Study on adaptive mesh method in the problem of underwater shock waves near water surface

Abstract This paper focuses on the application of the adaptive mesh method in the study of underwater shock waves near the water surface. By integrating theoretical analysis with a five-equation model under axisymmetric coordinates, we developed an optimized computational framework for multi-material fluid simulations. The moving mesh method (r-method) is used to accurately capture complex underwater shock wave systems. Multiple numerical experiments are conducted, including deep-water explosions, near-surface explosions for both spherical charge and cylindrical charge, and regular–irregular reflection interface calculations. The results show that compared to the fixed mesh method, the adaptive mesh method provides results closer to the theoretical values and achieves local high-resolution computation of multi-material fluids. By adjusting the adaptive function, different mesh refinement effects can be obtained. This method also has certain advantages in calculating the regular–irregular reflection interface in underwater explosions. This study establishes a validated computational framework for underwater explosion research, enhancing the predictive accuracy for underwater shock wave propagation in engineering assessments and providing new insights into the fundamental physics of multi-material explosion phenomena.