Local discontinuous Galerkin method for far-field underwater explosion shock wave and cavitation

The shock wave and cavitation are main effects in the far-field underwater explosion, which could cause serious damage to marine structures. In this paper, the fluid mechanical behavior of blast load is described by the propagation of pressure wave. The acoustic pressure caused by far-field explosion is determined by solving the wave equation, where a strongly discontinuous axisymmetric numerical model is established with the local discontinuous Galerkin (LDG) method. The model can calculate the dynamic pressure in the fluid field and capture the high-resolution shock wave. The pressure cutoff model is employed to deal with the cavitation effect due to the reflection of the shock wave. The numerical model is verified by comparing with the analytical solution of the cavitation effect near the structure in one dimension. With the same mesh discretization, the present model shows higher precision than the results calculated by the acoustic finite element method. In addition, the propagation of shock wave in the cylindrical water column is studied. Finally, the formation, growth and collapse of the cavitation region near the free surface are simulated. The LDG model can remove the spurious oscillations behind the shock front and it’s more accurate than the results of the acoustic finite element method, in terms of capturing the sharpness of shock wave and calculating the shock and cavitation loading. And the present model can be applied to calculate the structural damage caused by shock wave in three dimensions.