Irregular frequency removal methods: theory and applications in hydrodynamics
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2017, Sociedade Brasileira de Engenharia Naval. In the problem of multi-body hydrodynamics, it is of growing interest to understand the gap resonance. One important issue is to remove the irregular frequency effect, which can be confused with the physical resonance. In this paper, an extensive survey of the previous approaches to the irregular frequency problem has been undertaken. The matrix formulated in the boundary integral equations will become nearly singular for some frequencies. The existence of numerical round-off errors makes the matrix still solvable by a direct solver, however results in unreasonably large values in some aspects of the solution, namely the irregular frequency effect. This paper will mainly discuss the lid method on the internal free surface. To reach a higher accuracy, the singularity resulting from the Green function needs special care. Finally, results with and without irregular frequency removal are shown to demonstrate the effectiveness of our proposed method. The validation cases in this paper include a single mini-boxbarge and two mini-boxbarges side by side. The major contribution of this paper is that we have investigated the difference in jump condition caused by basic settings, supplemented Kleinmans uniqueness proof with a more detailed reasoning process, provided a different equation set for irregular frequency removal, proved the jump condition in a rigorous way, and further discussed Newmans question about the singular terms in the jump conditions.
