Issue 49

S.A. Bochkarev et alii, Frattura ed Integrità Strutturale, 49 (2019) 814-830; DOI: 10.3221/IGF-ESIS.49.15 816 Figure 1 : Schematic representation of the computational domain. An ideal compressible fluid is considered in the framework of a potential theory, in which the wave equation in the case of small perturbations takes the following form [27]:     2 2 1 t c   , (1) where  is the velocity potential, c is the speed of sound in the liquid,  is the differential Nabla operator,   t is the time derivative. Using the perturbation velocity potential as an unknown function allows to take into account both the flow or the rotation of the inviscid compressible fluid with a slight modification of the numerical algorithm. In the case of complete filling of the shell with a fluid, the following boundary conditions are prescribed for the velocity potential:     0, : 0 x L x  . (2a) In the case of partial filling, it is assumed that the free surface of the fluid free S remains stationary and is free from the dynamic pressure and surface tension. The corresponding boundary condition is given as [28]   : 0 x H  . (2b) On the wetted surfaces   ( ) ( ) i i f s S S S  the impermeability conditions hold true        ( ) ( ) i i w t n , (3) where ( ) i n is the vector of the normal to the shell surface; ( ) i w is the normal component of shell displacements; f S and ( ) i s S are the surfaces that bound the volumes of the fluid f V and shell ( ) i s V . In what follows,  1, 2 i . The hydrodynamic pressure p exerted on the elastic structures by the fluid is calculated using the Bernoulli equation: