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  • 1
    Electronic Resource
    Electronic Resource
    The stability of explicit Euler time-integration for certain finite difference approximations of the multi-dimensional advection-diffusion equation (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 853-897 
    Details
    ISSN: 0271-2091
    Keywords: Stability ; Advection-diffusion ; von Neumann method ; Matrix method ; Explicit Euler ; 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 comprehensive study is presented regarding the numerical stability of the simple and common forward Euler explicit integration technique combined with some common finite difference spatial discretizations applied to the advection-diffusion equation. One-dimensional results are obtained using both the matrix method (for several boundary conditions) and the classical von Neumann method of stability analysis and arguments presented showing that the latter is generally to be preferred, regardless of the type of boundary conditions. The less-well-known Godunov-Ryabenkii theory is also applied for a particular (Robin) boundary condition. After verifying portions of the one-dimensional theory with some numerical results, the stabilities of the two- and three-dimensional equations are addressed using the von Neumann method and results presented in the form of a new stability theorem. Extension of a useful scheme from one dimension, where the pure advection limit is known variously as Leith's method or a Lax-Wendroff method, to many dimensions via finite elements is also addressed and some stability results presented.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650040905
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Résumé and remarks on the open boundary condition minisymposium (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 983-1008 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Boussinesq ; Boundary condition ; Open ; Outflow ; 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 incompressible Navier-Stokes equations - and their thermal convection and stratified flow analogue, the Boussinesq equations - possess solutions in bounded domains only when appropriate/legitimate boundary conditions (BCs) are appended at all points on the domain boundary. When the boundary - or, more commonly, a portion of it - is not endowed with a Dirichlet BC, we are faced with selecting what are called open boundary conditions (OBCs), because the fluid may presumably enter or leave the domain through such boundaries. The two minisymposia on OBCs that are summarized in this paper had the objective of finding the best OBCs for a small subset of two-dimensional test problems. This objective, which of course is not really well-defined, was not met (we believe), but the contributions obtained probably raised many more questions/issues than were resolved - notable among them being the advent of a new class of OBCs that we call FBCs (fuzzy boundary conditions).
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650181006
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    Paper (German National Licenses)
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  • 3
    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)
    Fulltext
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