The Removal Of Irregular Frequencies And Its Application To The High-frequency And Near-trapping Problems In The Wave-structure Interactions

Boundary element method which is based on higher-order shape functions is applied to the researches of interactions between regular waves and single body or multiple bodies in the frequency domain.The emphasis is put on the effects and removal of irregular frequencies in numerical computation.The linear assumption can not predict the effects of wave accurately in many situations because of the existence of nonlinearity.Some novel phenomena will arise when waves interact with multiple bodies because of the effect of multiple scattering.Boundary element method is very suitable to simulate the interactions between waves and structures because the physical quantities of primary interest are only required on the boundaries of stimulation domain.On the other hand,boundary element method only needs integration on the boundaries by Using discrete elements,which has the advantages of generating meshes easily and can reduce the burden of calculation to some extent.However, irregular frequencies become a great obstacle in the application of boundary element method. Irregular frequencies will introduce sharp jump in numerical results.Extended boundary integral equations are adopted to remove the irregular frequencies.Continuous and discontinuous higher order boundary elements are used in different sub-domains according to the continuities on different boundaries.Careful considerations are taken for forcing terms on the free surface and body surface in the integral equations for second order problem. Furthermore,different strategies for numerical integration are applied to deal with singular and nearly singular integrals.Present method for removing irregular frequencies is applied in the nonlinear analysis of interaction between regular waves and single or multiple bodies.The effect of irregular frequencies on exciting forces,wave elevations and motions of bodies is analyzed by theoretical and numerical method.At the same time,validity of present method for removing irregular frequencies is conformed by extensive numerical results.Some novel physical phenomena which can threaten the safety of structures are found in the analysis of interactions between wave and multiple bodies.