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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 NTRS1994

On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.

Ibraheem, S. O.↗

NASA NTRS1987

Numerical simulation of viscous flows over transonic aircraft configurations

Numerical simulation of compressible viscous flow fields is performed for a transonic transport configuration. A single structured grid system is constructed using analytical transformations such as conformal mapping, shearing/twisting/rotating/clustering/stretching transformations. The Reynolds-averaged, thin-layer Navier-Stokes equations are solved on a supercomputer, FACOM VP-400, using the LU-ADI factorization method.

Takanashi, Susumu↗

NASA NTRS1991

Navier-Stokes Simulation Of Wind-Tunnel Flow

Report describes three-dimensional Navier-Stokes simulation of transonic flow past model wing in wind tunnel and in free air. Numerical integration performed by LU-ADI factorization algorithm. Simulation shows effects of walls of tunnel.

Obayashi, S.↗

NASA NTRS1991

Navier-Stokes computation of wing/rotor interaction for a tilt rotor in hover

A method has been developed to analyze the wing/rotor interaction of tilt rotor aircraft in hover. The unsteady, thin-layer compressible Navier-Stokes equations are solved using an implicit, finite difference scheme that employs LU-ADI factorization. The rotor is modeled as an actuator disk which imparts a radial and azimuthal distribution of pressure rise and swirl to the flowfield. The 'chimera' approach of grid point blanking is used to update the rotor boundary conditions. Results are presented for both a rotor alone and for wing/rotor interaction where the thrust coefficient is 0.0164 and wing flap deflection is 67 degrees. Many of the complex flow features are captured including the fountain effect, leading and trailing edge separation, and the unsteady wake beneath the wing. Wing surface pressures compare fairly well with experimental data although the time-averaged download is about twenty percent higher than the measured value. This discrepancy is due to a combination of factors that are discussed.

Fejtek, Ian↗

NASA NTRS1993

Computational analysis of methods for reduction of induced drag

The purpose of this effort was to perform a computational flow analysis of a design concept centered around induced drag reduction and tip-vortex energy recovery. The flow model solves the unsteady three-dimensional Euler equations, discretized as a finite-volume method, utilizing a high-resolution approximate Riemann solver for cell interface flux definitions. The numerical scheme is an approximately-factored block LU implicit Newton iterative-refinement method. Multiblock domain decomposition is used to partition the field into an ordered arrangement of blocks. Three configurations are analyzed: a baseline fuselage-wing, a fuselage-wing-nacelle, and a fuselage-wing-nacelle-propfan. Aerodynamic force coefficients, propfan performance coefficients, and flowfield maps are used to qualitatively access design efficacy. Where appropriate, comparisons are made with available experimental data.

Janus, J. M.↗

NASA NTRS1993

Navier-Stokes flowfield computation of wing/rotor interaction for a tilt rotor aircraft in hover

The download on the wing produced by the rotor-induced downwash of a tilt rotor aircraft in hover is of major concern because of its severe impact on payload-carrying capability. A method has been developed to help gain a better understanding of the fundamental fluid dynamics that causes this download, and to help find ways to reduce it. In particular, the method is employed in this work to analyze the effect of a tangential leading edge circulation-control jet on download reduction. Because of the complexities associated with modeling the complete configuration, this work focuses specifically on the wing/rotor interaction of a tilt rotor aircraft in hover. The three-dimensional, unsteady, thin-layer compressible Navier-Stokes equations are solved using a time-accurate, implicit, finite difference scheme that employs LU-ADI factorization. The rotor is modeled as an actuator disk which imparts both a radical and an azimuthal distribution of pressure rise and swirl to the flowfield. A momentum theory blade element analysis of the rotor is incorporated into the Navier-Stokes solution method. Solution blanking at interior points of the mesh has been shown here to be an effective technique in introducing the effects of the rotor and tangential leading edge jet. Results are presented both for a rotor alone and for wing/rotor interaction. The overall mean characteristics of the rotor flowfield are computed including the flow acceleration through the rotor disk, the axial and swirl velocities in the rotor downwash, and the slipstream contraction. Many of the complex tilt rotor flow features are captured including the highly three-dimensional flow over the wing, the recirculation fountain at the plane of symmetry, wing leading and trailing edge separation, and the large region of separated flow beneath the wing. Mean wing surface pressures compare fairly well with available experimental data, but the time-averaged download/thrust ratio is 20-30 percent higher than the measured value. The discrepancy is due to a combination of factors that are discussed. Leading edge tangential blowing, of constant strength along the wing span, is shown to be effective in reducing download. The jet serves primarily to reduce the pressure on the wing upper surface. The computation clearly shows that, because of the three-dimensionality of the flowfield, optimum blowing would involve a spanwise variation in blowing strength.

Fejtek, Ian G.↗

NASA NTRS1993

CFD analyses of combustor and nozzle flowfields

The objectives of the research are to improve design capabilities for low thrust rocket engines through understanding of the detailed mixing and combustion processes. A Computational Fluid Dynamic (CFD) technique is employed to model the flowfields within the combustor, nozzle, and near plume field. The computational modeling of the rocket engine flowfields requires the application of the complete Navier-Stokes equations, coupled with species diffusion equations. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an ongoing experimental program at NASA LeRC. The numerical procedure is performed on both time-marching and time-accurate algorithms, using an LU approximate factorization in time, flux split upwinding differencing in space. The integrity of fuel film cooling along the wall, its effectiveness in the mixing with the core flow including unsteady large scale effects, the resultant impact on performance and the assessment of the near plume flow expansion to finite pressure altitude chamber are addressed.

Tsuei, Hsin-Hua↗

NASA NTRS1994

Numerical study of the trailing vortex of a wing with wing-tip blowing

Trailing vortices generated by lifting surfaces such as helicopter rotor blades, ship propellers, fixed wings, and canard control surfaces are known to be the source of noise, vibration, cavitation, degradation of performance, and other hazardous problems. Controlling these vortices is, therefore, of practical interest. The formation and behavior of the trailing vortices are studied in the present research. In addition, wing-tip blowing concepts employing axial blowing and spanwise blowing are studied to determine their effectiveness in controlling these vortices and their effects on the performance of the wing. The 3D, unsteady, thin-layer compressible Navier-Stokes equations are solved using a time-accurate, implicit, finite difference scheme that employs LU-ADI factorization. The wing-tip blowing is simulated using the actuator plane concept, thereby, not requiring resolution of the jet slot geometry. Furthermore, the solution blanking feature of the chimera scheme is used to simplify the parametric study procedure for the wing-tip blowing. Computed results are shown to compare favorably with experimental measurements. It is found that axial wing-tip blowing, although delaying the rolling-up of the trailing vortices and the near-field behavior of the flowfield, does not dissipate the circulation strength of the trailing vortex farther downstream. Spanwise wing-tip blowing has the effect of displacing the trailing vortices outboard and upward. The increased 'wing-span' due to the spanwise wing-tip blowing has the effect of lift augmentation on the wing and the strengthening of the trailing vortices. Secondary trailing vortices are created at high spanwise wing-tip blowing intensities.

Lim, Hock-Bin↗

NASA NTRS1992

Electromagnetic scattering calculations on the Intel Touchstone Delta

During the first year's operation of the Intel Touchstone Delta system, software which solves the electric field integral equations for fields scattered from arbitrarily shaped objects has been transferred to the Delta. To fully realize the Delta's resources, an out-of-core dense matrix solution algorithm that utilizes some or all of the 90 Gbyte of concurrent file system (CFS) has been used. The largest calculation completed to date computes the fields scattered from a perfectly conducting sphere modeled by 48,672 unknown functions, resulting in a complex valued dense matrix needing 37.9 Gbyte of storage. The out-of-core LU matrix factorization algorithm was executed in 8.25 h at a rate of 10.35 Gflops. Total time to complete the calculation was 19.7 h-the additional time was used to compute the 48,672 x 48,672 matrix entries, solve the system for a given excitation, and compute observable quantities. The calculation was performed in 64-b precision.

Cwik, Tom↗

NASA NTRS1994

Multi-dimensional combustor flowfield analyses in gas-gas rocket engine

The objectives of the present research are to improve design capabilities for low thrust rocket engines through understanding of the detailed mixing and combustions processes. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an on-going experimental program at NASA LeRC. Detailed computational modeling requires the application of the full three-dimensional Navier Stokes equations, coupled with species diffusion equations. The numerical procedure is performed on both time-marching and time-accurate algorithms and using an LU approximate factorization in time, flux split upwinding differencing in space. The emphasis in this paper is focused on using numerical analysis to understand detailed combustor flowfields, including the shear layer dynamics created between fuel film cooling and the core gas in the vicinity on the nearby combustor wall; the integrity and effectiveness of the coolant film; three-dimensional fuel jets injection/mixing/combustion characteristics; and their impacts on global engine performance.

Tsuei, Hsin-Hua↗

NASA NTRS1995

Spectral ordering techniques for incomplete LU preconditoners for CG methods

The effectiveness of an incomplete LU (ILU) factorization as a preconditioner for the conjugate gradient method can be highly dependent on the ordering of the matrix rows during its creation. Detailed justification for two heuristics commonly used in matrix ordering for anisotropic problems is given. The bandwidth reduction and weak connection following heuristics are implemented through an ordering method based on eigenvector computations. This spectral ordering is shown to be a good representation of the heuristics. Analysis and test cases in two and three dimensional diffusion problems demonstrate when ordering is important, and when an ILU decomposition will be ordering insensitive. The applicability of the heuristics is thus evaluated and placed on a more rigorous footing.

Clift, Simon S.↗

NASA NTRS1996

NASA flow fields analysis

The objectives of the present research are to improve design capabilities for low thrust rocket engines through understanding the detailed mixing and combustion processes in a representative combustor. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an on-going experimental program at NASA LERC. Detailed computational modeling involves the solution of both the two- and three-dimensional Navier Stokes equations, coupled with chemical reactions and the species diffusion equations. Computations of interest include both steady state and time-accurate flowfields and are obtained by means of LU approximate factorization in time and flux split upwinding differencing in space. The emphasis in the research is focused on using numerical analysis to understand detailed combustor flowfields, including the shear layer dynamics created between fuel film cooling and the core gas in the vicinity on the nearby combustor wall; the integrity and effectiveness of the coolant film; and three-dimensional fuel and oxidizer jet injection/mixing/combustion characteristics in the primary combustor along with their joint impacts on global engine performance.

Merkle, Charles L.↗

NASA NTRS1988

The ijk forms of factorization methods. II - Parallel systems

The paper considers the 'ijk forms' of LU and Cholesky factorization on certain parallel computers. This extends an earlier analysis for vector computers. Attention is restricted to local memory systems with processors that may or may not have vector capability. Special attention is given to bus architectures but qualitative analyses are given for other interconnection systems.

Ortega, J. M.↗

NASA NTRS1988

The ijk forms of factorization methods. I - Vector computers

This paper gives a detailed exposition of the 'ijk forms' of LU and Choleski factorization. Several aspects of these different organizations are discussed and their properties on vector computers are compared. Extensions of the ijk formalism to other algorithms is also given.

Ortega, J. M.↗

NASA NTRS1990

Characteristic-based algorithms for flows in thermo-chemical nonequilibrium

A generalized finite-rate chemistry algorithm with Steger-Warming, Van Leer, and Roe characteristic-based flux splittings is presented in three-dimensional generalized coordinates for the Navier-Stokes equations. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed.

Walters, Robert W.↗

NASA NTRS2000

Bithermal Low-Cycle Fatigue Evaluation of Automotive Exhaust System Alloy SS409

This investigation provides, for the first time, cyclic strainrange-controlled, thermomechanical fatigue results for the ferritic stainless steel alloy SS409. The alloy has seen extensive application for automotive exhaust system components. The data were generated to calibrate the Total Strain Version of the Strainrange Partitioning (TS-SRP) method for eventual application to the design and durability assessment of automotive exhaust systems. The thermomechanical cyclic lifetime and cyclic stress-strain constitutive behavior for alloy SS409 were measured using bithermal tests cycling between isothermal extremes of 400 and 800 C. Lives ranged up to 10,000 cycles to failure with hold-times of 0.33 to 2.0 minutes. The bithermal fatigue behavior is compared to isothermal, strain-controlled fatigue behavior at both 400 and 800 C. Thermomechanical cycling was found to have a profound detrimental influence on the fatigue failure resistance of SS409 compared to isothermal cycling. Supplementary bithermal cyclic stress-strain constitutive tests with hold-times ranging from 40 seconds up to 1.5 hours were conducted to calibrate the TS-SRP equation for extrapolation to longer lifetime predictions. Observed thermomechanical (bithermal) fatigue lives correlated well with lives calculated using the calibrated TS-SRP equations: 70% of the bithermal fatigue data fall within a factor of 1.2 of calculated life; 85% within a factor of 1.4; and 100% within a factor of 1.8.

Lu, Gui-Ying↗

NASA NTRS2016

Vortex Generators in a Two-Dimensional, External-Compression Supersonic Inlet

Vortex generators within a two-dimensional, external-compression supersonic inlet for Mach 1.6 were investigated to determine their ability to increase total pressure recovery, reduce total pressure distortion, and improve the boundary layer. The vortex generators studied included vanes and ramps. The geometric factors of the vortex generators studied included height, length, spacing, and positions upstream and downstream of the inlet terminal shock. The flow through the inlet was simulated through the computational solution of the steady-state Reynolds-averaged Navier-Stokes equations on multi-block, structured grids. The vortex generators were simulated by either gridding the geometry of the vortex generators or modeling the vortices generated by the vortex generators. The inlet performance was characterized by the inlet total pressure recovery, total pressure distortion, and incompressible shape factor of the boundary-layer at the engine face. The results suggested that downstream vanes reduced the distortion and improved the boundary layer. The height of the vortex generators had the greatest effect of the geometric factors.

computational fluid dynamics↗