A spectral-element method for modelling cavitation in transient fluid-structure interaction

In an underwater-shock environment, cavitation (boiling) occurs as a result of reflection of the shock wave from the free surface and/or wetted structure causing the pressure in the water to fall below its vapour pressure. If the explosion is sufficiently distant from the structure, the motion of the fluid surrounding the structure may be assumed small, which allows linearization of the governing fluid equations. In 1984, Felippa and DeRuntz developed the cavitating acoustic finite-element (CAFE) method for modelling this phenomenon. While their approach is robust, it is too expensive for realistic 3D simulations. In the work reported here, the efficiency and flexibility of the CAFE approach has been substantially improved by: (i) separating the total field into equilibrium, incident, and scattered components, (ii) replacing the bilinear CAFE basis functions with high-order Legendrepolynomial basis functions, which produces a cavitating acoustic spectral element (CASE) formulation, (iii) employing a simple, non-conformal coupling method for the structure and fluid finite-element models, and (iv) introducing structure–fluid time-step subcycling. Field separation provides flexibility, as it admits non-acoustic incident fields that propagate without numerical dispersion. The use of CASE affords a significant reduction in the number of fluid degrees of freedom required to reach a given level of accuracy. The combined use of subcycling and non-conformal coupling affords orderof- magnitude savings in computational effort. These benefits are illustrated with 1D and 3D canonical underwatershock problems