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  • 1
    Electronic Resource
    Electronic Resource
    A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows (1983)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 493-506 
    Details
    ISSN: 0271-2091
    Keywords: Modified ; Dodge ; Algorithm ; Parabolized ; Navier-Stokes ; Computational Fluid Dynamics ; Low Speed Flow ; Channel Flow ; Zebra Algorithm ; Mass Balancing ; 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 revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow has been developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (chequerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A chequerboard iteration is ued to solve the resulting implicit non-linear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results has been obtained for some flows with well-known solutions.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650030505
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Application of an explicit TVD scheme for unsteady, axisymmetric, muzzle brake flow (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 621-633 
    Details
    ISSN: 0271-2091
    Keywords: TVD Schemes ; Shock Capturing ; Muzzle Brake Flow ; Blast Wave Simulation ; Harten's Method ; Operator Splitting ; 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: Operator splitting in the presence of source terms is necessary in order to apply Harten's second-order accurate, total-variation-diminishing (TVD), shock-capturing scheme to higher-dimensional problems. By employing Godunov boundary treatment at the muzzle brake, such splitting is applied to the problem of muzzle brake flow simulation for the case of blasts which are impeded, by vertical and slanted baffles, respectively. Results from numerical studies of various types of wall boundary condition treatment which are consistent with Harten's TVD scheme are indicated.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070607
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The natural occurrence of flux splitting in a hyperbolic setting (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 1-11 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Classical derivations of the so-called Riemann invariants for hyperbolic partial differential equations have depended upon the strong-solution concept. Thus, invariance may rigorously be guaranteed only in regions of smooth flow. In general, this is as much as can be said. However, by restricting attention to linear hyperbolic systems, it further emerges that the Riemann invariant fully justifies its title. By using distribution-theoretical arguments based on the weak-solution concept. Riemann invariants of a more generalized nature are studied. For a particular weak solution u there exists, among the equivalence class [u] of weak solutions that differ from u at most on a set of measure zero, a weak solution u whose Riemann invariant corresponding to characteristic direction λ is constant on lines C: dx/dt = λ. Moreover, every piecewise-smooth weak solution has Riemann invariants that are continuous across a finite jump discontinuity. This result is used to establish for a certain Riemann problem that the one-sided time derivative at a point of discontinuity exhibits a character usually regarded in the literature as flux splitting. This result sheds light upon the validity of some upstream-biased approximation techniques for the numerical solution of hyperbolic systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010103
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On operator splitting of the Euler equations consistent with Harten's second-order accurate TVD scheme (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 1 (1985), S. 315-327 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Operator splitting is necessary in order to apply Harten's second-order accurate, total-variation-diminishing (TVD) method for shock capturing to higher-dimensional problems. Here two such splittings of the Euler equations are considered. By analytical means, one splitting is shown to be inconsistent; the other, scheme satisfies a fundamental necessary condition for consistency. Numerical results from a typical blast wave calculation employing this scheme are exhibited.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690010406
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    Paper (German National Licenses)
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