Approximation of underwater explosion bubble by singularities based on BEM

•We deduced the singularities approximation for underwater explosion bubble.•Bubble deformation is considered in our numerical model of approximation.•We analyzed the relationship between singularities strength and bubble parameters.•The traditional model is revised to consider the bubble deformation.

On the basis of boundary element method, this paper constructs a numerical model of underwater explosion bubble, and then develops singularities approximation method of bubble induced flow field from the view point of potential flow theory. A point source is adopted to simulate bubble pulsation, and meanwhile a point dipole is applied to simulate asymmetry caused by both the migration and deformation of the bubble. Through the analysis of the relationship between the strength of equivalent singularities and dimensionless parameters, we find that strength parameter has few effects on equivalent point source. And with the increase of buoyancy parameter, considerable strength is added to point dipole instead of point source. Through the comparison with the numerical results of point dipole strength under the traditional spherical hypothesis, the traditional method is revised to consider non-spherical deformation in order to shed some light on research on underwater explosion bubble dynamics and anti-shock performance of ships.