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  • 1
    Electronic Resource
    Electronic Resource
    Magnetohydrodynamic channel flow study (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 992-997 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A finite-difference study of a steady, incompressible, viscous, magnetohydrodynamic (MHD) channel flow which has direct application to dc electromagnetic pumps is presented. The study involves the numerical solution of the coupled Navier–Stokes and Maxwell equations at low magnetic Reynolds numbers. It is shown that the axial velocity profiles have a characteristic M shape as the fluid approaches and passes the electrode. The electric potential varies almost linearly from the channel centerline to the channel wall. The current shows a steep gradient near the electrodes. Comparison between the finite-difference solution and a quasi-one-dimensional approach are presented. The two-dimensional numerical calculations predict a larger pressure rise, a smaller net current, and a smaller pump efficiency than the quasi-one-dimensional model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865695
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An analysis of laminar boundary layers on liquid curtains (1989)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 40 (1989), S. 721-739 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A simplified analysis of the laminar boundary layer along an isothermal liquid curtain falling under gravity is presented. The analysis uses a von Kármán-Pohlhausen integral method and includes the effects of gravity, pressure differences, surface tension and nozzle exit geometry on the convergence length of liquid curtains which have applications as chemical reactors and as protection systems in laser fusion reactors. It is shown that the effects of the surrounding gases on the curtain shape and convergence length are small, and that good approximations to the liquid curtain shape can be obtained by using inviscid flow analyses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945873
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Hermitian operator methods for reaction-diffusion equations (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 3 (1987), S. 241-287 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A variety of time-linearization, quasilinearization, operator-splitting, and implicit techniques which use compact or Hermitian operators has been developed for and applied to one-dimensional reaction-diffusion equations. Compact operators are compared with second-order accurate spatial approximations in order to assess the accuracy and efficiency of Hermitian techniques. It is shown that time-linearization, quasilinearization, and implicit techniques which use compact operators are less accurate than second-order accurate spatial discretizations if first-order approximations are employed to evaluate the time derivatives. This is attributed to first-order accurati temporal truncation errors. Compact operator techniques which use second-order temporal approximations are found to be more accurate and efficient than second-order accurate, in both space and time, algorithms. Quasilinearization methods are found to be more accurate than time-linearization schemes. However, quasilinearization techniques are less efficient because they require the inversion of block tridiagonal matrices at each iteration. Some improvements in accuracy can be obtained by using partial quasilinearization and linearizing each equation with respect to the variable whose equation is being solved. Operator-splitting methods which use compact differences to evaluate the diffusion operator were found to be less accurate than operator-splitting procedures employ second-order accurate spatial approximations. Comparisons among the methods presented in this paper are shown in terms of the L2-norm errors and computed wave speeds for a variety of time steps and grid spacings: The numerical efficiency is assessed in terms of the CPU time required to achieve the same accuracy.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690030402
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical solution of reaction-diffusion equations by compact operators and modified equation methods (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 337-351 
    Details
    ISSN: 0271-2091
    Keywords: Compact Differences ; Modified Equation Methods ; Reaction-Diffusion Equations ; 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 system of reaction-diffusion equations which governs the propagation of an ozone decomposition laminar flame in Lagrangian co-ordinates is analysed by means of compact operators and modified equation methods. It is shown that the use of fourth-order accurate compact operators yields very accurate solutions if sufficient numbers of grid points are located at the flame front, where very steep gradients of temperature and species concentrations exist. Modified equation methods are shown to impose a restriction on the time step under certain conditions. The solutions obtained by means of compact operators and modified equation methods are compared with solutions obtained by other methods; good agreement is obtained.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070404
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  • 5
    Electronic Resource
    Electronic Resource
    Development and application of an adaptive finite element method to reaction-diffusion equations (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 13-23 
    Details
    ISSN: 0271-2091
    Keywords: Adaptive Finite Element Method ; Combustion ; 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: An adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed-node finite-difference schemes and an adaptive finite-difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth-order accurate, fixed-node, finite-difference methods when 272 collocation points are employed in the calculations.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050103
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    Paper (German National Licenses)
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