Calculation model for whole-process loading of underwater explosion

A dramatic increase in flow-field pressure characterizes the early stage of an underwater explosion. The highly non-linear nature of this phenomenon makes it challenging to derive accurate solutions using analytical methods. This study addresses this phase by employing a numerical approach to solve the conservative-form Euler equations. Based on results under different scenarios, a set of calculation formulas was established by fitting least squares to estimate key parameters during the early stage. These primarily include the pressure–time profiles of the shock wave and the initial conditions for bubble motion. The moment of the initial bubble is defined based on fluid compressibility considerations when the propagation distance of the shock wavefront reaches six times the radius of the current bubble. In addition, it is necessary to investigate how the propagation of the shock wave and these initial conditions of the bubble vary as functions of critical parameters such as the depth of the water and the weight of the charge. Comparative analyses of the present model against the results of numerical methods and experiments demonstrate its accuracy and applicability. Combined with the equations of bubble dynamics in weakly compressible fluids, this methodology enables an accurate and efficient simulation of the whole process of underwater explosion. This study provides valuable references for fundamental research and engineering applications in underwater explosions.