Investigation of far-field underwater explosion shock wave-induced cavitation based on Runge–Kutta discontinuous Galerkin method

The shock waves and cavitation of far-field underwater explosion seriously threaten submerged structures. By employing the Runge–Kutta discontinuous Galerkin method to solve a first-order system, we establish a three-dimensional axisymmetric far-field underwater explosion model, which can be coupled with both linear and nonlinear equations of state (EOS) of the fluid. A pressure cutoff model is employed to simulate the cavitation phenomenon near the free surface or structure. Different boundary conditions are applied by setting the values in Guardcell, which is a layer of meshes surrounding the boundary. The high-order and compact features of the discontinuous Galerkin method are fully exploited by introducing the block-based adaptive mesh refinement technology such that the resolution around the shock front and the cavitation regions is improved. The accuracy order, the h-adaptivity refinement, and the cavitation results of the present model are validated by comparing the results of a series of test cases with reference values. By analyzing the results of different cases, we found that it is more economical to improve the resolution by increasing the accuracy order than by refining the mesh. The cavitation region obtained by the Tait EOS is significantly larger than linear EOS in the later stages of evolution. The presence of a spherical shell near the free surface has an impact on the shape and collapse of the bulk cavitation. Furthermore, the expansion and collapse of bulk cavitation also affect the kinematic response of the spherical shell, especially when the spherical shell is closer to the free surface.