A Coupled Eulerian–Lagrangian (CEL) analysis of an underwater explosion near a pipeline is a numerical simulation approach widely used in nonlinear dynamics and hydrodynamics to model the interaction of shock waves and bubble effects from an explosion with nearby structures.

In this case, to model ice material, the Johsnon-Holmquist brittle damage model, JWL equation of state for TNT, and ideal gas formulation for air, Us-Up model for water, and Mohr-Coulomb plasticity for soil are selected. Three sea mines or bombs are embedded in the water to consider the maximum effect of the shock wave on the pipeline, taking into account the depth of water and soil.

Modeling underwater explosions (UNDEX) is challenging because the event involves extreme pressures, rapid fluid–structure interaction, large deformation, and material failure. Traditional numerical methods struggle to handle both the expanding explosion bubble and the structural deformation of the pipeline at the same time.

The Coupled Eulerian–Lagrangian (CEL) method, commonly implemented in ABAQUS software, addresses this challenge by combining two representations:

• Eulerian domain (water, explosive gases, ice, and surrounding fluid environment):
  The mesh is fixed in space, and the material flows through it. This avoids mesh distortion during the violent displacement of water and the detonation bubble.

• Lagrangian domain (pipeline, ice, and soil or structural components):
  The mesh deforms with the structure, allowing stresses, strains, plastic failure, and damage to be accurately computed.