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NASA NTRS1992

Fuzzy simulation in concurrent engineering

Concurrent engineering is becoming a very important practice in manufacturing. A problem in concurrent engineering is the uncertainty associated with the values of the input variables and operating conditions. The problem discussed in this paper concerns the simulation of processes where the raw materials and the operational parameters possess fuzzy characteristics. The processing of fuzzy input information is performed by the vertex method and the commercial simulation packages POLYMATH and GEMS. The examples are presented to illustrate the usefulness of the method in the simulation of chemical engineering processes.

Kraslawski, A.↗

NASA NTRS1992

Instability and transition in three-dimensional supersonic boundary layers

Linear stability of three-dimensional flow past a 5 deg semi-vertex sharp cone at 2 deg incidence in Mach 3.5 free-stream is studied. Computed laminar mean flow profiles along the leeward line of symmetry are highly inflectional and, hence, much more unstable than the profiles along the windward line of symmetry. Accordingly, transition occurs much earlier along the leeward line both in the present calculations (based upon eN approach) and in the experiments of King (1991) performed in NASA Langley 'quiet' tunnel. Boundary-layer transition in the region between the two symmetry lines is influenced by the crossflow generated due to the angle of attack and, as a consequence, it progressively moves upstream with increasing azimuthal angle measured from the windward line. The computed transition front is qualitatively similar to the experimental results, although some differences remain.

Malik, M. R.↗

NASA NTRS1993

A multi-dimensional kinetic-based upwind solver for the Euler equations

A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.

Eppard, W. M.↗

NASA NTRS1950

Theoretical stability derivatives of thin sweptback wings tapered to a point with sweptback or sweptforward trailing edges for a limited range of supersonic speeds

The stability derivatives valid for a limited range of supersonic speeds are presented for a series of sweptback wings tapered to a point with sweptback or sweptforward trailing edges. These wings were derived by modifying the trailing edge of a basic triangular wing so that it coincided with lines drawn from the wing tips to the wing axis of symmetry. The stability derivatives were formulated by using the pressure distributions previously obtained for the basic triangular wing for angle of attack, constant vertical acceleration, sideslip, pitching, rolling, and yawing. Explicit expressions are given for the stability derivatives with respect to principal body axes, and conversion formulas are provided for the transformation to stability axes. The results are limited to Mach numbers for which the wing is contained within the Mach cones springing from the vertex and from the trailing edge of the center section of the wing.

Malvestuto, Frank S , Jr↗

NASA NTRS1953

Laminar boundary layer on cone in supersonic flow at large angle of attack

The laminar boundary-layer flow about a circular cone at large angles of attack to a supersonic stream has been analyzed in the plane of symmetry by a method applicable in general to the flow about conical bodies. At the bottom of the cone, velocity profiles were obtained showing the expected tendency of the boundary layer to become thinner on the under side of the cone as the angle of attack is increased. At the top of the cone, the analysis failed to yield unique solutions except for small angles of attack. Beyond a certain critical angle of attack, boundary-layer flow does not exist in the plane of symmetry, thus indicating separation. This critical angle is presented as a function of Mach number and cone vertex angle.

Moore, Franklin K↗

NASA NTRS1994

Global Geodesy Using GPS Without Fiducial Sites

Global Positioning System, GPS, used to make global geodetic measurements without use of fiducial site coordinates. Baseline lengths and geocentric radii for each site determined without having to fix any site coordinates. Given n globally distributed sites, n baseline lengths and n geocentric radii form polyhedron with each site at vertex and with geocenter at intersection of all radii. Geodetic information derived from structure of polyhedron and its change with time. Approach applied to any global geodetic technique.

Heflin, Michael B.↗

NASA NTRS1993

MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements

MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.

Mitchell, William F.↗

NASA NTRS1993

A multigrid method for steady Euler equations on unstructured adaptive grids

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Riemslagh, Kris↗

NASA NTRS1993

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Cowsar, Lawrence C.↗

NASA NTRS1993

Compressible turbulent flow simulation with a multigrid multiblock method

We describe a multigrid multiblock method for compressible turbulent flow simulations and present results obtained from calculations on a two-element airfoil. A vertex-based spatial discretization method and explicit multistage Runge-Kutta time-stepping are used. The slow convergence of a single grid method makes the multigrid method, which yields a speed factor of about 20, indispensable. The numerical predictions are in good agreement with experimental results. It is shown that the convergence of the multigrid process depends considerably on the ordering of the various loops. If the block loop is put inside the stage loop, the process converges more rapidly than if the block loop is situated outside the stage loop when a three-stage Runge-Kutta method is used. If a five-stage scheme is used, the process does not converge in the latter block ordering. Finally, the process based on the five-stage method is about 60 percent more efficient than with the three-stage method, if the block loop is inside the stage loop.

Kuerten, Hans↗

NASA NTRS1994

Exploiting structure: Introduction and motivation

This annual report summarizes the research activities that were performed from 26 Jun. 1993 to 28 Feb. 1994. We continued to investigate the Robust Stability of Systems where transfer functions or characteristic polynomials are affine multilinear functions of parameters. An approach that differs from 'Stability by Linear Process' and that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty was found for low order, 2-order, and 3-order cases. We proved a crucial theorem, the so-called Face Theorem. Previously, we have proven Kharitonov's Vertex Theorem and the Edge Theorem by Bartlett. The detail of this proof is contained in the Appendix. This Theorem provides a tool to describe the boundary of the image of the affine multilinear function. For SPR design, we have developed some new results. The third objective for this period is to design a controller for IHM by the H-infinity optimization technique. The details are presented in the Appendix.

Xu, Zhong Ling↗

NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on an MIMD (multiple instruction/multiple data stream) parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed, one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the iPSC/860.

Venkatakrishnan, V.↗

NASA NTRS1994

High precision moving magnet chopper for variable operation conditions

In the context of an ESTEC technology contract, a Chopping Mechanism was developed and built with the Far Infrared and Submillimeter Telescope (FIRST) astronomy mission as a reference. The task of the mechanism is to tilt the subreflector of the telescope with an assumed mass of 2.5 kg about one chopping axis at nominal frequencies of up to 5 Hz and chopping angles of up to +/- 11.25 mrad with high efficiency (minimum time for position change). The chopping axis is required to run through the subreflector vertex. After performing a concept trade-off also considering the low operational temperatures in the 130 K range, a design using moving magnet actuators was found to be the favorite one. In addition, a bearing concept using flexible pivots was chosen to meet the high chopping accuracy required. With this approach, a very reliable design could be realized, since the actuators work without any mechanical contact between its moving and fixed parts, and the only bearings used are two flexible pivots supporting the subreflector mounting interface. The mechanism was completely built in titanium in a lightweight and stiff design. The moving magnet actuators were designed to meet the stringent requirements for minimum risetime (time necessary to move from one angular position to a new one) in the 20 msec range. The angular position and the corresponding chopping frequency as well can be arbitrarily selected by the user.

Aicher, Winfried↗

NASA NTRS1994

Equilibrium fluid interface behavior under low- and zero-gravity conditions

We describe here some of our recent mathematical work, which forms a basis for the Interface Configuration Experiment scheduled for USML-2. The work relates to the design of apparatus that exploits microgravity conditions for accurate determination of contact angle. The underlying motivation for the procedures rests on a discontinuous dependence of the capillary free surface interface S on the contact angle gamma, in a cylindrical capillary tube whose section (base) omega contains a protruding corner with opening angle 2 alpha. Specifically, in a gravity-free environment, omega can be chosen so that, for all sufficiently large fluid volume, the height of S is uniquely determined as a (single-valued) function mu(x,y) entirely covering the base; the height mu is bounded over omega uniformly in gamma throughout the range absolute value of (gamma -(pion/2)) less than or equal to alpha, while for absolute value of (gamma - (pion/2)) greater than alpha fluid will necessarily move to the corner and uncover the base, rising to infinity (or falling to negative infinity) at the vertex, regardless of volume. We mention here only that procedures based on the phenomenon promise excellent accuracy when gamma is close pion/2 but may be subject to experimental error when gamma is close to zero (orpion), as the 'singular' part of the domain over which the fluid accumulates (or disappears) when a critical angle gamma theta is crossed then becomes very small and may be difficult to observe. We ignore the trivial case gamma is equal to pion/2 (planar free surface), to simplify the discussion.

Concus, Paul↗

NASA NTRS1994

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

Chang, Sin-Chung↗

NASA NTRS1992

A MIMD implementation of a parallel Euler solver for unstructured grids

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a MIMD (multiple instruction/multiple data stream) parallel computer. Three partitioning strategies for distributing the work load onto the processors are discussed. Issues pertaining to the communication costs are also addressed. We find that the spectral bisection strategy yields the best performance. The performance of this unstructured computation on the Intel iPSC/860 compares very favorably with that on a one-processor CRAY Y-MP/1 and an earlier implementation on the Connection Machine.

Venkatakrishnan, V.↗

NASA NTRS1994

On the ellipticity of the Galactic disk

We investigate two kinds of constraints on the ellipticity of the Galactic disk: local constraints, based on the kinematics of the solar neighborhood (such as the Oort constants, the axis ratio of the velocity ellipsoid, the vertex deviation, and the radial velocity of the local standard of rest relative to the Galactic center), and global constraints (H I tangent point velocities, the velocity fields of distant carbon stars, Cepheids and H II regions, and the kinematics of distant H I). Local and global constraints independently suggest that the Sun lies near the minor axis of the potential of an elliptical Galactic disk, with equipotential axis ratio 0.9. The kinematic data are consistent with a flat rotation curve of constant ellipticity, with a mean rotation speed of 200 km/s. In this model, the present velocity of the local standard of rest is 180 km/s.

Kuijken, Konrad↗

NASA NTRS1994

NCAR CCM2 simulation of the modern Antarctic climate

The National Center for Atmospheric Research (NCAR) community climate model version 2 (CCM2) simulation of the circumpolar trough, surface air temperature, the polar vortex, cloudiness, winds, and atmospheric moisture and energy budgets are examined to validate the model's representation of the present-day Antarctic climate. The results show that the CCM2 can well simulate many important climate features over Antarctica, such as the location and intensity of the circumpolar trough, the coreless winter over the plateau, the intensity and horizontal distribution of the surface inversion, the speed and streamline pattern of the katabatic winds, the double jet stream feature over the southern Indian and Pacific oceans, and the arid climate over the continent. However, there are also some serious errors in the model. Some are due to old problems but some are caused by the new parameterizations in the model. The model errors over high southern latitudes can be summarized as follows: The circumpolar trough, the polar vertex, and the westerlies in midlatitudes are too strong; the semiannual cycle of the circumpolar trough is distorted compared to the observations; the low centers of the circumpolar trough and the troughs in the middle and upper troposphere are shifted eastward by 15 deg - 40 deg longitude; the surface temperatures are too cold over the plateau in summer and over the coastline in winter; the polar tropopause continues to have a cold bias; and the cloudiness is too high over the continent. These biases are induced by two major factors: (1) the cloud optical properties in tropical and middle latitudes, which cause the eastward shift of troughs and surface low centers and the error in the semiannual cycle, and (2) the cold bias of the surface air temperature, which is attributed to the oversimulation of cloudiness over the continent, especially during summer, and the uniform 2-m-thick sea ice. The constant thickness of sea ice suppresses the energy flux from the ocean to the atmosphere and hence reduces the air temperature near the coast during winter. Finally, although the simulated Antarctic climate still suffers these biases, the overall performance of the CCM2 is much better than that of the CCM1-T42. Therefore the CCM2 is good enough to be used for climate change studies, especially over Antarctica.

Tzeng, Ren-Yow↗