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  • 1
    Electronic Resource
    Electronic Resource
    Combining arc-length control and line searches in path following (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 793-803 
    Details
    ISSN: 1069-8299
    Keywords: arc-length control ; line search ; path-following ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When solving non-linear algebraic equations resulting from a typical finite element discretization it is quite common that the popular Newton-Raphson iteration fails to converge or requires an excessive number of iterations. To solve this problem, line searches have been proposed in conjunction with load control and quadratic arc-length control, which has proved to be highly successful. In the paper we first review a number of the most popular arc-length controls. Then we highlight the severe drawbacks associated with the coupling of the cylindrical arc-length control and line searches. Next, various other forms of arc-length controls are scrutinized in the light of this coupling. It is shown that for some of the arc-length controls such a combination is extremely simple and straightforward, yet at the same time efficient and effective. For the rest the same complications incurred for the cylindrical arc-length method remain.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640111003
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    FULLY DISCRETE HIGH-ORDER SHOCK-CAPTURING NUMERICAL SCHEMES (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 241-269 
    Details
    ISSN: 0271-2091
    Keywords: fully discrete ; high-order ; conservative ; upwind ; shock-capturing ; TVD ; 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 present paper is a sequel to a previous one by the same authors in which a family of up to fourth-order fully discrete (FD) upwind numerical schemes was presented. In this paper we extend those high-order FD schemes to solutions with discontinuities, e.g. shocks. A rigorous anlaysis of the total variation diminishing (TVD) constraint for the high-order FD schemes is carried out. For non-linear systems the TVD constraint is, as usual, applied empirically. These schemes are validated by solving a test problem for the time-dependent shallow water equations.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    FINITE ELEMENT SIMULATION OF GUST LOADING (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 1197-1210 
    Details
    ISSN: 0271-2091
    Keywords: finite element method ; gust ; 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: In the structural design of civil aircraft the critical loads are often those encountered in a gust or atmospheric turbulence. The traditional ‘indicial’ solution is restricted to a simple plate. In this paper a finite element formulation is proposed for an aerofoil or arbitrary shape entering a uniform sharp-edged or sinusoidal gust. The thin rotational gust front and wake in an irrotational flow field are successfully modelled by a novel superposition technique. The finite element solutions are compared with the Kussner function and results by other numerical methods. The agreement is good.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    FULLY DISCRETE HIGH-RESOLUTION SCHEMES FOR HYPERBOLIC CONSERVATION LAWS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 309-323 
    Details
    ISSN: 0271-2091
    Keywords: fully discrete ; upwind scheme ; TVD high-order ; hyperbolic ; 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 present paper is a sequel to two previous papers in which rigorous, up to fourth-order, fully discrete (FD) upwind TVD schemes have been presented. In this paper we discuss in detail the extension of these schemes to solutions of non-linear hyperbolic systems. The performance of the schemes is assessed by solving test problems for the time-dependent Euler equations of gas dynamics in one and two space dimensions. We use exact solutions and experimental data to validate the results.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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