaya Babuska Brezzi (LBB) consistency condition which precludes the use of equal order interpolations and many seemingly natural pairs of velocity and pressure elements. In a previous paper a least-squares finite element method based on the first order velocity-pressure-vorticity formulation for the Stokes problem was proposed. This method leads to a minimization problem. The choice of combination of elements is thus not subject to the LBB condition. The numerical experiments exhibit the optimal rate of convergence for all variables with equal order interpolations. A theoretical error analysis supports the numerical results. In this paper the least-squares finite element method is extended to solving the incompressible Navier-Stokes problem.

Jiang, Bonan↗

NASA NTRS1990

Microbiological methods for the water recovery systems test, revision 1.1

Current microbiological parameters specified to verify microbiological quality of Space Station Freedom water quality include the enumeration of total bacteria, anaerobes, aerobes, yeasts and molds, enteric bacteria, gram positives, gram negatives, and E. coli. In addition, other parameters have been identified as necessary to support the Water Recovery Test activities to be conducted at the NASA/MSFC later this year. These other parameters include aerotolerant eutrophic mesophiles, legionellae, and an additional method for heterotrophic bacteria. If inter-laboratory data are to be compared to evaluate quality, analytical methods must be eliminated as a variable. Therefore, each participating laboratory must utilize the same analytical methods and procedures. Without this standardization, data can be neither compared nor validated between laboratories. Multiple laboratory participation represents a conservative approach to insure quality and completeness of data. Invariably, sample loss will occur in transport and analyses. Natural variance is a reality on any test of this magnitude and is further enhanced because biological entities, capable of growth and death, are specific parameters of interest. The large variation due to the participation of human test subjects has been noted with previous testing. The resultant data might be dismissed as 'out of control' unless intra-laboratory control is included as part of the method or if participating laboratories are not available for verification. The purpose of this document is to provide standardized laboratory procedures for the enumeration of certain microorganisms in water and wastewater specific to the water recovery systems test. The document consists of ten separate cultural methods and one direct count procedure. It is not intended nor is it implied to be a complete microbiological methods manual.

Rhoads, Tim↗

NASA NTRS1992

Improved astigmatic focus error detection method

All easy-to-implement focus- and track-error detection methods presently used in magneto-optical (MO) disk drives using pre-grooved media suffer from a side effect known as feedthrough. Feedthrough is the unwanted focus error signal (FES) produced when the optical head is seeking a new track, and light refracted from the pre-grooved disk produces an erroneous FES. Some focus and track-error detection methods are more resistant to feedthrough, but tend to be complicated and/or difficult to keep in alignment as a result of environmental insults. The astigmatic focus/push-pull tracking method is an elegant, easy-to-align focus- and track-error detection method. Unfortunately, it is also highly susceptible to feedthrough when astigmatism is present, with the worst effects caused by astigmatism oriented such that the tangential and sagittal foci are at 45 deg to the track direction. This disclosure outlines a method to nearly completely eliminate the worst-case form of feedthrough due to astigmatism oriented 45 deg to the track direction. Feedthrough due to other primary aberrations is not improved, but performance is identical to the unimproved astigmatic method.

Bernacki, Bruce E.↗

NASA NTRS1993

Advanced display object selection methods for enhancing user-computer productivity

The User-Interface Technology Branch at NCCOSC RDT&E Division has been conducting a series of studies to address the suitability of commercial off-the-shelf (COTS) graphic user-interface (GUI) methods for efficiency and performance in critical naval combat systems. This paper presents an advanced selection algorithm and method developed to increase user performance when making selections on tactical displays. The method has also been applied with considerable success to a variety of cursor and pointing tasks. Typical GUI's allow user selection by: (1) moving a cursor with a pointing device such as a mouse, trackball, joystick, touchscreen; and (2) placing the cursor on the object. Examples of GUI objects are the buttons, icons, folders, scroll bars, etc. used in many personal computer and workstation applications. This paper presents an improved method of selection and the theoretical basis for the significant performance gains achieved with various input devices tested. The method is applicable to all GUI styles and display sizes, and is particularly useful for selections on small screens such as notebook computers. Considering the amount of work-hours spent pointing and clicking across all styles of available graphic user-interfaces, the cost/benefit in applying this method to graphic user-interfaces is substantial, with the potential for increasing productivity across thousands of users and applications.

Osga, Glenn A.↗

NASA NTRS1993

A class of hybrid finite element methods for electromagnetics: A review

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.

Volakis, J. L.↗

NASA NTRS1992

A brief description of a new numerical framework for solving conservation laws: The method of space-time conservation element and solution element

A new numerical method for solving conservation laws is being developed. It differs substantially from the well established methods, i.e., finite difference, finite volume, finite element, and spectral methods, in both concept and methodology. It is much simpler than a typical high resolution method. No flux limiter or any technique related to characteristics is involved. No artificial viscosity or smoothing is introduced, and no moving mesh is used. Yet this method is capable of generating highly accurate shock tube solutions. The slight numerical overshoot and/or oscillations generated can be removed if a simple averaging formula initially used is replaced by a weighted formula. This modification has little effect on other parts of the solution. Because of its simplicity, generalization of this new method for multi-dimensional problems is straightforward.

Chang, Sin-Chung↗

NASA NTRS1992

Calculation of fully three-dimensional separated flow with an unsteady viscous-inviscid interaction method

Three previous papers have shown that the viscous inviscid numerical methods were capable of calculating separated turbulent flows. The 'Semi-inverse method' and the models of the first author allow the computation of massive separations, stalled flows, and shock wave-boundary layer interactions, in two-dimensional or quasi-three-dimensional conditions, from low speeds to supersonic speeds. The 'Semi-implicit' method for time-consistent coupling allows for the computation of time-accurate transonic separated flow and buffer computations in two-dimensions. The present paper shows that the viscous-inviscid interaction approach is also able to compute the fully three-dimensional flow separation phenomena. The method is based on a thin-layer approximation of the theory of 'Defect-Formulation' that provides the viscous-inviscid splitting of the Navier-Stokes equations. A parametric analytical modelling of the 3D-turbulent velocity profiles is involved. Numerically, the 3D-velocity profiles are discretized in the normal z-direction and driven by parametric integral 3D-equations in direct or inverse modes in the x-direction. The viscous-inviscid coupling is fully 3D and solved the time-consistency problem with an extension of the 'Semi-implicit' method previously suggested in two-dimensions. A 3D inviscid subroutine with TSP approximation is used. Results are obtained for transonic steady flows over wings with shock-induced transonic separation. The method provides results for highly three-dimensional flow separations, such as induced by a three-dimensional through at the wall of a flat plate. The 3D viscous-inviscid coupling and the 3D model of the velocity field provide three-dimensional instantaneous skin-friction lines whose patterns exhibit the same complex topology as Navier-Stokes solvers, with foci, nodes, and saddle-points.

Leballeur, J. C.↗