Numerical study of two-dimensional cylindrical underwater explosion by a modified method of characteristics

Abstract

A modified method of characteristics (mMOC) is introduced for solution of 2D axisymmetric supersonic flow, as well as its application to simulation of a cylindrical underwater explosion, which is a typical non-homentropic flow problem. The modifications include a family of compatibility equations which contains entropy term in streamline direction, an improved backward scheme with second-order accuracy, a modified forward scheme that uses adaptive technique, which in total make this mMOC be appropriate for a branch fluid dynamics with isentropic or non-isentropic flows. The numerical results show good agreement between the mMOC and experiments. It is established that this mMOC yields shock location, shock peak pressure, and gas-water interface location with an acceptable accuracy. Compared with an explicit dynamics program AUTODYN, which needs to select an appropriate artificial viscosity to handle shock discontinuity properly, the mMOC typically requires far less computer time with the same accuracy in the calculation of the underwater shock wave. Besides, the formation of a secondary shock is well revealed in the pressure nephogram, which suggests the mMOC is able to capture small variation in flow field. In addition, this mMOC can clearly display the domain of dependence in characteristic net, which makes it possible to quantitatively describe the connection between near field shock and detonation products expansion.