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At least 289 records · Page 16

A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations

A scheme of solving the two-dimensional Euler equations is developed. The scheme is genuinely two-dimensional. At each iteration, the data are locally decomposed into four variables, allowing convection in appropriate directions. This is done via a cell-vertex scheme with a downwind-weighted distribution step. The scheme is conservative and third-order accurate in space. The derivation and stability analysis of the scheme for the convection equation, and the derivation of the extension to the Euler equations are given. Preconditioning techniques based on local values of the convection speeds are discussed. The scheme for the Euler equations is applied to two channel-flow problems. It is shown to converge rapidly to a solution that agrees well with that of a third-order upwind solver.

Powell, Kenneth G.↗

Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

Design of optimally smoothing multi-stage schemes for the Euler equations

In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-frequencies for a given spatial-differencing operator. The objective of the method is to design schemes that combine well with multi-grid acceleration. The schemes are tested on a nonlinear scalar equation, and compared to Runge-Kutta schemes with the maximum stable time-step. The optimally smoothing schemes perform better than the Runge-Kutta schemes, even on a single grid. The analysis is extended to the Euler equations in one space-dimension by use of 'characteristic time-stepping', which preconditions the equations, removing stiffness due to variations among characteristic speeds. Convergence rates independent of the number of cells in the finest grid are achieved for transonic flow with and without a shock. Characteristic time-stepping is shown to be preferable to local time-stepping, although use of the optimally damping schemes appears to enhance the performance of local time-stepping. The extension of the analysis to the two-dimensional Euler equations is hampered by the lack of a model for characteristic time-stepping in two dimensions. Some results for local time-stepping are presented.

Van Leer, Bram↗

Convergence acceleration of viscous and inviscid hypersonic flow calculations

The convergence of inviscid and viscous hypersonic flow calculations using a two-dimensional flux-splitting code is accelerated by applying a Richardson-type overrelaxation method. Successful results are presented for various cases; and a 50 percent savings in computer time is usually achieved. An analytical formula for the overrelaxation factor is derived, and the performance of this scheme is confirmed numerically. Moreover, application of this overrelaxation scheme produces a favorable preconditioning for Wynn's epsilon-algorithm. Both techniques have been extended to viscous three-dimensional flows and applied to accelerate the convergence of the compressible Navier-Stokes code. A savings of 40 percent in computer time is achieved in this case.

Cheer, A.↗

The stratospheric major warming of early December 1987

The NMC observations of temperature and geopotential carried out during the stratospheric major warming event of early December 1987 are analyzed. The December 1987 warming event displayed features typical of other major warmings, including vortex displacement, erosion, and splitting and, as such, was the earliest major warming yet observed in the Northern Hemisphere winter. The December 1987 major warming was unusual in that it took place during the (deep) westerly phase of the equatorial quasi-biennial oscillation and was not preceded by any significant preconditioning of the extratropical vortex. It is suggested that this unusually early major warming was mainly attributable to an anomalously large tropospheric forcing.

Baldwin, Mark P.↗

Concurrent Finite-Element Analysis On Hypercube Computers

Improved approach to execution of finite-element codes on hypercube and similar concurrent data processors increases efficiency of computation for many different types of problems. Based on flexible general model of computation on, and communication among, large-node parallel processors. Hybrid combining direct methods within subdomains and preconditioned-conjugate-gradient (PCG) iteration on remaining boundary system to obtain method of solution both robust and efficient. Preserves general structure and function of conventional sequential finite-element-method software. Generalized to both distributed- and shared-memory multicomputers, eliminating degree of machine specificity restricting general usefulness.

Lyzenga, G. A.↗

Gravity and animal embryos

Out of more than 4,500 rat hours in space there was only one experimental attempt (Cosmos 1129) at mating with an apparent absence of fertilization, implantation and subsequent development to term and partuition. Portions of this process were successfully flown, however, including the major portion of organogenesis in the rat (Cosmos 1524). These observations show that the cellular and molecular events underlying morphogenesis and differentiation in a small mammal can proceed normally in-utero under microgravity and other conditions encountered during short-duration flight. However, it is not known whether this situation will hold for larger mammals over several generations during extended missions that venture outside of near Earth. Furthermore, it is not understood why the previous attempt at obtaining copulation, fertilization and implantation in orbit failed but may be related to limitations of the rat habitat for meeting the preconditions for reproductive behavior. With respect to mammalian development it is important to appreciate that fertilization and development occur internally within the female and take a long time to complete and their success will, therefore, be contingent upon the maternal response to the space environment. One process central to development (the establishment of cell lines) is initiated prior to implantation by environmental asymmetries preceived by progenitor cells. These asymmetries appear to result from the formation of asymmetric cell-cell contacts and the concommitant development of an electrical axis across the progenitor cells. Other asymmetries were also documented. It is not known whether any of the known asymmetries perceived by progenitor cells are influenced by gravity vectors and/or by the maternal response to microgravity and other conditions encountered in space.

Wiley, Lynn M.↗

Application of the TRANAIR rectangular grid approach to the aerodynamic analysis of complex configurations

A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.

Johnson, Forrester T.↗

Parallel conjugate gradient algorithms for manipulator dynamic simulation

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

Fijany, Amir↗

Phase compatibilities of YBa2Cu3O(9-delta) type structure in quintenary systems Y-Ba-Cu-O-X (impurity)

Electrical transport properties of the oxidic high T(sub c) superconductors are significantly affected by the presence of minor amounts of various elements adventing as impurities, e.g., from the chemical environment during manufacturing. YBa2Cu3O(9-delta) is prone to an extinction of the superconductivity on (partial) substitution of all four elemental components. E.g., Pr (for Y), La (for Ba), Zn (for Cu) or peroxygroup (for O) substituents will alter some of the superconductivity preconditions, like mixed valence state in Cu3O7/O(9-delta) network or structural distortion of the network. Although various pseudoternary chemical equilibrium phase diagrams of the Y(O)-Ba(O)-Cu(O) system now are available, no consensus is generally shown, however, this is partly due to lack of compatible definitions of the equilibrium conditions. Less information is available about the phase compatibilities in the appropriate quaternary phase diagram (including oxygen) and virtually no information exists about any pentenary phase diagrams (including one impurity). Unfortunately, complexity of such systems, stemming both from number of quaternary or pentenary compounds and from visualizing the five-component phase system, limits this presentation to more or less close surroundings of the YBa2Cu3O(9-delta) type phase in appropriate pseudoquaternary or pseudopseudoternary diagrams, involving Y-Ba-Cu and O, O-CO2, alkaline metals, Mg and alkaline earths, and Sc and most of the 3-d and 4-f elements. The systems were investigated by means of x ray diffraction, neutron diffraction and chemical analytical methods on samples prepared by sol-gel technique from citrates. The superconductivity was characterized by measuring the diamagnetic susceptibility by SQUID.

Karen, P.↗

Efficient conjugate gradient algorithms for computation of the manipulator forward dynamics

The applicability of conjugate gradient algorithms for computation of the manipulator forward dynamics is investigated. The redundancies in the previously proposed conjugate gradient algorithm are analyzed. A new version is developed which, by avoiding these redundancies, achieves a significantly greater efficiency. A preconditioned conjugate gradient algorithm is also presented. A diagonal matrix whose elements are the diagonal elements of the inertia matrix is proposed as the preconditioner. In order to increase the computational efficiency, an algorithm is developed which exploits the synergism between the computation of the diagonal elements of the inertia matrix and that required by the conjugate gradient algorithm.

Fijany, Amir↗

An investigation of resonant waves in a numerical model of an observed sudden stratospheric warming

A global quasi-linear time-dependent model that is able to represent the interaction of a single planetary Rossby wave with the zonal flow is used to investigate several questions concerning the role of resonance in the major stratospheric warming of February 1979. Special attention is given to the examination of the degree of dependence of the warming development on the phase speed of the wave and the initial mean flow. The results indicate that the preconditioning occurred early in the month, just after the minor sudden warming around February 5-7, and that a fairly broad range of eastward traveling phase speeds was capable of generating a warming. The model sensitivity tests indicate that the warming simulation has a weak dependence on the frequency of wave forcing and on the day used for initializing the basic state.

Smith, Anne K.↗

Compressible flow calculations employing the Galerkin/least-squares method

A multielement group, domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in the finite-element analysis of compressible flows employing the Galerkin/least-squares method. The iterative strategy employed is based on the generalized minimum residual (GMRES) procedure originally proposed by Saad and Shultz. Two levels of preconditioning are investigated. Applications to problems of high-speed compressible flow illustrate the effectiveness of the scheme.

Shakib, F.↗

Parallel iterative methods for sparse linear and nonlinear equations

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Saad, Youcef↗

Numerical study of vortical flow over a sideslipping delta wing

The three-dimensional vortical viscous flow past a sideslipping delta wing at a high angle of attack is numerically investigated. A computational method for calculating low-speed viscous flowfields is developed. The time-iterative method uses an implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. An algebraic turbulence model is implemented to account for the eddy viscosity. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. Computed results are compared with experimental data.

Hsu, C.-H.↗

Characterization of metal oxide absorbents for regenerative carbon dioxide and water vapor removal for advanced portable life support systems

Characterization of the performance of a silver-oxide-based absorbent in terms of its ability to remove both gaseous CO2 and water vapor in an astronaut portable life support systems (PLSS) is discussed. Attention is focused on regeneration of the absorbent from the carbonite state of the oxide state, preconditioning of the absorbent using a humidified gas stream, and absorption breakthrough testing. Based on the results of bench-scale experiments, a test plan is carried out to further characterize the silver-oxide-based absorbent on a larger scale; it calls for examination of the absorbent in both an adiabatic packed bed and a near-isothermal cooled bed configuration. It is demonstrated that the tested absorbent can be utilized in a way that removes substantial amounts of CO2 and water vapor during an 8-hour extravehicular activity mission, and that applying the absorbent to PLSS applications can simplify the ventilation loop.

Kast, Timothy P.↗

Analysis of the SSME HPOTP bearing inlet cavity

Analysis of the flow in the Space Shuttle Main Engine (SSME) high pressure oxygen turbopump (HPOTP) bearing no. 1 inlet cavity was completed in support of return-to-flight. With the incorporation of several design changes in the Phase 2 turbopump, rotordynamic stability of the pumps was enhanced, but the durability and life of the LOX-cooled bearings has decreased. During the post-Challenger SSME recertification, the causes of limited bearing durability were investigated. One topic addressed was the flow environment upstream of the pump-end bearing and the effect of seal exit swirl and a cavity anti-vortex rib on the bearing environment and life. The objective is to define the hydrodynamic environment upstream of the pump-end bearing and determine the effect of seal exit swirl and the anti-vortex rib on bearing inlet swirl. The problem was posed as an axisymmetric cavity flow with the computational domain extending from the seal exit to the bearing inlet. This domain was discretized with 22800 grid points. Boundary conditions were obtained from a 1-D model of the SSME coolant path. The inlet Mach number was 0.19 and the problem was solved with the CMINT code utilizing the Briley-McDonald/Beam-Warming algorithm with preconditioning to speed convergence at low Mach numbers. Three parametric cases with inlet swirl of 50 percent shaft speed (labyrinth seal), 20 percent shaft speed (damping seal), and no inlet swirl were considered. Computational results indicate large vortical flow structures in the cavity, with the labyrinth, damping, and no-swirl cases yielding bearing inlet swirl rates of 14, 10, and 9 percent of shaft speed, respectively. When these results were used as input to the SHABRETH bearing model, limited durability could not be explained by these small differences in swirl. Also, based on these results, a proposed design change for the cavity anti-vortex rib was not implemented by the SSME chief engineer.

Mcconnaughey, P. K.↗

High-performance equation solvers and their impact on finite element analysis

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

Poole, Eugene L.↗