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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 275-294 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Fully-coupled solution ; Iterative solvers ; Finite-element methods ; Parallel algorithm ; Block diagonal preconditioning ; CFD ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents the parallelization aspects of a solution method for the fully coupled 3D compressible Navier-Stokes equations. The algorithmic thrust of the approach, embedded in a finite element code NS3D, is the linearization of the governing equations through Newton methods, followed by a fully coupled solution of velocities and pressure at each non-linear iteration by preconditioned conjugate gradient-like iterative algorithms. For the matrix assembly, as well as for the linear equation solver, efficient coarse-grain parallel schemes have been developed for shared memory machines, as well as for networks of workstations, with a moderate number of processors. The parallel iterative schemes, in particular, circumvent some of the difficulties associated with domain decomposition methods, such as geometry bookkeeping and the sometimes drastic convergence slow-down of partitioned non-linear problems.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1347-1358 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, yet effective, finite element approach to aerodynamic problems is presented. A better approximation of the geometry is obtained by the mapping of airfoils into near-circles. The mapping serves in homogenizing the gradients of the problem by magnifying regions of high gradients such as the leading and trailing edges while geometrically condensing the lower gradient regions on the main part of the airfoil. The mapping also permits the use of an effective automated mesh generation scheme that greatly reduces the amount of preparatory work involved in finite elements. To limit the size of the solution domain, an asymptotic analytical solution, with unknown coefficients, is assumed on a finite radius outer contour. The coefficients are obtained along with the finite element nodal unknowns. An accrued advantage of this patching asymptotic procedure is its ability to obtain the lift as a solution variable without having to resort to the numerical integration of the pressure field over the body. Solutions to non-lifting and lifting bodies are obtained.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1261-1271 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Analytical comparative solutions are often needed to assess the accuracy of proposed elements or proposed iterative schemes for potential flow numerical calculations. Traditionally, the flow over a circular cylinder, placed in a wind tunnel, has served for such a test and the results compared to what is thought to be an exact solution. We point out here that there is no exact solution for the flow over a circular cylinder in a wind tunnel, for practical values of wind tunnel height to cylinder radius, but that an exact solution can only be found for the flow over an oval cylinder. We derive that exact solution and provide numerical comparisons, using triangular elements, with both the stream function and the velocity potential for the incompressible case. In addition, numerical results for compressible flows up to critical Mach number are presented.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 127-144 
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The finite-element method is applied to the stream function formulation of transonic flows. Numerical dissipation, necessary for the calculation of mixed flows with shocks, is introduced via the artificial compressibility method. The classical problem of double-valuedness of the mass flux versus Mach number is resolved by direct integration of the vorticity equation. Solutions are obtained for isolated airfoils, the blade-to-blade cascade equation, as well as the radial equilibrium equation governing the hub-to-shroud through flow in turbomachinery.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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