Added mass computation by the boundary integral method

Abstract

SUMMARYComputational techniques for the treatment of fluid-structure interaction effects by discrete boundary integral methods are examined. Attention is focused on the computation of the added mass matrix by finite element methods for a structure submerged in an infinite, inviscid, incomljressible fluid. A general computational procedure is presented that is based upon a variational approach involving the assumption of constant source strength over each surface element. This is followed by an analysis of the discretization error for a spherical body that is then used to develop a hierarchy of computational schemes. These schemes are then evaluated numerically in terms of 'fluid boundary modes' for a submerged spherical surface. One scheme has been found to be surprisingly accurate in relation to its computational demands. INTRODUCllONIn recent years, growing interest has been shown in the forced response analysis &'submerged complex structures (see, e.g. Reference 1). During this same period, substantial progress has been made in the continuing development of discrete element (finite element, finite difference) methods of structural analysis, which make possible very sophisticated forced response analyses of complex structures in vucuo. A key element in the extension of this capability to submerged structures is the development of techniques for the treatment of the fluid-structure interaction that are compatible with discrete element structural analysis methods. This paper deals with the finite element analysis of the fluid-structure interaction in situations where fluid viscosity effects are negligible and where the dominant frequency components characterizing the motion of the structure are low-frequency in nature. The latter condition refers to cases in which A: r << A; , where A,r is a characteristic structural wavelength for the motion of the structure's surface and A,, = c/f is a characteristic acoustic wavelength for that motion; in this last expression, f is a characteristic frequency of the motion and c is the speed of sound in the fluid. When these conditions are satisfied, which occurs in a great number of practical situations, the fluid can be treated in the inviscid, incompressible limit.*The governing equation for an inviscid, incompressible fluid of infinite extent that is set into motion by the movement of a body submerged in it is simply Laplace's e q~a t i o n .~ The solution of this equation is readily effected with discrete boundary integral techniques through the construction of a finite element mesh over the surface of the submerged body.4 The end result of this procedure is an added mass matrix that accounts for the entrainment of fluid caused by the rigid-body and/or deformational motion of the body.5 The appropriate combination of the added mass matrix with the in vucuo structural mass matrix accounts for the effects of the * Research Scientist. t Staff Scientist.

An Overview of the Common Fluid Models Used in Fluid-Structure Interactions

“…The presentation in [14] is, in fact, given in terms of matrices originating from a finite element discretization. The force on the solid per unit area due to the fluid is -pni and hence, by Newton's second law and (83), the A can be interpreted as an "added mass per unit area" operator (or matrix) which is due to the presence of the fluid.…”

Partitioned formulation of internal and gravity waves interacting with flexible structures

“…Specifically, the difference in the normals should be taken care of as shown in (41). DeRuntz and Geers [95] used a similar approach in their computation of added mass when boundary element method was used to account for the pressure acting on the structural surface via added mass modification. …”

Augmentation of DAA Staggered – Solution Equations in Underwater Shock Problems for Singular Structural Mass Matrices

“…This matrix is produced by a boundary -element treatment of Laplace's equation for the irrotational flow generated in an infinite, inviscid, incompressible fluid by motions of the structure's wet surface; it is fully populated with non -zero matrix elements. When transformed into structural coordinates, the fluid mass matrix yields the added mass matrix, which, when combined with the structural mass matrix, yields the virtual mass matrix for motions of a structure submerged in an incompressible fluid [7].…”