An indirect boundary element method for three-dimensional explosion bubbles

This paper suggests the implementation of indirect boundary element method (IBEM) to simulate three-dimensional underwater explosion bubbles. The source is assumed distributed continuously on the boundary surface. An expression for the self-induced velocity of a point on the boundary surface is obtained via mathematical analysis, and with it a new definition of the normal vector valid even for a non-smooth surface is given. Elastic mesh technique (EMT), which is a new mesh regulation technique, is further applied to maintain the regularity of the triangular-element mesh used to discretize the dynamic boundary surfaces during the evolution of explosion bubble(s). The Bi-CG iterative solver is employed to solve the resulting linear system. All these efforts make the present approach viable and robust, and which is validated by computations of several bubble dynamics problems.