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Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

A highly efficient, edge-based viscous (EBV) discretization method has been recently implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver and evaluated for Reynolds-averaged Navier-Stokes (RANS) formulations. In comparison to a well-established cell-based viscous (CBV) method, the EBV method has demonstrated multifold acceleration of all viscous-kernel computations on general unstructured mixed-element grids. The viscous kernels include evaluation of viscous fluxes, diffusion terms in turbulence models, and the corresponding Jacobian terms. In this paper, an EBV implementation of a nonlinear extension of the Spalart-Allmaras turbulence model, SA-neg-QCR2000, is presented and verified. The SA-neg-QCR2000 model is used for simulating turbulent corner flows. Previously reported EBV computations have been conducted on traditional computing architectures based on central processing units (CPU). This paper assesses benefits of the EBV method on modern high-performance computing architectures based on graphics processing units (GPU). The GPU implementations of the CBV and EBV methods are verified by comparing solutions and iterative convergence with those observed in CPU computations on the same grids. A comprehensive assessment of the EBV speedup on CPU and GPU architectures is presented for established benchmark corner flows, namely, a supersonic flow through a long square duct and a subsonic flow around a NASA juncture flow model.

CFD↗

NASA NTRS1994

Parallel Preconditioning for CFD Problems on the CM-5

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Simon, Horst D.↗

NASA NTRS1989

A new second-order integration algorithm for simulating mechanical dynamic systems

A new integration algorithm which has the simplicity of Euler integration but exhibits second-order accuracy is described. In fixed-step numerical integration of differential equations for mechanical dynamic systems the method represents displacement and acceleration variables at integer step times and velocity variables at half-integer step times. Asymptotic accuracy of the algorithm is twice that of trapezoidal integration and ten times that of second-order Adams-Bashforth integration. The algorithm is also compatible with real-time inputs when used for a real-time simulation. It can be used to produce simulation outputs at double the integration frame rate, i.e., at both half-integer and integer frame times, even though it requires only one evaluation of state-variable derivatives per integration step. The new algorithm is shown to be especially effective in the simulation of lightly-damped structural modes. Both time-domain and frequency-domain accuracy comparisons with traditional integration methods are presented. Stability of the new algorithm is also examined.

Howe, R. M.↗

NASA NTRS2020

Multiple Shaker Placement for Ground Vibration Test of X-59 Aircraft Using Topology Optimization

A multiple shaker placement methodology is developed and tested using a topology optimization technique. Current multiple shaker placement methodology requires optimum accelerometer placement and optimum single-shaker placement techniques. The proposed methodology is tested using a finite element model of the X-59 Low Boom Flight Demonstrator aircraft. The effective independence and the driving point acceleration transfer function (DPATF) methods are used for the accelerometer placement study. In this study, four shakers are used to excite each mode more effectively during the ground vibration test; all the modes of interest thus are separated into four groups. Each shaker takes care of a separate group of modes. Grouping the modes of interest is performed utilizing topology optimization. The number of modes for each group therefore will be automatically decided during grouping. For each group of modes, perform the following two steps to determine optimal location of four shakers: 1) At each accelerometer location, compare the magnitude of DPATF values at natural frequencies, select the minimum value, and make a vector with these minimum values of the DPATF magnitudes for each group; and 2) Select the degrees of freedom corresponding to the maximum value of this vector. The objective function value is the maximum value of the vector with minimum value of the magnitude of the superposed acceleration transfer function. This objective function value is maximized by changing the modes for each group. Forty accelerometers are enough to have good correlation between mode shapes obtained from the reduced order model and the simulated ground vibration test.

Optimization Analysis↗

NASA NTRS1993

A search for energetic ion directivity in large solar flares

One of the key observational questions for solar flare physics is: What is the number, the energy spectrum, and the angular distribution of flare accelerated ions? The standard method for deriving ion spectral shape employs the ratio of influences observed on the 4-7 MeV band to the narrow neutron capture line at 2.223 MeV. The 4-7 MeV band is dominated by the principal nuclear de-excitation lines from C-12 and O-16 which are generated in the low chromosphere by the direct excitation or spallation of nuclei by energetic ions. In contrast, the narrow 2.223 MeV line is produced by the capture of thermal neutrons on protons in the photosphere. These capture neutrons are generated by energetic ion interactions and thermalized by scattering in the solar atmosphere. In a series of papers, Ramaty, Lingenfelter, and their collaborators have calculated the expected ratio of fluence in the 4-7 MeV band to the 2.223 MeV line for a wide range of energetic ion spectral shapes (see, e.g. Hua and Lingenfelter 1987). Another technique for deriving ion spectral shapes and angular distributions uses the relative strength of the Compton tail associated with the 2.223 MeV neutron capture line (Vestrand 1988, 1990). This technique can independently constrain both the angular and the energy distribution of the energetic parent ions. The combination of this tail/line strength diagnostic with the line/(4-7) MeV fluence ratio can allow one to constrain both properties of the energetic ion distributions. The primary objective of our Solar Maximum Mission (SMM) guest investigator program was to study measurements of neutron capture line emission and prompt nuclear de-excitation for large flares detected by the Solar Maximum Mission/ Gamma-Ray Spectrometer (SMM/GRS) and to use these established line diagnostics to study the properties of flare accelerated ions.

Vestrand, W. Thomas↗

NASA NTRS1973

A study of rapid engine response systems for an advanced high subsonic, long range commercial aircraft

A dynamic model representing the characteristics of an advanced technology study engine (1985 certification time period) was constructed and programmed on an analogue/digital computer. This model was then exercised to study and evaluate a large number of techniques, singly and in combination, to improve engine response. Several effective methods to reduce engine accelerating time are identified.

Barber, J. H.↗

NASA NTRS1979

Research in navigation and optimization for space trajectories

Topics covered include: (1) initial Cartesian coordinates for rapid precision orbit prediction; (2) accelerating convergence in optimization methods using search routines by applying curvilinear projection ideas; (3) perturbation-magnitude control for difference-quotient estimation of derivatives; and (4) determining the accelerometer bias for in-orbit shuttle trajectories.

Pines, S.↗

NASA NTRS1981

Analytical testing

Analytical methods for combining flight acceleration and strain data with shake test mobility data to predict the effects of structural changes on flight vibrations and strains are presented. This integration of structural dynamic analysis with flight performance is referred to as analytical testing. The objective of this methodology is to analytically estimate the results of flight testing contemplated structural changes with minimum flying and change trials. The category of changes to the aircraft includes mass, stiffness, absorbers, isolators, and active suppressors. Examples of applying the analytical testing methodology using flight test and shake test data measured on an AH-1G helicopter are included. The techniques and procedures for vibration testing and modal analysis are also described.

Flannelly, W. G.↗

NASA NTRS1982

Relaxation solution of the full Euler equations

A numerical procedure for the relaxation solution of the full steady Euler equations is described. By embedding the Euler system in a second order surrogate system, central differencing may be used in subsonic regions while retaining matrix forms well suited to iterative solution procedures and convergence acceleration techniques. Hence, this method allows the development of stable, fully conservative differencing schemes for the solution of quite general inviscid flow problems. Results are presented for both subcritical and shocked supercritical internal flows. Comparisons are made with a standard time dependent solution algorithm.

Johnson, G. M.↗

NASA NTRS1982

Application of a systematic finite-element model modification technique to dynamic analysis of structures

A systematic finite-element model modification technique has been applied to two small problems and a model of the main wing box of a research drone aircraft. The procedure determines the sensitivity of the eigenvalues and eigenvector components to specific structural changes, calculates the required changes and modifies the finite-element model. Good results were obtained where large stiffness modifications were required to satisfy large eigenvalue changes. Sensitivity matrix conditioning problems required the development of techniques to insure existence of a solution and accelerate its convergence. A method is proposed to assist the analyst in selecting stiffness parameters for modification.

Robinson, J. C.↗

NASA NTRS1982

Analysis and design of steady transonic flow over airfoils by the method of parametric differentiation

The results reported here are based on applying the method of parametric differentiation (MPD) to transform the nonlinear differential equation governing small-disturbance transonic flow to a linear equation. Implicit approximate factorization and monotone methods were used to accelerate convergence of the linear problem by an order of magnitude over successive line over-relaxation. The relative merits of using MPD are discussed in comparison to conventional small-disturbance applications. Several MPD analyses are performed on an array of airfoils. A design procedure utilizing MPD is discussed and demonstrated for two nonlifting cases.

Halt, D. W.↗

NASA NTRS1982

Relaxation solution of the full Euler equations

Johnson, G. M.↗

NASA NTRS1985

Algorithms for the Euler and Navier-Stokes equations for supercomputers

The steady state Euler and Navier-Stokes equations are considered for both compressible and incompressible flow. Methods are found for accelerating the convergence to a steady state. This acceleration is based on preconditioning the system so that it is no longer time consistent. In order that the acceleration technique be scheme-independent, this preconditioning is done at the differential equation level. Applications are presented for very slow flows and also for the incompressible equations.

Turkel, E.↗

NASA NTRS1985

Algorithms for the Euler and Navier-Stokes equations for supercomputers

Turkel, E.↗

NASA NTRS1987

Perception of linear acceleration in weightlessness

Eye movements and subjective detection of acceleration were measured on human experimental subjects during vestibular sled acceleration during the D1 Spacelab Mission. Methods and results are reported on the time to detection of small acceleration steps, the threshold for detection of linear acceleration, perceived motion path, and CLOAT. A consistently shorter time to detection of small acceleration steps is found. Subjective reports of perceived motion during sinusoidal oscillation in weightlessness were qualitatively similar to reports on earth.

Arrott, A. P.↗

NASA NTRS1989

Aerodynamics of high-lift, low-aspect-ratio unswept wings

It is presently demonstrated that highly cambered, low aspect ratio airfoil configurations can be neither experimentally nor numerically developed on the basis of two-dimensional methods; the strong dependency of airfoil shape on aspect ratio requires the definition of a planform to be conducted first, in order to serve as input for three-dimensional optimization methods. It is found that even the simplified three-dimensional computational method presently employed can accelerate a multielement-airfoil wing development.

Katz, Joseph↗

NASA NTRS1991

Characteristics of 3D turbulent jets in crossflow

Three dimensional turbulent jets in crossflow at low to medium jet-to-crossflow velocity ratios are computed with a finite volume numerical procedure which utilizes a second-moment closure model to approximate the Reynolds stresses. A multigrid method is used to accelerate the convergence rate of the procedure. Comparison of the computations to measured data show good qualitative agreement. All trends are correctly predicted, though there is some uncertainty on the height of penetration of the jet. The evolution of the vorticity field is used to explore the jet-crossflow interaction.

Demuren, A. O.↗

NASA NTRS1991

A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code

This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment.

Chen, H. C.↗