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  • Other Sources  (21)
  • 2010-2014  (11)
  • 1990-1994  (10)
  • 1
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    Supersonic combustor modeling (1990)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: The physical phenomena involved when a supersonic flow undergoes chemical reaction are discussed. Detailed physical models of convective and diffusive mixing, and finite rate chemical reaction in supersonic flow are presented. Numerical algorithms used to solve the equations governing these processes are introduced. Computer programs using these algorithms are used to analyze the structure of the reacting mixing layer. It is concluded that, as in subsonic flow, exothermic heat release in unconfined supersonic flows retards fuel/air mixing. Non mixing is shown to be a potential problem in reducing the efficiency of supersonic as well as subsonic combustion. Techniques for enhancing fuel/air mixing and combustion are described.
    Keywords: AIRCRAFT PROPULSION AND POWER
    Type: VKI, Gas Turbine Combustion, Volume 1; 95 p
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  • 2
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    Fourth-order 2N-storage Runge-Kutta schemes (1994)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations. A particular scheme is identified that has desirable efficiency characteristics for hyperbolic and parabolic initial (boundary) value problems. This scheme is competitive with the classical fourth-order method (high-storage) and is considerably more efficient and accurate than existing third-order low-storage schemes.
    Keywords: AERODYNAMICS
    Type: NASA-TM-109112 , NAS 1.15:109112
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  • 3
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    Third-order 2N-storage Runge-Kutta schemes with error control (1994)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A family of four-stage third-order explicit Runge-Kutta schemes is derived that requires only two storage locations and has desirable stability characteristics. Error control is achieved by embedding a second-order scheme within the four-stage procedure. Certain schemes are identified that are as efficient and accurate as conventional embedded schemes of comparable order and require fewer storage locations.
    Keywords: AERODYNAMICS
    Type: NASA-TM-109111 , NAS 1.15:109111
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  • 4
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    Numerical simulation of shock-induced combustion/detonation in a premixed H2-air mixture using Navier-Stokes equations (1991)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: A numerical study was conducted to address the structural stability of the oblique detonation wave. An attempt was made to isolate the structural instability predicted by Buckmaster's (1990) linear stability analysis. For this study a detailed viscous flowfield with finite-rate chemistry was computed past a 20-deg wedge. The finite-rate chemistry was modeled by using a seven-species and seven-reaction model. Instability modes were isolated by analyzing the Fourier power spectrum of the H2O mass fraction at selected sample stations. No unstable temporal modes with dominant frequency were isolated. It was concluded that the instability which is predicted by the Buckmaster work was a high-frequency low-amplitude phenomenon. For engineering purposes, the oblique detonation wave is a stable phenomenon as long as sufficient levels of overdrive are present.
    Keywords: INORGANIC AND PHYSICAL CHEMISTRY
    Type: AIAA PAPER 91-3359
    Format: text
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  • 5
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    High-order cyclo-difference techniques: An alternative to finite differences (1993)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.
    Keywords: AERODYNAMICS
    Type: NASA-TM-107745 , NAS 1.15:107745
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  • 6
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    Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes (1993)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-191436 , NAS 1.26:191436 , ICASE-93-9 , AD-A262950
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  • 7
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    On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations (1994)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.
    Keywords: NUMERICAL ANALYSIS
    Type: AD-A288759 , ICASE-94-79 , NAS 1.26:194989 , NASA-CR-194989
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  • 8
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    The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error (1993)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-191561 , NAS 1.26:191561 , ICASE-93-83 , AD-A274824
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  • 9
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    The stability of numerical boundary treatments for compact high-order finite-difference schemes (1991)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The stability characteristics of various compact fourth and sixth order spatial operators are assessed using the theory of Gustafsson, Kreiss and Sundstrom (G-K-S) for the semi-discrete Initial Boundary Value Problem (IBVP). These results are then generalized to the fully discrete case using a recently developed theory of Kreiss. In all cases, favorable comparisons are obtained between the G-K-S theory, eigenvalue determination, and numerical simulation. The conventional definition of stability is then sharpened to include only those spatial discretizations that are asymptotically stable. It is shown that many of the higher order schemes which are G-K-S stable are not asymptotically stable. A series of compact fourth and sixth order schemes, which are both asymptotically and G-K-S stable for the scalar case, are then developed.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-187628 , NAS 1.26:187628 , ICASE-91-71 , AD-A241939
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  • 10
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    Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations (2014)
    In:  CASI
    Details
    Publication Date: 2019-07-12
    Description: Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
    Keywords: Aeronautics (General)
    Type: NASA/TM-2014-218282 , L-20431 , NF1676L-19188
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