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  • 1
    Electronic Resource
    Electronic Resource
    The Lagrangian approach of advective term treatment and its application to the solution of Navier - Stokes equations (1981)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 365-387 
    Details
    ISSN: 0271-2091
    Keywords: Lagrangian Advective Schemes ; Numerical Diffusion ; Navier-Stokes ; 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: A one-dimensional transport test applied to some conventional advective Eulerian schemes shows that linear stability analyses do not guarantee the actual performances of these schemes. When adopting the Lagrangian approach, the main problem raised in the numerical treatment of advective terms is a problem of interpolation or restitution of the transported function shape from discrete data. Several interpolation methods are tested. Some of them give excellent results and these methods are then extended to multi-dimensional cases.The Lagrangian formulation of the advection term permits an easy solution to the Navier-Stokes equations in primitive variables V, p, by a finite difference scheme, explicit in advection and implicit in diffusion.As an illustration steady state laminar flow behind a sudden enlargement is analysed using an upwind differencing scheme and a Lagrangian scheme. The importance of the choice of the advective scheme in computer programs for industrial application is clearly apparent in this example.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650010407
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  • 2
    Electronic Resource
    Electronic Resource
    A finite element method to solve the Navier-Stokes equations using the method of characteristics (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 247-269 
    Details
    ISSN: 0271-2091
    Keywords: Finite Elements ; Navier-Stokes ; Driven Cavity ; Flow Past a Cylinder ; 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: We present a simple and efficient finite element method to solve the Navier-Stokes equations in primitive variables V, p. It uses (a) an explicit advection step, by upwind differencing. Improvement with regard to the classical upwind differencing scheme of the first order is realized by accurate calculation of the characteristic curve across several elements, and higher order interpolation; (b) an implicit diffusion step, avoiding any theoretical limitation on the time increment, and (c) determination of the pressure field by solving the Poisson equation. Two laminar flow calculations are presented and compared to available numerical and experimental results.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650040304
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