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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 937-950 
    ISSN: 1069-8299
    Keywords: thermal convection ; slender multigrid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The flow in a shallow, laterally heated air-filled cavity is investigated numerically using a primitive variable formulation of the governing equations of motion. Solutions are obtained for the entire flow field using a coupled solver combined with an FAS non-linear multigrid convergence accelerator. While care is taken to use a high-order, bounded discretization scheme for convective transport, the overall stability and efficiency of the approach is enhanced through the use of defect correction. This combination of features enables solutions to be found on extremely fine grids. Results for the flow in the end region of such cavities are compared qualitatively with the predictions of asymptotic theory for large aspect ratio, A (length:height), up to values of A higher than previously reported (A= 100); the particular case of A = 20 is considered for Rayleigh numbers in the range 103 to 108. Finally it is demonstrated how such solutions can be further enhanced by using locally refined grids in the end regions.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 1203-1215 
    ISSN: 0271-2091
    Keywords: Unsegregated ; Multigrid ; High-order ; Finite-difference ; 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: The paper describes and compares two different approaches to solving the equations of motion for fluid flow in a three-dimensional lid-driven cavity, when a higher-order approximation to convective transport is employed. One is based on the traditional pressure correction approach in conjunction with a pentadiagonal ADI solver; the other follows a new unsegregated variable and FAS multigrid methodology. The results generated by both approaches, for laminar flow conditions, at Reynolds numbers of 100 and 1000 are compared with each other and with corresponding solutions obtained with a well known low-order approximation to convection. Cross-reference is also made to flow in a two-dimensional cavity at the same Reynolds numbers.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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