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At least 217 records · Page 12
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NASA NTRS1992

Convergence acceleration of the Proteus computer code with multigrid methods

Presented here is the first part of a study to implement convergence acceleration techniques based on the multigrid concept in the Proteus computer code. A review is given of previous studies on the implementation of multigrid methods in computer codes for compressible flow analysis. Also presented is a detailed stability analysis of upwind and central-difference based numerical schemes for solving the Euler and Navier-Stokes equations. Results are given of a convergence study of the Proteus code on computational grids of different sizes. The results presented here form the foundation for the implementation of multigrid methods in the Proteus code.

Demuren, A. O.↗
NASA NTRS1992

Upper bounds for convergence rates of vector extrapolation methods on linear systems with initial iterations

The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.

Sidi, Avram↗
NASA NTRS1992

Oblique convergence and deformation along the Kuril and Japan trenches

The hypothesis that present-day deformation within the southern Kuril forearc is driven by oblique subduction of the Pacific plate is tested using 397 horizontal slip directions derived from shallow-thrust earthquakes from the Kuril and Japan trenches for the period 1963-1991. A simple two-plate model fits the 397 slip vectors significantly worse than a model that permits strike-slip motion of the southern Kuril forearc relative to the overlying plate. Weighted, mean slip directions along the southern Kuril trench are systematically rotated toward the direction orthogonal to the trench, which implies that the net convergence is partitioned into less oblique subduction and trench-parallel displacement of the southern Kuril forearc. The angular discrepancy between the observed slip direction and the direction predicted by the NUVEL-1 Pacific-North America Euler vector implies that the southern Kuril forearc translates 6-11 mm/yr to the southwest relative to the overlying North American plate. These results are consistent with geologically, geodetically, and seismologically observed convergence at the leading edge of the forearc sliver in southern Kokkaido and with previously inferred extension at the trailing edge of the sliver, which is located at the Bussol Strait at 46 deg N.

Demets, Charles↗
NASA NTRS1993

Acceleration of convergence and spectrum transformation of implicit finite difference operators associated with Navier-Stokes equations

Implicit difference operator spectra are presently computed by applying eigensystem analysis techniques to finite-difference formulations of 2D Euler and Navier-Stokes equations, and attention is given to these iterative methods' convergence and stability characteristics by taking into account the effects of grid geometry, time-step, numerical viscosity, and boundary conditions. On the basis of the eigenvalue distributions for various flow configurations, the feasibility of applying such convergence-acceleration techniques as eigenvalue annihilation and relaxation is discussed. Spectrum-shifting is applied to NASA-Ames' ARC2D flow code, achieving a 20-33 percent efficiency.

Saleem, M.↗
NASA NTRS1947

An Investigation of Convergent-Divergent Diffusers at Mach Number 1.85

An investigation has been conducted in the Cleveland 18- by 18-inch supersonic tunnel at a Mach number of 1.85 and angles of attack from 0 deg to 5 deg to determine optimum design configurations for a convergent-divergent type of supersonic diffuser with a subsonic diffuser of 5 deg included divergence angle. Total pressure recoveries in excess of theoretical recovery across a normal shock at a free-stream Mach number of 1.85 wore obtained with several configurations. The highest recovery for configurations without a cylindrical throat section was obtained with an inlet having an included convergence angle of 20 deg. Insertion of a 2-inch throat section between a 10 deg included angle inlet and the subsonic diffuser stabilized the shock inside the diffuser and resulted in recoveries as high as 0.838 free-stream total pressure at an angle of attack of 0 deg, corresponding to recovery of 92.4 percent of the kinetic energy of the free air stream. Use of the throat section also lessened the reduction in recovery of all configurations due to angle of attack.

Wyatt, Demarquis D↗
NASA NTRS1954

Thrust characteristics of a series of convergent-divergent exhaust nozzles at subsonic and supersonic flight speeds

An experimental investigation of a series of four convergent-divergent exhaust nozzles was conducted in the Lewis 8-by-6 foot supersonic wind tunnel at Mach numbers of 0.1, 0.6, 1.6, and 2.0 over a range of nozzle pressure ratios. The thrust characteristics of these nozzles were determined by a pressure-integration technique. From a thrust standpoint, a nozzle designed to give uniform parallel flow at the exit had no advantage over the simple geometric design with conical convergent and divergent sections. The rapid-divergent nozzles might be competitive with the more gradual-divergent nozzles since the relatively short length of these nozzles would be advantageous from a weight standpoint and might result in smaller thrust losses due to friction. The thrusts, with friction losses neglected, were predicted satisfactorily by one-dimensional theory for the nozzles with relatively gradual divergence. The thrusts of the rapid-divergent designs were several percentages below the theoretical values at the design pressure ratio or above, while at low pressure ratios there was a considerable effect of free-stream Mach number, with thrusts considerably above theoretical values at subsonic speeds and somewhat above theoretical values at supersonic speeds. This Mach numb effect appeared to be related to the variation of the model base pressure with free-stream Mach number.

Fradenburgh, Evan A↗
NASA NTRS1993

Reliability enhancement of Navier-Stokes codes through convergence enhancement

Reduction of total computing time required by an iterative algorithm for solving Navier-Stokes equations is an important aspect of making the existing and future analysis codes more cost effective. Several attempts have been made to accelerate the convergence of an explicit Runge-Kutta time-stepping algorithm. These acceleration methods are based on local time stepping, implicit residual smoothing, enthalpy damping, and multigrid techniques. Also, an extrapolation procedure based on the power method and the Minimal Residual Method (MRM) were applied to the Jameson's multigrid algorithm. The MRM uses same values of optimal weights for the corrections to every equation in a system and has not been shown to accelerate the scheme without multigriding. Our Distributed Minimal Residual (DMR) method based on our General Nonlinear Minimal Residual (GNLMR) method allows each component of the solution vector in a system of equations to have its own convergence speed. The DMR method was found capable of reducing the computation time by 10-75 percent depending on the test case and grid used. Recently, we have developed and tested a new method termed Sensitivity Based DMR or SBMR method that is easier to implement in different codes and is even more robust and computationally efficient than our DMR method.

Choi, K.-Y.↗
NASA NTRS1995

Convergence acceleration of the Proteus computer code with multigrid methods

This report presents the results of a study to implement convergence acceleration techniques based on the multigrid concept in the two-dimensional and three-dimensional versions of the Proteus computer code. The first section presents a review of the relevant literature on the implementation of the multigrid methods in computer codes for compressible flow analysis. The next two sections present detailed stability analysis of numerical schemes for solving the Euler and Navier-Stokes equations, based on conventional von Neumann analysis and the bi-grid analysis, respectively. The next section presents details of the computational method used in the Proteus computer code. Finally, the multigrid implementation and applications to several two-dimensional and three-dimensional test problems are presented. The results of the present study show that the multigrid method always leads to a reduction in the number of iterations (or time steps) required for convergence. However, there is an overhead associated with the use of multigrid acceleration. The overhead is higher in 2-D problems than in 3-D problems, thus overall multigrid savings in CPU time are in general better in the latter. Savings of about 40-50 percent are typical in 3-D problems, but they are about 20-30 percent in large 2-D problems. The present multigrid method is applicable to steady-state problems and is therefore ineffective in problems with inherently unstable solutions.

Demuren, A. O.↗
NASA NTRS1995

Numerical simulations of small amplitude acoustic wave propagation in a converging-diverging nozzle

Numerical simulations of the small amplitude acoustic wave propagation in a converging-diverging nozzle proposed in Category 5 are performed and presented here. The quasi 1-D unsteady flow equations in conservative form are discretized by the DRP scheme with the artificial damping developed by Tam and Webb. Characteristic boundary conditions are used at both the inlet and outlet of the nozzle. The effect of different numerical implementations of the subsonic inflow boundary conditions on the convergence of the solution to the steady state is studied. In the case of a subsonic outflow in which a shock is formed in the nozzle, the interaction between acoustics and the shock is also investigated.

Dong, Thomas Z.↗
NASA NTRS1996

Convergence Acceleration of the Navier-Stokes Equations Through Time-Derivative Preconditioning

Chorin's method of artificial compressibility is extended to both compressible and incompressible fluids by using physical arguments to define artificial fluid properties that make up a local preconditioning matrix. In particular, perturbation expansions are used to provide appropriate temporal derivatives for the equations of motion at both low speeds and low Reynolds numbers. These limiting forms are then combined into a single function that smoothly merges into the physical time derivatives at high speeds so that the equations are left unchanged at transonic, high Reynolds number conditions. The effectiveness of the resulting preconditioning procedures for the Navier-Stokes equations is demonstrated for a wide speed and Reynolds number ranges by means of stability results and computational solutions. Nevertheless, the preconditioned equations sometimes fail to provide a solution for applications for which the non-preconditioned equations converge. Often this is because the reduced dissipation in the preconditioned equations results in an unsteady solution while the more dissipative non-preconditioned equations result in a steady state. Problems of this type represent a computational challenge; it is important to distinguish between non-convergence of algorithms, and the non-existence of steady state solutions.

Merkle, Charles L.↗
NASA NTRS1998

A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds

We give a pattern search adaptation of an augmented Lagrangian method due to Conn, Gould, and Toint. The algorithm proceeds by successive bound constrained minimization of an augmented Lagrangian. In the pattern search adaptation we solve this subproblem approximately using a bound constrained pattern search method. The stopping criterion proposed by Conn, Gould, and Toint for the solution of this subproblem requires explicit knowledge of derivatives. Such information is presumed absent in pattern search methods; however, we show how we can replace this with a stopping criterion based on the pattern size in a way that preserves the convergence properties of the original algorithm. In this way we proceed by successive, inexact, bound constrained minimization without knowing exactly how inexact the minimization is. So far as we know, this is the first provably convergent direct search method for general nonlinear programming.

Lewis, Robert Michael↗
NASA NTRS1998

Development of a Convergent Spray Technologies(tm) Spray Process for a Solventless Sprayable Coating, MCC-1

This paper discusses the application of Convergent Spray Technologies (TM) Spray Process to the development and successful implementation of Marshall Convergent Coating (MCC-1) as a primary Thermal Protection System (TPS) for the Space Shuttle Solid Rocket Boosters (SRBs). This paper discusses the environmental and process benefits of the MCC-1 technology, shows the systematic steps taken in developing the technology, including statistical sensitivity studies of about 35 variables. Based on the process and post-flight successes on the SRB, it will be seen that the technology is "field-proven". Application of this technology to other aerospace and commercial programs is summarized to illustrate the wide range of possibilities.

Patel, Anil K.↗
NASA NTRS1998

The Successful Transfer of Space Derived Convergent Spray: An Application for Industrial Roof Coatings and Interstate Bridge Repair

A partnership was formed between the National Aeronautics and Space Administration (NASA), the Environmental Protection Agency (EPA), and United Technologies USBI Company to develop, demonstrate, and evaluate a technology that uses a solventless spray process for depositing a lightweight, highly filled roof coating on low-sloped commercial roofs. Although the levels of volatile organic compound (VOC) emissions from industrial roof coating's and paint operations have been reduced in recent years, this partnership,was an effort to further reduce VOC emission levels and to also demonstrate the use of reclaimed automobile tire rubber as a filler material in roof coating systems. Different materials and coatings were evaluated and tested before the final selection used to coat the roofs of two small buildings at NASA's Marshall Space Flight Center during fiscal year 1997. The project successfully leveraged the investment of EPA, NASA and private sector resources to demonstrate a pre-commercial roofing coating process. This process utilizes the Convergent Spray Technologies process, which was initially developed by USBI to apply highly-filled, thermal protection coatings to the Space Shuttle Solid Rocket Boosters. A second partnership between the NASA, Federal Highway Administration, Alabama Department of Transportation and USBI Company was formed to develop and demonstrate the Convergent Spray Technology as a method of applying a skid resistant coating to interstate roads and concrete bridge decking's. Again, different materials and coatings were evaluated and tested before the final selection of ground flint and resin. Two field demonstrations were performed during fiscal year 1997 for the purpose of evaluating the coating system under actual highway conditions. These coatings were applied on Interstate 65 near Huntsville Alabama, and in the Mobile Bankhead tunnel. The system performed this task without the use of harmful solvents, and accomplished the process in a single application. This project successfully leveraged the investment of NASA, Federal Highway Administration, the Alabama Department of Transportation, and private sector funding.

McMillan, Vernotto C.↗
NASA NTRS2000

Marshall Convergent Coating Development Team: An Aerospace Success Story

The external thermal insulation systems for the Space Shuttle solid rocket boosters and the Air Force Titan IV payload fairings were in jeopardy due to EPA regulatory problems, endangering the flight status of both vehicles. The Marshall Convergent Coating (MCC-1) Development Team was formed in February 1994 to develop and implement an EPA-compliant external thermal insulation system for both systems. MCC-1 made use of a process known as Convergent Spray Technology (CST), a solventless, sprayable process that eliminated the environmentally hazardous chemicals involved with the old methods. Implemented in record time, the new insulation was so successful that it was selected for two additional flight vehicles, Boeing's Sea Launch and Delta TV. The activity also led to commercial spin-off pilot projects. The team continues today to share data between the various production sites, resolve production issues, expand the material's use, and consider potential improvements for the future.

Lester, Carl N.↗
NASA NTRS2002

Otolith-Canal Convergence In Vestibular Nuclei Neurons

The current final report covers the period from June 1, 1999 to May 31, 2002. The primary objective of the investigation was to determine how information regarding head movements and head position relative to gravity is received and processed by central vestibular nuclei neurons in the brainstem. Specialized receptors in the vestibular labyrinths of the inner ear function to detect angular and linear accelerations of the head, with receptors located in the semicircular canals transducing rotational head movements and receptors located in the otolith organs transducing changes in head position relative to gravity or linear accelerations of the head. The information from these different receptors is then transmitted to central vestibular nuclei neurons which process the input signals, then project the appropriate output information to the eye, head, and body musculature motor neurons to control compensatory reflexes. Although a number of studies have reported on the responsiveness of vestibular nuclei neurons, it has not yet been possible to determine precisely how these cells combine the information from the different angular and linear acceleration receptors into a correct neural output signal. In the present project, rotational and linear motion stimuli were separately delivered while recording responses from vestibular nuclei neurons that were characterized according to direct input from the labyrinth and eye movement sensitivity. Responses from neurons receiving convergent input from the semicircular canals and otolith organs were quantified and compared to non-convergent neurons.

Dickman, J. David↗
NASA NTRS2006

ALPS: The Age-Layered Population Structure for Reducing the Problem of Premature Convergence

To reduce the problem of premature convergence we define a new attribute of an individual, its age, and propose the Age-Layered Population Structure (ALPS), in which age is used to restrict competition and breeding between members of the population. ALPS differs from a typical EA by segregating individuals into different age-layers by their age - a measure of how long the genetic material has been in the population - and by regularly replacing all individuals in the bottom layer with randomly generated ones. The introduction of new, randomly generated individuals at regular intervals results in an EA that is never completely converged and is always looking at new parts of the fitness landscape. By using age to restrict competition and breeding search is able to develop promising young individuals without them being dominated by older ones. We demonstrate the effectiveness of the ALPS algorithm on an antenna design problem in which evolution with ALPS produces antennas more than twice as good as does evolution with two other types of EAs. Further analysis shows that the ALPS model does allow the offspring of newly generated individuals to move the population out of mediocre local-optima to better parts of the fitness landscape.

Hornby, Gregory S.↗
NASA NTRS2006

Convergence Acceleration for Multistage Time-Stepping Schemes

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Swanson, R. C.↗
NASA NTRS2007

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

Swanson, Roy C., Jr.↗