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  • 1
    Electronic Resource
    Electronic Resource
    Remarks on the Bénard and related stability problems (1966)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 17 (1966), S. 642-645 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Zusammenfassung Für gewisse mathematische Probleme, die im Zusammenhang mit dem Verhalten einer von unten beheizten Schicht Newtonscher Flüssigkeit und mit der Couette-Strömung Stokesscher Flüssigkeiten auftreten, wird gezeigt, dass sie in einem geeigneten Hilbert-Raum selbstadjungierten Charakter annehmen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01597247
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the stability of the steady state in systems of coupled diffusion and reaction (1973)
    Springer
    Archive for rational mechanics and analysis 52 (1973), S. 266-296 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00247738
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Dual variational statements viewed from function space (1963)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 9 (1963), S. 277-279 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690090227
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On finite amplitude roll cell disturbances in a fluid layer subjected to heat and mass transfer (1965)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 11 (1965), S. 971-980 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The system consists of a thin, transversely infinite horizontal fluid layer initially in mechanical but not thermostatic or speciestatic equilibrium. The top and bottom surfaces of the layer are assumed to be unconstrained, and the stability of the system to buoyancy driven finite amplitude roll cell disturbances is investigated. The system is capable of exhibiting both a subcritical stationary and oscillatory instability. The average vertical transport of heat and mass is computed and it is found that the convective transport associated with a stationary type of instability is much greater then that corresponding to an oscillatory instability.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690110607
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    The cause and cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations: Part 1 (1981)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 17-43 
    Details
    ISSN: 0271-2091
    Keywords: Finite Element ; Navier-Stokes ; Incompressible Flows ; Penalty Methods ; Pressure Filters ; 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 spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of both mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two-dimensions and one element in three-dimensions. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650010104
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    The cause and cure (!) of the spurious pressures generated by certain fem solutions of the incompressible Navier-Stokes equations: Part 2 (1981)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 171-204 
    Details
    ISSN: 0271-2091
    Keywords: Finite Element ; Navier-Stokes ; Incompressible Flows ; Penalty Methods ; Pressure Filters ; 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 spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two-dimensions and one element in three-dimensions. The automatic pressure filter associated with the penalty method is also explained. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650010206
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements (1982)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 25-42 
    Details
    ISSN: 0271-2091
    Keywords: Penalty Method ; Incompressible Flow ; Reduced Quadrature ; Finite Elements ; 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 frequently used reduced integration method for solving incompressible flow problems ‘a la penalty’ is critically examined vis-a-vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2-D) or triquadratic (3-D) velocity and linear pressure over that using the same velocity but employing bilinear (2-D) or trilinear (3-D) pressure approximation.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650020103
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  • 8
    Electronic Resource
    Electronic Resource
    The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow (1982)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 225-238 
    Details
    ISSN: 0271-2091
    Keywords: Normal Direction ; Boundary Conditions ; Incompressible ; Mass Conservation ; 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: Various techniques for implementing normal and/or tangential boundary conditions in finite element codes are reviewed. The principle of global conservation of mass is used to define a unique direction for the outward pointing normal vector at any node on an irregular boundary of a domain containing an incompressible fluid. This information permits the consistent and unambiguous application of essential or natural boundary conditions (or any combination thereof) on the domain boundary regardless of boundary shape or orientation with respect to the co-ordinate directions in both two and three dimensions. Several numerical examples are presented which demonstrate the effectiveness of the recommended technique.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650020302
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. Part I: General theory and stationary stability results (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 79-117 
    Details
    ISSN: 0271-2091
    Keywords: Fluid mechanics ; Stability ; Soret effect ; Buoyancy-driven ; Double diffusive ; 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: Buoyancy-driven instability of a monocomponent or binary fluid which is completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and the resulting linear stability problem is solved using Galerkin's technique. The analysis considers various types of fluid mixtures, ranging from gases to liquid metals, in cylinders with a variety of radius-to-height ratios. The flow structure is found to depend strongly on both the cylinder aspect ratio and the magnitude of the Soret effect. Comparisons are made with experiments and other theories, and the predicted stability limits are shown to agree closely with observations.
    Additional Material: 22 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100106
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. Part II: Weakly non-linear solutions (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 755-786 
    Details
    ISSN: 0271-2091
    Keywords: Stability ; Soret ; Buoyancy ; Bifurcation ; Non-linear ; 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 buoyancy-driven instability of a monocomponent or binary fluid that is completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and weakly-non-linear solutions are generated via Galerkin's technique using an expansion in the eigensolutions of the associated linear stability problem. Various types of fluid mixtures and cylindrical domains are considered. Flow structure and associated heat transfer are computed and experimental observations are cited when possible.
    Additional Material: 32 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170903
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    Paper (German National Licenses)
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