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NASA NTRS1991

Parallel algorithms for placement and routing in VLSI design

The computational requirements for high quality synthesis, analysis, and verification of very large scale integration (VLSI) designs have rapidly increased with the fast growing complexity of these designs. Research in the past has focused on the development of heuristic algorithms, special purpose hardware accelerators, or parallel algorithms for the numerous design tasks to decrease the time required for solution. Two new parallel algorithms are proposed for two VLSI synthesis tasks, standard cell placement and global routing. The first algorithm, a parallel algorithm for global routing, uses hierarchical techniques to decompose the routing problem into independent routing subproblems that are solved in parallel. Results are then presented which compare the routing quality to the results of other published global routers and which evaluate the speedups attained. The second algorithm, a parallel algorithm for cell placement and global routing, hierarchically integrates a quadrisection placement algorithm, a bisection placement algorithm, and the previous global routing algorithm. Unique partitioning techniques are used to decompose the various stages of the algorithm into independent tasks which can be evaluated in parallel. Finally, results are presented which evaluate the various algorithm alternatives and compare the algorithm performance to other placement programs. Measurements are presented on the parallel speedups available.

Brouwer, Randall Jay↗

NASA NTRS1991

Liquid rocket combustion instability analysis by CFD methods

Combustion instability in liquid rocket engines is simulated computationally by using a simple two-parameter model for the combustion response function. The objectives of the study are to assess the capabilities of CFD algorithms for instability studies and to investigate the response to parametric effects such as bombs and distributed combustion. Results indicate that numerical solutions of high accuracy can be obtained if a sufficient number of grid points are used per wavelength of the disturbance. The short-term response to bombs or pulses triggers a large number of modes in the combustor whose faithful resolution requires highly dense grids, although there is evidence that correct long-term solutions can be obtained even if all the short-term frequencies are not resolved. Long-term responses to pulses are shown to decay to the most unstable mode in small amplitude cases, and to exhibit limit cycles in large amplitude cases. Comparison of distributed with concentrated heat release indicates the former is more stable for given values of the combustion response parameters, and that the distributed heat release gives rise to higher frequency disturbances. Wave steepening is observed in the solutions, but its effect is less pronounced in multidimensional waves than in one-dimensional waves.

Grenda, J. M.↗

NASA NTRS2005

CFD - Mature Technology?

Over the past 30 years, numerical methods and simulation tools for fluid dynamic problems have advanced as a new discipline, namely, computational fluid dynamics (CFD). Although a wide spectrum of flow regimes are encountered in many areas of science and engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to a large demand for predicting the aerodynamic performance characteristics of flight vehicles, such as commercial, military, and space vehicles. As flow analysis is required to be more accurate and computationally efficient for both commercial and mission-oriented applications (such as those encountered in meteorology, aerospace vehicle development, general fluid engineering and biofluid analysis) CFD tools for engineering become increasingly important for predicting safety, performance and cost. This paper presents the author's perspective on the maturity of CFD, especially from an aerospace engineering point of view.

Kwak, Dochan↗

NASA NTRS2013

Faster Heavy Ion Transport for HZETRN

The deterministic particle transport code HZETRN was developed to enable fast and accurate space radiation transport through materials. As more complex transport solutions are implemented for neutrons, light ions (Z < 2), mesons, and leptons, it is important to maintain overall computational efficiency. In this work, the heavy ion (Z > 2) transport algorithm in HZETRN is reviewed, and a simple modification is shown to provide an approximate 5x decrease in execution time for galactic cosmic ray transport. Convergence tests and other comparisons are carried out to verify that numerical accuracy is maintained in the new algorithm.

Slaba, Tony C.↗

NASA NTRS1979

Utility of a finite element solution algorithm for initial-value problems

The Galerkin criterion within a finite element Weighted Residuals formulation is employed to establish an implicit solution algorithm for an initial-value partial differential equation. Numerical solutions of a transient parabolic and a hyperbolic equation, obtained using linear, quadratic and two cubic finite element basis functions, are employed to quantize accuracy and confirm and refine theoretical convergence rate estimates. The linear basis algorithm for the hyperbolic equation displays excellent accuracy on a coarse computational grid and a high-order convergence rate with discretization refinement. Good accuracy and a strong convergence rate in surface flux are determined for a nonhomogeneous Neumann boundary constraint applied to a parabolic equation. The results amply demonstrate the impact of the nondiagonal finite element initial-value matrix structure on solution accuracy and/or convergence rate.

Baker, A. J.↗

NASA NTRS1981

Optimum structural design with plate bending elements - A survey

A survey is presented of recently published papers in the field of optimum structural design of plates, largely with respect to the minimum-weight design of plates subject to such constraints as fundamental frequency maximization. It is shown that, due to the availability of powerful computers, the trend in optimum plate design is away from methods tailored to specific geometry and loads and toward methods that can be easily programmed for any kind of plate, such as finite element methods. A corresponding shift is seen in optimization from variational techniques to numerical optimization algorithms. Among the topics covered are fully stressed design and optimality criteria, mathematical programming, smooth and ribbed designs, design against plastic collapse, buckling constraints, and vibration constraints.

Haftka, R. T.↗

NASA NTRS1987

Structural tailoring of advanced turboprops

A computer program has been developed for the performance of numerical optimizations of highly swept propfan blades by minimizing an objective function that is defined either as direct operating cost or the aeroelastic difference between a blade and its scaled model. Three component analysis categories are employed: an optimization algorithm, approximate analysis procedures for objective function and constraint evaluation, and refined analysis procedures for optimum design validation. The analyses conducted by the program encompass aerodynamic efficiency evaluation, finite element stress and vibration analysis, acoustics, flutter, and forced response life prediction.

Brown, K. W.↗

NASA NTRS1989

On eigensystem assignment with output feedback

A new approach for the eigenvalue assignment of linear, first-order, time-invariant systems using output feedback is developed. The approach can assign the maximum allowable number of closed-loop eigenvalues through output feedback provided that the system is fully controllable and observable, and both the input influence and output influence matrices are full rank. First, a collection of bases for the space of attainable closed-loop eigenvectors is generated using the Singular Value Decomposition or QR Decomposition techniques. Then, an algorithm based on subspace intersections is developed and used to compute the corresponding coefficients of the bases, and the required output feedback gain matrix. Moreover, the additional freedom provided by the multi-inputs and multi-outputs beyond the eigenvalue assignment is characterized for possible exploitation. A numerical example is given to demonstrate the viability of the proposed approach.

Maghami, Peiman G.↗

NASA NTRS1991

Comparison of SMAC, PISO, and iterative time-advancing schemes for unsteady flows

Calculations of unsteady flows using a simplified marker and cell (SMAC), a pressure implicit splitting of operators (PSIO), and an iterative time advancing scheme (ITA) are presented. A partial differential equation for incremental pressure is used in each time advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillating flows over a circular and a square cylinder. For a large time step size, the SMAC and ITA are more strongly convergent and yield more accurate results than PSIO. The SMAC is the most efficient computationally. For a small time step size, the three time advancing schemes yield equally accurate Strouhal numbers. The capability of each time advancing scheme to accurately resolve unsteady flows is attributed to the use of new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.

Kim, Sang-Wook↗

NASA NTRS1992

Comparison of the SMAC, PISO, and iterative time-advancing schemes for unsteady flows

Calculations of unsteady flows using a simplified marker and cell (SMAC), a pressure implicit splitting of operators (PISO), and an iterative time advancing scheme (ITA) are presented. A partial differential equation for incremental pressure is used in each time advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillating flows over a circular and a square cylinder. For a large time step size, the SMAC and ITA are more strongly convergent and yield more accurate results than PISO. The SMAC is the most efficient computationally. For a small time step size, the three time advancing schemes yield equally accurate Strouhal numbers. The capability of each time advancing scheme to accurately resolve unsteady flows is attributed to the use of new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.

Kim, S.-W.↗

NASA NTRS1994

3D visualization of unsteady 2D airplane wake vortices

Air flowing around the wing tips of an airplane forms horizontal tornado-like vortices that can be dangerous to following aircraft. The dynamics of such vortices, including ground and atmospheric effects, can be predicted by numerical simulation, allowing the safety and capacity of airports to be improved. In this paper, we introduce three-dimensional techniques for visualizing time-dependent, two-dimensional wake vortex computations, and the hazard strength of such vortices near the ground. We describe a vortex core tracing algorithm and a local tiling method to visualize the vortex evolution. The tiling method converts time-dependent, two-dimensional vortex cores into three-dimensional vortex tubes. Finally, a novel approach calculates the induced rolling moment on the following airplane at each grid point within a region near the vortex tubes and thus allows three-dimensional visualization of the hazard strength of the vortices. We also suggest ways of combining multiple visualization methods to present more information simultaneously.

Ma, Kwan-Liu↗

NASA NTRS2003

Toward Immersed Boundary Simulation of High Reynolds Number Flows

In the immersed boundary (IB) method, the surface of an object is reconstructed with forcing terms in the underlying flow field equations. The surface may split a computational cell removing the constraint of the near wall gridlines to be aligned with the surface. This feature greatly simplifies the grid generation process which is cumbersome and expensive in particular for structured grids and complex geometries. The IB method is ideally suited for Cartesian flow solvers. The flow equations written in Cartesian coordinates appear in a very simple form and several numerical algorithms can be used for an efficient solution of the equations. In addition, the accuracy of numerical algorithms is dependent on the underlying grid and it usually deteriorates when the grid deviates from a Cartesian mesh. The challenge for the IB method lies in the representation of the wall boundaries and in providing an adequate near wall flow field resolution. The issue of enforcing no-slip boundary conditions at the immersed surface has been addressed by several authors by imposing a local reconstruction of the solution. Initial work by Verzicco et al. was based on a simple linear, one-dimensional operator and this approach proved to be accurate for boundaries largely aligned with the grid lines. Majumdar et al. used various multidimensional and high order polynomial interpolations schemes. These high order schemes, however, are keen to introduce wiggles and spurious extrema. Iaccarino & Verzicco and Kalitzin & Iaccarino proposed a tri-linear reconstruction for the velocity components and the turbulent scalars. A modified implementation that has proven to be more robust is reported in this paper. The issue of adequate near wall resolution in a Cartesian framework can initially be addressed by using a non-uniform mesh which is stretched near the surface. In this paper, we investigate an unstructured approach for local grid refinement that utilizes Cartesian mesh features. The computation of high Reynolds number wall bounded flows is particularly challenging as it requires the consideration of thin turbulent boundary layers, i.e. near wall regions with large gradients of the flow field variables. For such flows, the representation of the wall boundary has a large impact on the accuracy of the computation. It is also critical for the robustness and convergence of the flow solver.

Kalitzin, Georgi↗

NASA NTRS1974

Square-root algorithm for evaluating mismodeled process noise

As the application of sequential filters has grown, the need has arisen to evaluate the sensitivity of these filters to mismodeling of the random process. A numerically reliable square-root algorithm is developed for calculating the covariances of estimates from a sequential filter which incorrectly models process noise. Mismodeling is restricted to the correlation time and standard deviation of a random process represented as a first-order Gauss-Markov sequence. Using a computer program which employs this algorithm, a sensitivity analysis was performed for several types of earth-based tracking data from an interplanetary spacecraft.

Thornton, C. L.↗

NASA NTRS1981

Computation of wing-vortex interaction in transonic flow using implicit finite difference algorithm

An implicit delta form finite difference algorithm for Euler equations in conservation law form was used in preliminary calculations of three dimensional wing vortex interaction. Both steady and unsteady transonic flow wing vortex interactions are computed. The computations themselves are meant to guide upcoming wind tunnel experiments of the same flow field. Various modifications to the numerical method that are intended to improve computational efficiency are also described and tested in both two and three dimensions. Combination of these methods can reduce the overall computational time by a factor of 4.

Srinivasan, G.↗

NASA NTRS1983

Spline Classification Methods

The use of spline functions in the development of classification algorithms is discussed. A method is formulated for producing spline approximations to univariate density functions when each density function is described by a histogram of measurements. The resulting approximations are then incorporated into a Bayesian classification procedure for which the probability of misclassification can be readily computed. Some preliminary numerical results are presented to illustrate the method.

Guseman, L. F., Jr.↗

NASA NTRS1987

Numerical study of finite-rate supersonic combustion using parabolized equations

A set of partial differential equations, describing the two-dimensional supersonic chemically-reacting flow of the hydrogen-air system, is formulated such that the equations are parabolic in the streamwise direction. A fully-implicit fully-coupled finite-difference algorithm is used to develop a computer code which solves the governing equations by marching in the streamwise direction. The combustion process is modeled by a two-step finite-rate chemistry whereas turbulence is simulated by an algebraic turbulence model. Results of two calculations of internal supersonic reacting flow show fairly good agreement with the results obtained by the more costly full Navier-Stokes procedure.

Chitsomboon, T.↗

NASA NTRS1989

STRUTEX: A prototype knowledge-based system for initially configuring a structure to support point loads in two dimensions

Only recently have engineers begun making use of Artificial Intelligence (AI) tools in the area of conceptual design. To continue filling this void in the design process, a prototype knowledge-based system, called STRUTEX has been developed to initially configure a structure to support point loads in two dimensions. This prototype was developed for testing the application of AI tools to conceptual design as opposed to being a testbed for new methods for improving structural analysis and optimization. This system combines numerical and symbolic processing by the computer with interactive problem solving aided by the vision of the user. How the system is constructed to interact with the user is described. Of special interest is the information flow between the knowledge base and the data base under control of the algorithmic main program. Examples of computed and refined structures are presented during the explanation of the system.

Robers, James L.↗

NASA NTRS1989

Collisional dynamics of perturbed particle disks in the solar system

Theoretical and computational studies were carried out on galactic and planetary disks. With the goal of addressing important open questions centered on galactic structure, the cloudy interstellar medium, giant molecular clouds, and star formation in galactic disks and the collisional dynamics of perturbed particulate matter in planetary disks, focus was largely on the self-gravitational effects, dissipative effects, and collisional dynamics of cloud-particle disks. N-body, 'cloud-particle' computational algorithms were developed for the purpose of isolating the role of gaseous self gravity from the roles of other dominant physical mechanisms and dynamical processes, e.g. the collisional dynamics and dissipative processes. The efforts focused largely on galactic disks show that observational constraints provide stringent tests of the numerical simulation techniques developed. Self gravitational effects of the galactic interstellar medium's gas clouds are included by means of Fourier Transform technique.

Roberts, William W., Jr.↗