Ivan S. Sandler

A new computational procedure for wave propagation problems and a new procedure for non-reflecting boundaries

Abstract This paper provides a brief qualitative description of some of the important ideas and features of the FUSE code, a newly developed hydrodynamics shock code based upon a Lagrangian treatment of material motion and deformation. The Lagrangian nature of the analysis allows it to proceed without the non-physical numerical diffusion of dissimilar materials across interfaces. The FUSE procedure is outlined together with brief descriptions of some of the new techniques by which the code avoids the adverse effects of large distortion on conventional Lagrangian codes. FUSE is capable of dealing with arbitrarily large deformations and motions of materials of any properly posed constitutive type. It can accurately represent wave propagation and transport phenomena simultaneously. Examples involve the high-explosive gas expansion resulting from explosions in water and soil. An important aspect of the new code is the nature of its discretization scheme. This scheme differs from the standard finite element approach in that the ‘nodes’ carry only acceleration/velocity information, but do not carry position or deformation data. These, instead, are carried at the element or cell centers only. Further, the laws of conservation of mass, momentum and energy are exactly satisfied (to the numerical accuracy of the computer) for the discretized system. A new scheme for treating shock fronts is also included in the code. Finally, the code utilizes an automatic time step subcycling scheme to accommodate large distortions with a minimum of computer time. The purpose of this paper is to briefly describe these new features of the FUSE scheme. In addition, a new boundary treatment used in FUSE as well as in some other codes is briefly outlined, and the relationship of this method for ‘non-reflecting boundaries’ to the solution of structure-medium interaction problems is examined. This paper is presented in the expectation that one or more of these techniques may be of interest to analysts working in a wide range of fields.

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, Laxs 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.