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  • 1
    Electronic Resource
    Electronic Resource
    Bifurcation analysis of solutal convection during directional solidification (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 535-550 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Techniques of bifurcation theory are used to analyze the possible forms of steady, two-dimensional, buoyancy-driven flow present during the vertical directional solidification of a dilute binary mixture. Morphological instabilities of the crystal–melt interface are ignored and the interface is assumed to be planar. The focus of the study concerns the effect of lateral confinement on the flow patterns observable in this simple model system. The use of a time-dependent numerical scheme by McFadden and Coriell [Proceedings of the First National Fluid Dynamics Congress, Cincinnati (AIAA, Washington, DC, 1988), p. 1572] to investigate this same problem resulted in gaps in the bifurcation structure, because unstable steady states exist that cannot be computed by their method. The present work extends and completes the description of the possible steady states. In particular, the complex modal exchanges that occur as the separation between the lateral walls varies are elucidated, and stable flow regimes and the sensitivity of the results to the closure condition at the upper boundary are determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858115
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable? (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 501-541 
    Details
    ISSN: 0271-2091
    Keywords: Backward-facing step ; Flow stability ; Incompressible flow ; 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 detailed case study is made of one particular solution of the 2D incompressible Navier-Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high-order finite-element method solving the unsteady equations by time-marching; (2) a high-order finite-element method solving both the steady equations and the associated linear-stability problem; (3) a second-order finite difference method solving the unsteady equations in streamfunction form by time-marching; and (4) a spectral-element method solving the unsteady equations by time-marching. The unanimous conclusion is that the correct solution for flow over the backward-facing step at Re = 800 is steady - and it is stable, to both small and large perturbations.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170605
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A finite-element study of the bénard problem using parameter-stepping and bifurcation search (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 127-145 
    Details
    ISSN: 0271-2091
    Keywords: Finite Element ; Bénard Connection ; Bifurcation ; Continuation ; 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 problem of fluid motion in a cavity with rigid sidewalls that is heated uniformly from below is studied by the finite-element method. The techniques of parameter-stepping and monitoring the determinant of the Jacobian matrix to find bifurcations are used. Results are presented for width-to-height ratios in the range 1 to 4, and for three different boundary conditions on the horizontal surfaces, namely both rigid, both free, and rigid bottom with free top. The non-linear branches above the critical Rayleigh number are examined. Extensions to non-Boussinesq flow are trivial.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650040203
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  • 4
    Electronic Resource
    Electronic Resource
    The finite element method for laminar flow with chemical reaction (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 239-253 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation of laminar flow with finite rate chemical reaction and heat release is made. Results are presented for steady flow in a channel, a special case of which is solved analytically, and for transverse flow around a cylinder. These illustrate the power of the finite element method for the calculation of reacting flows in complex geometries.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620170208
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  • 5
    Electronic Resource
    Electronic Resource
    Oscillatory convection in liquid metals in a horizontal temperature gradient (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 401-414 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When growing semiconductor crystals from the melt, the free convection induced in the liquid phase by the imposed thermal boundary conditions can become periodic in time. Recently, the onset of this oscillatory convection has been simulated directly through solution of the time-dependent governing equations for the particular case of an imposed horizontal temperature gradient. In this paper a new approach for detecting the oscillatory instability is presented in which the transition from steady to periodic flow is identified with a Hopf bifurcation in the solution of the steady equations. The critical Grashof number and frequency are predicted by solving an extended system of steady equations that locates exactly the Hopf bifurcation point, and the variation with aspect ratio and Prandtl number of the threshold for oscillations is obtained through continuation methods. By introducing a homotopy parameter into the boundary conditions the variation of the critical Grashof number is computed as the thermal and viscous conditions on the upper surface vary.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250210
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Flow in a coiled tube: The effect of mesh pattern on the convergence rate of predicted critical pointsHarwell Report AERE TP.1128. (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 519-522 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Non-unique flows are possible in a coiled tube when the axial pressure gradient driving the flow exceeds a critical value. For a tube of square cross-section, it is shown that the rate of convergence of the critical value with mesh size depends strongly on the mesh pattern. In the particular, the predictions obtained with mesh patterns which respect the symmetry of the problem converge more rapidly as the mesh size is reduced.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020510
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  • 7
    Electronic Resource
    Electronic Resource
    Anomalous convection at low Prandtl number (1989)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 5 (1989), S. 401-404 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The steady-state natural convection of a fluid of low Prandtl number contained within a two-dimensional rectangular box is simulated for conditions of an imposed horizontal temperature gradient and conducting horizontal surfaces. By the application of numerical bifurcation and continuation techniques combined with the finite-element method the solution structure of the steady state equations is determined and a stable anomalous bicellular flow is found. In contrast to the normal unicellular flow that develops smoothly for increasing Prandtl number, the anomalous flow is associated with a disconnected branch that arises at a limit point. The derived solution structure clarifies certain phenomena observed in recent time-dependent simulations of this problem.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630050606
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  • 8
    Electronic Resource
    Electronic Resource
    On a finite element method for the calculation of steady cellular interfaces in the one-sided model of solidification (1989)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 5 (1989), S. 309-320 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we reconsider the work of Ungar and Brown.15 These authors reported calculations of the non-linear families of steady-state solutions of the one-sided model of unidirectional solidification of a binary alloy. They combined a finite element method with a Landau transformation13 to deal with the free boundary, and predicted the non-linear solutions using numerical continuation and bifurcation techniques. We show that the numerical scheme that they used to calculate these families is mesh-dependent when the solid-liquid interface becomes sufficiently deformed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630050504
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