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  • 1
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    Upwind relaxation methods for the Navier-Stokes equations using inner iterations (1992)
    In:  Other Sources
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    Publication Date: 2011-08-24
    Description: A subsonic and a supersonic problem are respectively treated by an upwind line-relaxation algorithm for the Navier-Stokes equations using inner iterations to accelerate steady-state solution convergence and thereby minimize CPU time. While the ability of the inner iterative procedure to mimic the quadratic convergence of the direct solver method is attested to in both test problems, some of the nonquadratic inner iterative results are noted to have been more efficient than the quadratic. In the more successful, supersonic test case, inner iteration required only about 65 percent of the line-relaxation method-entailed CPU time.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 99; 68-78
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  • 2
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    An efficient method for estimating neighboring steady-state numerical solutions to the Euler equations (1991)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: The paper concentrates on a linear approximation method for predicting the changes occurring in steady-state numerical solutions of the Euler equations as a consequence of small changes in the independent variables which control the problem. The importance of proper boundary-condition treatment and other issues concerning the problem are covered along with the importance of proper algorithm selection for a fully supersonic inviscid flow. The method is applied to a subsonic nozzle involving variation of the pressure on the outflow boundary and to a supersonic inlet involving variation of the inflow Mach number. In the subsonic test case, the comparisons between the predicted and conventional numerical solutions are shown to be good, while in the supersonic test case, the agreement between the approximation method and conventional numerical solution starts out well but rapidly degenerates at some point in the flowfield as the perturbation of the boundary conditions is increased.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 91-1680
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  • 3
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    An incremental strategy for calculating consistent discrete CFD sensitivity derivatives (1992)
    In:  CASI
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    Publication Date: 2019-06-28
    Description: In this preliminary study involving advanced computational fluid dynamic (CFD) codes, an incremental formulation, also known as the 'delta' or 'correction' form, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods appear to be needed for future 3D applications; however, because direct solver methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form result in certain difficulties, such as ill-conditioning of the coefficient matrix, which can be overcome when these equations are cast in the incremental form; these and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two laminar sample problems: (1) transonic flow through a double-throat nozzle; and (2) flow over an isolated airfoil.
    Keywords: AERODYNAMICS
    Type: NASA-TM-104207 , NAS 1.15:104207 , AVSCOM-TR-92-B-006
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  • 4
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    Multidisciplinary analysis and sensitivity derivatives for isolated helicopter rotors in hover (1992)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: A new method is presented for using Navier-Stokes results in the system analysis and sensitivity derivative computations for a helicopter rotor in hover. The system coupling includes the interactions between rotor performance, rotor structural properties and aerodynamics (i.e., airfoil shape). Emphasis is placed on the use of high fidelity Navier-Stokes algorithms for the aerodynamic problem. The present formulation is chosen to reduce the number of sensitivity derivative equations and their dimensions as much as possible. In addition, an alternative adjoint formulation is presented which dramatically reduces the computational requirement for disciplines in which there may be a large number of design variables (e.g., aerodynamics). The theoretical method makes use of a combination of derivatives from each discipline; the computation of these derivatives has already been shown to be feasible. Sample computations for the aerodynamic-rotor model coupling and an associated sensitivity derivative are also presented.
    Keywords: AIRCRAFT DESIGN, TESTING AND PERFORMANCE
    Type: AIAA PAPER 92-4696 , In: AIAA(USAF)NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, 4th, Cleveland, OH, Sept. 21-23, 1992, Technical Papers. Pt. 1 (A93-20301 06-66); p. 63-86.
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  • 5
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    Sensitivity analysis, approximate analysis, and design optimization for internal and external viscous flows (1991)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: A gradient-based design optimization strategy for practical aerodynamic design applications is presented, which uses the 2D thin-layer Navier-Stokes equations. The strategy is based on the classic idea of constructing different modules for performing the major tasks such as function evaluation, function approximation and sensitivity analysis, mesh regeneration, and grid sensitivity analysis, all driven and controlled by a general-purpose design optimization program. The accuracy of aerodynamic shape sensitivity derivatives is validated on two viscous test problems: internal flow through a double-throat nozzle and external flow over a NACA 4-digit airfoil. A significant improvement in aerodynamic performance has been achieved in both cases. Particular attention is given to a consistent treatment of the boundary conditions in the calculation of the aerodynamic sensitivity derivatives for the classic problems of external flow over an isolated lifting airfoil on 'C' or 'O' meshes.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 91-3083
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  • 6
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    Discrete shape sensitivity equations for aerodynamic problems (1991)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Intensive research and development in Computational Fluid Dynamics (CFD) has recently produced many powerful CFD codes to simulate complex aerodynamic phenomena. However, in order to enhance the usefulness of these CFD codes for design practice, development of design sensitivity equations compatible to these codes becomes very important. This paper represents a part of such an effort to develop a sensitivity analysis methodology that enables the sensitivity equations to be implemented into existing CFD codes with minimal code modification. The methodology is based upon a preelimination procedure which accounts for consistently linearized boundary conditions. Formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 91-2259
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  • 7
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    Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications (1996)
    In:  CASI
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    Publication Date: 2019-07-20
    Description: An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.
    Keywords: Fluid Mechanics and Heat Transfer
    Type: NASA-CR-201941 , NAS 1.26:201941
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  • 8
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    Discrete sensitivity derivatives of the Navier-Stokes equations with a parallel Krylov solver (1994)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: This paper solves an 'incremental' form of the sensitivity equations derived by differentiating the discretized thin-layer Navier Stokes equations with respect to certain design variables of interest. The equations are solved with a parallel, preconditioned Generalized Minimal RESidual (GMRES) solver on a distributed-memory architecture. The 'serial' sensitivity analysis code is parallelized by using the Single Program Multiple Data (SPMD) programming model, domain decomposition techniques, and message-passing tools. Sensitivity derivatives are computed for low and high Reynolds number flows over a NACA 1406 airfoil on a 32-processor Intel Hypercube, and found to be identical to those computed on a single-processor Cray Y-MP. It is estimated that the parallel sensitivity analysis code has to be run on 40-50 processors of the Intel Hypercube in order to match the single-processor processing time of a Cray Y-MP.
    Keywords: PROPELLANTS AND FUELS
    Type: NASA-TM-106481 , ICOMP-94-2 , E-8411 , NAS 1.15:106481 , AIAA PAPER 94-0091 , Aerospace Sciences Meeting and Exhibit; Jan 10, 1994 - Jan 13, 1994; Reno, NV; United States
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  • 9
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    Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD (2004)
    In:  CASI
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    Publication Date: 2019-07-13
    Description: A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.
    Keywords: Statistics and Probability
    Type: PMC2004 , 9th ASCE Engrg. Mechanics Div., Structural Engrg. Inst, Geotechnical Inst. Aerospace Div. and the Sandia National Labs. Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability; Jul 26, 2004 - Jul 28, 2004; Albuquerque, NM; United States
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  • 10
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    Sensitivity derivatives for three dimensional supersonic Euler code using incremental iterative strategy (1994)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: In a recent work, an incremental strategy was proposed to iteratively solve the very large systems of linear equations that are required to obtain quasianalytical sensitivity derivatives from advanced computational fluid dynamics (CFD) codes. The technique was sucessfully demonstrated for two large two-dimensional problems: a subsonic and a transonic airfoil. The principal feature of this incremental iterative stategy is that it allows the use of the identical approximate coefficient matrix operator and algorithm to solve the nonlinear flow and the linear sensitivity equations; at convergence, the accuracy of the sensitivity derivatives is not compromised. This feature allows a comparatively straightforward extension of the methodology to three-dimensional problems; this extension is successfully demonstrated in the present study for a space-marching solution of the three-dimensional Euler equations over a Mach 2.4 blended wing-body configuration.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA Journal (ISSN 0001-1452); 32; 6; p. 1319-1321
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