Application of a variational method to the vertical hydrodynamic impact of axisymmetric bodies

• Published in: Applied ocean research 2013-01, Vol.39, p.75-82
• Main Authors: Santos, Flávia M., Casetta, Leonardo, Pesce, Celso P.
• Format: Article
• Language: English
• Subjects: Axisymmetric bodies; Desingularized variational numerical method; Hydrodynamic impact problem; Weak formulation
• ISSN: 0141-1187; 1879-1549
• DOI: 10.1016/j.apor.2012.10.002

The application of a desingularized variational numerical method to the vertical hydrodynamic impact problem of axisymmetric bodies is addressed here within the so-called Generalized von Kármán Model (GvKM). A weak formulation is used and the velocity potential is numerically approximated in a Sobolev space. Trial functions are conveniently written as finite summations of elementary potentials. A main advantage of the proposed technique is the fact that a first-order error in the velocity potential computation implies a second-order error in the added mass value. Good agreement in added mass calculations is verified for a sphere and for an oblate spheroid in comparison with results obtained from WAMIT®. ▸ A desingularized variational numerical method is presented to treat the hydrodynamic impact problem. ▸ Trial functions are constructed from elementary potential solutions. ▸ An integral measurement for the boundary condition error contained in the weak solution is proposed. ▸ Added mass calculation follows a Rayleigh-like quotient scheme leading to second order errors results.