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  • Articles: DFG German National Licenses  (5)
  • Engineering General  (5)
  • Conjugate gradients  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Numerical simulation of the horizontal Bridgman growth. Part III: Calculation of the interface (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 131-153 
    Details
    ISSN: 0271-2091
    Keywords: Finite Elements ; Transient Flows ; Three-dimensional Flows ; Natural Convection ; Interfaces Oscillatory Flows ; Crystal Growth ; Semiconductors ; Gallium Arsenide ; 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 study the transient motion of the solidification front during the growth of semiconductor crystals in the horizontal Bridgman geometry. The calculation is based on a two-dimensional flow. We use finite elements which deform with the motion of the interface. The energy equation is coupled with the isothermal constraint of the interface in an implicit transient algorithm. Several examples show the oscillatory motion of the interface caused by the periodic flow of the melt, and they reveal the importance of the growth rate on the shape of the interface.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070204
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical simulation of the horizontal Bridgman growth. Part I: Two-dimensional flow (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 29-47 
    Details
    ISSN: 0271-2091
    Keywords: Finite Elements ; Transient Flows ; Three-dimensional Flows ; Natural Convection ; Interfaces Oscillatory Flows ; Crystal Growth ; Semiconductors ; Gallium Arsenide ; 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 study the generation of periodic velocity and temperature fields in a plane horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals, although the present paper is limited to two-dimensional flows. We use transient finite difference and finite element algorithms which lead to identical results. We demonstrate the oscillatory mechanism in two different geometries.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070104
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A comparison of mixed methods for solving the flow of a Maxwell fluid (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 1065-1081 
    Details
    ISSN: 0271-2091
    Keywords: Viscoelastic Fluids ; Polymer Flow ; 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 proficiency of available mixed methods for solving the flow of a Maxwell fluid is evaluated through their application to the same problem. The reasons for the usual degeneracy of the numerical results beyond some level of elasticity are investigated. The best-performing technique is applied to the flow through an abrupt 4/1 contraction.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650041106
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical simulation of the horizontal Bridgman growth. Part II: Three-dimensional flow (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 49-67 
    Details
    ISSN: 0271-2091
    Keywords: Finite Elements ; Transient Flows ; Three-dimensional Flows ; Natural Convection ; Interfaces Oscillatory Flows ; Crystal Growth ; Semiconductors ; Gallium Arsenide ; 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 study the steady-state three-dimensional flow which occurs in a horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals. We find that three-dimensional effects can have a dramatic influence upon the flow, which, before the onset of periodic disturbances, differs appreciably from its two-dimensional counterpart. We also investigate the sensitivity of the flow to non-symmetric disturbances.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070105
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Transient finite element method for calculating steady state three-dimensional free surfaces (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 343-360 
    Details
    ISSN: 0271-2091
    Keywords: Free surfaces ; Extrusion ; Conjugate gradients ; Finite elements ; Three-dimensional free surfaces ; 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: In order to reduce the cost of large three-dimensional calculations of steady state free surfaces, we have combined a time-dependent approach, a decoupling algorithm and a conjugate gradient solver along the lines introduced earlier by Gresho and Chan. The free surface is calculated separately by applying the kinematic condition to a number of faces defined on the undeformed surface. For the pseudo-time-marching technique we show that it is economical to adopt different time steps for the free surface calculation and the other fields. The accuracy of the method is tested on the well-known circular die problem; the method is then used to reveal the effects of inertia and shear thinning on square and rectangular dies.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140307
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    Paper (German National Licenses)
    Fulltext
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