Interactive approximations for a cavitating fluid around a floating structure

Abstract A method is investigated for determining the response of floating structures to underwater explosions strong enough to cause bulk cavitation. In such problems the difference between the actual and free field pressures on any surface surrounding the structure and cavitated region is related to the corresponding velocity differences by a linear functional relation. In this paper, it is proposed that approximate functionals, called interactive approximations, be applied on these surfaces, called interaction horizons. In the limit, the interaction horizon can be taken as the wet surface of the structures, eliminating the consideration of fluid field equations. The technique is applied to the two-dimensional problem of a rigid rectangular structure, floating on a fluid with a bilinear constitutive relation, subjected to a plane, exponentially decaying wave having an angle of incidence. First the exact solution of the nonlinear, steady state, free field problem, including determination of the cavity, is obtained by the method of characteristics. Then the interaction problem is solved by finite differences, using both plane wave and doubly asymptotic interactive approximations, at interaction horizons and on the wet surface. When an interaction horizon is used, Lax's one-dimensional scheme is modified to discretize the fluid equations. It is found that, for this example, the plane wave approximation applied directly to the wet surface is sufficiently accurate to determine structural response.