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  • 1
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    Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations (1994)
    In:  CASI
    Details
    Publication Date: 2004-12-03
    Description: Basic algorithms for unstructured mesh generation and fluid flow calculation are discussed. In particular the following are addressed: preliminaries of graphs and meshes; duality and data structures; basic graph operations important in CFD (Computational Fluid Dynamics); triangulation methods, including Varonoi diagrams and Delaunay triangulation; maximum principle analysis; finite volume schemes for scalar conservation law equations; finite volume schemes for the Euler and Navier-Stokes equations; and convergence acceleration for steady state calculations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: VKI, Computational Fluid Dynamics, Volume 1; 141 p
    Format: text
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  • 2
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    Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations (1994)
    In:  Other Sources
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    Publication Date: 2011-08-24
    Description: One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. These algorithms are now used in the practical engineering design of devices such as cars and airplanes as well as theoretical studies of complex phenomena such as fluid turbulence. In past years, limited computer resources have motivated the development of efficient numerical methods in computational fluid dynamics (CFD) utilizing structured meshes. These meshes are comprised of systematic arrays of quadrilateral or hexahedral cells. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Structured meshes also permit the use of highly efficient solution techniques such as alternating direction implicit (ADI) iteration schemes or multigrid. Following the dramatic improvement in computing speed in recent years, emphasis has shifted towards the design of algorithms capable of treating complex geometries. The automatic generation of structured grids about complex geometries is problematic. Unstructured grids offer one promising alternative technique for treating these general geometries. Unstructured meshes have irregular connectivity and usually contain triangles and/or quadrilaterals in two dimensions and tetrahedra and/or hexahedra in three dimensions. The generation and use of unstructured grids poses new challenges in computational fluid dynamics. This is true for both grid generation as well as for the design of algorithms for flow solution. The purpose of these notes is to present recent developments in the unstructured grid generation and flow solution technology.
    Keywords: Fluid Mechanics and Heat Transfer
    Type: High Resolution Upwind and TVD Methods for the Compressible Flow Equations; D/1994/0238/423
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  • 3
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    On unstructured grids and solvers (1990)
    In:  CASI
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    Publication Date: 2013-08-31
    Description: The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: VKI, Computational Fluid Dynamics, Volume 2; 66 p
    Format: application/pdf
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  • 4
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    An efficient approximate factorization implicit scheme for the equations of gasdynamics (1984)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: An efficient implicit finite-difference algorithm for the gas dynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved while maintaining the same favorable stability characteristics and generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows about a NACA 0012 airfoil. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations. It is shown that the method offers advantages over the conventional Beam and Warming scheme and can retrofit existing Beam and Warming codes with minimal effort.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-85957 , A-9744 , NAS 1.15:85957
    Format: application/pdf
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  • 5
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    Navier-Stokes computations for exotic airfoils (1985)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: An efficient hyperbolic grid generator with improvements for handling sharp corners and concave surfaces is combined with an efficient and accurate Navier-Stokes flow solver. This combination is applied to some rather complex two-dimensional airfoil configurations. Steady separated flow about an iced leading edge of an airfoil is presented. Unsteady viscous separated flows past an airfoil at two angles of attack with a spoiler deployed at 60 degrees are presented and compared with experiment. The spoiler computations are performed with two different topological maps of the physical domain to the computational domain. Innovative graphical techniques for both the static and unsteady display of the flow fields are presented and discussed.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 85-0109
    Format: text
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  • 6
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    A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique (1985)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 85-0439
    Format: text
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  • 7
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    Navier-Stokes computations for exotic airfoils (1986)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: A hyperbolic grid generator with improvements for handling sharp corners and concave surfaces combined with a Navier-Stokes flow solver is applied to complex two dimensional airfoil configurations. Steady separated flow about an iced leading edge of an airfoil is presented. Unsteady viscous separated flows past an airfoil at two angles of attack with a spoiler deployed at 60 deg are compared with experiment. The spoiler computations are performed with two different topological maps of the physical domain to the computational domain. Graphical techniques for the static and unsteady display of the flow fields are discussed.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 85-0109 , AIAA Aerospace Science Meeting; Jan 14, 1985 - Jan 17, 1985; Reno, NV; United States|Von Karman Inst. for Fluid Dynamics Numerical Techniques for Viscous Flow Calculations in Turbomachinery Bladings; 17 p
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  • 8
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    One-Equation Algebraic Model Of Turbulence (1993)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.
    Keywords: MECHANICS
    Type: ARC-13127 , NASA Tech Briefs (ISSN 0145-319X); 17; 3; P. 86
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  • 9
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    Navier-Stokes computations for circulation controlled airfoils (1986)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 85-1587 , AIAA Fluid Dynamics and Plasmadynamics and Lasers Conference; Jul 16, 1985 - Jul 18, 1985; Cincinnati, OH; United States|Von Karman Inst. for Fluid Dynamics Numerical Techniques for Viscous Flow Calculations in Turbomachinery Bladings; 18 p
    Format: text
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