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  • Mathematics and Statistics  (4)
  • 1
    Electronic Resource
    Electronic Resource
    Linearized stability analysis of staggered-grid difference schemes for multidimensional viscous incompressible flows (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 313-322 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a systematic linearized (frozen coefficient) von Neumann stability analysis for various staggered-grid marker-and-cell (MAC) finite difference schemes for solving viscous incompressible fluid flows. These schemes employ the primitive variables formulation and require the velocity field to be divergent free at every time step. It is illustrated that the stability results for staggered-grid MAC schemes are similar to that for the multidimensional convective-diffusion equation with constant coefficients. © 1993 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090308
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Fractional step algorithm for solving a multi-dimensional diffusion-migration equation (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 389-397 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The earlier fractional step algorithm for solving the diffusion-migration equation in electrochemistry is extended to a multi-dimensional multi-species system with second-order spatial accuracy. For each time-step increment, the algorithm consists of three stages: (i) diffusion, (ii) satisfaction of the electroneutrality constraint, and (iii) migration. Each stage accounts for one individual physical process. Exact analytical solutions are derived for a two-species system and comparisons between exact and numerical results are made. Numerical results are also obtained for a two-dimensional three-species electrochemical model. © 1995 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110407
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Accuracy and stability analysis of numerical schemes for the shallow water model (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 85-98 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The accuracy and stability properties of several two-level and three-level difference schemes for solving the shallow water model are analyzed by the linearized Fourier Method. The effects of explicit or implicit treatments of the gravity, Coriolis, convective and friction terms on accuracy and stability are examined. The use of Miller's properties on von Neumann polynomial plays a crucial role to resolve the tedious mathematical procedures in the Fourier analysis. As a best compromise between efficiency and stability, we recommend the semi-implicit schemes, where the surface elevation and friction terms are treated implicitly while the convective and Coriolis terms are treated explicitly. © 1996 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    Convergence analysis of a staggered pressure correction scheme for viscous incompressible flows (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 459-482 
    Details
    ISSN: 0749-159X
    Keywords: Convergence analysis ; pressure correction scheme ; viscous incompressible flows ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This article performs the convergence analysis of a staggered pressure correction scheme for solving unsteady viscous incompressible flows in a bounded domain using the energy method. Error estimates for the numerical velocity field of the difference scheme are established. The analysis adopts the method of bounded truncation functions as advocated by Arnold et al. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 459-482, 1997
    Type of Medium: Electronic Resource
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