The hydrodynamics of planing ships have been studied numerically using a finite pressure element method and the hydrodynamic parameters such as wetted area, pressure distribution and lift coefficient have been calculated. This method is based on the mathematical model and pressure representation developed by Doctors originally. The problem of numerical instability found in Doctors' work has been successfully addressed and new calculation results for flat-bottomed and prismatic planing ships have been presented. Specifically, the following has been achieved in this study: The evaluation of the integral for the wave elevation induced by a pressure tent has been analysed thoroughly and effective numerical techniques have been employed. In comparison to Doctors' results, the precision of the influence coefficient, which is the wave elevation at a field point induced by a source element, has been improved. The wave patterns at near- and far-field caused by a pressure element have been illustrated and the reasonable results have verified the accuracy of the influence coefficient and the feasibility of the present numerical schemes. From a practical point of view, the geometrical profile of a planing ship is known but the wetted area is unknown; therefore, an iteration procedure needs to be employed for the adjustment of the wetted area. An optimization algorithm in the least-squares sense has been used by which convergent results could be obtained more effectively and quickly. Another outcome of this study is that the oscillation of the pressure distribution occurring in Doctors' work has been eliminated. Through a detailed investigation by case testing, it has been found that the oscillatory solution is due to the ill-conditioned coefficient matrix of the linear algebraic equations which must be solved to determine the pressure distribution. By utilizing the SVD technique, this ill-posed problem has been solved numerically and consequently the pressure oscillation has been removed. Comparing the new numerical results with Savitsky's empirical relations shows that although some discrepancies have been predicted in the results of lift coefficient at higher beam Froude number, the accuracy, feasibility and validity of the present mathematical model and numerical techniques have nevertheless been verified, and sufficient consistence has been achieved.


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    Titel :

    Numerical instability in linearized planing problems


    Weitere Titelangaben:

    Numerische Instabilität bei linearisierten Abrichtungsproblemen


    Beteiligte:
    Wang, Xuelian (Autor:in) / Day, Alexander H. (Autor:in)


    Erscheinungsdatum :

    2007


    Format / Umfang :

    36 Seiten, 39 Bilder, 2 Tabellen, 25 Quellen




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Print


    Sprache :

    Englisch