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  • 1
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    High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows (1990)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: Hypersonic computations are presently conducted with an extension of a class of high-resolution implicit TVD algorithms suited to transonic multidimensional Euler and Navier-Stokes equations. These conservative shock-capturing schemes, which are spatially second- and third-order, may be first- and second-order accurate in time and suitable for either steady or unsteady calculations. Attention is given to the enhancement of hypersonic flows' convergence rate and stability; accuracy and efficiency is achieved by these means for very complex two-dimensional hypersonic viscous and inviscid shock interactions.
    Keywords: AERODYNAMICS
    Type: Journal of Computational Physics (ISSN 0021-9991); 88; 31-61
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  • 2
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    Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations (1985)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The novel implicit and unconditionally stable, high resolution Total Variation Diminishing (TVD) scheme whose application to steady state calculations is presently examined is a member of a one-parameter family of implicit, second-order accurate systems developed by Harten (1983) for the computation of weak solutions for one-dimensional hyperbolic conservation laws. The scheme will not generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments for a quasi-one-dimensional nozzle problem show that the experimentally determined stability limit correlates exactly with the theoretical stability limit for the nonlinear scalar hyberbolic conservation laws.
    Keywords: AERODYNAMICS
    Type: Journal of Computational Physics (ISSN 0021-9991); 57; 327-360
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  • 3
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    Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates (1987)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Keywords: AERODYNAMICS
    Type: AIAA Journal (ISSN 0001-1452); 25; 266-274
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  • 4
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    Construction of explicit and implicit symmetric TVD schemes and their applications (1987)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: A one-parameter family of explicit and implicit total variation diminishing (TVD) schemes is developed which permits incorporation of an expanded group of slope and flux limiters. The numerical technique is intended for use in calculations which include a time-differencing scheme and an optional Lax-Wendroff scheme. Methods of extending the TVD models to nonlinear scalar equations and systems of hyperbolic conservation equations are described. Sample results are presented from calculations of shocked flows around NACA 0012 and NACA 0018 airfoils.
    Keywords: AERODYNAMICS
    Type: Journal of Computational Physics (ISSN 0021-9991); 68; 151-179
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  • 5
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    Linearized form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations (1986)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: Linearized alternating direction implicit (ADI) forms of a class of total variation diminishing (TVD) schemes for the Euler and Navier-Stokes equations have been developed. These schemes are based on the second-order-accurate TVD schemes for hyperbolic conservation laws developed by Harten (1983, 1984). They have the property of not generating spurious oscillations across shocks and contact discontinuities. In general, shocks can be captured within 1-2 grid points. These schemes are relatively simple to understand and easy to implement into a new or existing computer code. One can modify a standard three-point central-difference code by simply changing the conventional numerical dissipation term into the one designed for the TVD scheme. For steady-state applications, the only difference in computation is that the current schemes require a more elaborate dissipation term for the explicit operator; no extra computation is required for the implicit operator. Numerical experiments with the proposed algorithms on a variety of steady-state airfoil problems illustrate the versatility of the schemes.
    Keywords: AERODYNAMICS
    Type: Computers and Mathematics with Applications (ISSN 0886-9553); 12A; 4-5,
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  • 6
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    Nonlinear dynamics and numerical uncertainties in CFD (1996)
    In:  CASI
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    Publication Date: 2019-06-28
    Description: The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.
    Keywords: Numerical Analysis
    Type: NASA-TM-110398 , NAS 1.15:110398 , A-96173
    Format: application/pdf
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  • 7
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    Viscous hypersonic shock-on-shock interaction on blunt cowl lips (1988)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: The effects of impinging ramp shocks on a two-dimensional viscous inlet cowl of the National Aerospace Plane (NASP) or blunt body flow fields for various impingement locations are numerically simulated by a recently developed second-order implicit total variation diminishing (TVD) algorithm. The results demonstrate that accurate computation of heat transfer rate is crucially dependent on adequate normal grid resolution at the wall. The various numerical results are compared with recent experimental data. Due to the complex flow patterns that occur for the shock-on-shock flows, adaptive grid procedures are utilized.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 88-0233
    Format: text
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  • 8
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    Enhancements to Program LAURA for computation of three-dimensional hypersonic flow (1987)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Changes to Program Laura (Langley Aerothermodynamic Upwind Relaxation Algorithm) are presented which enhance both stability and accuracy of the algorithm. A discussion of iteration/sweeping strategies and their relation to computer architectures is included to best exploit the capabilities of serial, vector, and parallel processor machines. Test cases for Mach 10 perfect gas flow and Mach 32 real gas flow in chemical nonequilibrium over a blunt, raked elliptic cone using the thin-layer Navier-Stokes equations are presented in order to demonstrate the current improved capabilities. Algorithm changes include the use of volume averaging, application of a symmetric total variation diminishing (TVD) scheme, and stronger interaction between the grid/shock alignment routine and the relaxation algorithm. Good comparisons with heat transfer and pitching moment data at three different angles of attack for the Mach 10 tests serve to further validate the present algorithm. Parameters are defined which control the coupling of the specie continuity equations with the solution of the mixture conservation equations. A discussion of the consequences involved in the choice of strong versus weak coupling is presented, and a sample nonequilibrium calculation on a fine grid over a full scale model of the Aeroassist Flight Experiment (AFE) demonstrates current capabilities.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 87-0280
    Format: text
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  • 9
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    Hypersonic blunt body computations including real gas effects (1989)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Various second-order explicit and implicit TVD shock-capturing methods, a generalization of Roe's approximate Riemann solver, and a generalized flux-vector splitting scheme are used to study two-dimensional hypersonic real-gas flows. Special attention is given to the identification of some of the elements and parameters which can affect the convergence rate for high Mach numbers or real gases, but have negligible effect for low Mach numbers, for cases involving steady-state inviscid blunt flows. Blunt body calculations at Mach numbers of greater than 15 are performed to treat real-gas effects, and impinging shock results are obtained to test the treatment of slip surfaces and complex structures. Even with the addition of improvements, the convergence rate of algorithms in the hypersonic flow regime is found to be generally slower for a real gas than for a perfect gas.
    Keywords: AERODYNAMICS
    Type: ONERA, TP NO. 1989-85 , ONERA; 1989-
    Format: text
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  • 10
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    Numerical simulation by TVD schemes of complex shock reflections from airfoils at high angle of attack (1987)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: The shock-capturing capability of total variation diminishing (TVD) schemes is demonstrated for a more realistic complex shock-diffraction problem for which the experimental data are available. Second-order explicit upwind and symmetric TVD schemes are used to solve the time-dependent Euler equations of gas dynamics for the interaction of a blast wave with an airfoil at high angle-of-attack. The test cases considered are a time-dependent moving curved-shock wave and a contant moving planar-shock wave impinging at an angle-of-attack 30 deg on a NACA 0018 airfoil. Good agreement is obtained between isopycnic contours computed by the TVD schemes and those from experimental interferograms. No drastic difference in flow-field structure is found between the curved- and planar-shock wave cases, except for a difference in density level near the lower surface of the airfoil. Computation for cases with higher shock Mach numbers is also possible. Numerical experiments show that the symmetric TVD scheme is less sensitive to the boundary conditions treatment than the upwind scheme.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 87-0350
    Format: text
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