Finite Element Modeling of a Two-Dimensional Explosion in an Ideal Gas

This paper presents a two-dimensional numerical model of blast-wave propagation in a gaseous medium based on the compressible Euler equations and an ideal-gas equation of state. The governing conservation laws are discretised with a triangular finite-element formulation and stabilised using a local Lax–Friedrichs (Rusanov) numerical flux; time integration employs an explicit Euler scheme. The implementation generates an n × n mesh over a square domain, assembles the semi-discrete system, and advances the solution to capture the spatio-temporal evolution of pressure, density, and energy. Simulations reproduce the salient physics of explosions in air: rapid energy release at the epicentre, formation and outward propagation of a supersonic shock, a positive overpressure phase followed by rarefaction, and compression/expansion trends consistent with gas dynamics. Quantitatively, the model yields large transient overpressures (up to ~400× atmospheric at early times in the reported case) and density jumps across the shock front. The approach offers a practical tool for analysing sensitivity to initial/boundary conditions and for exploring parameter effects relevant to underground safety and protective-structure design. Limitations and extensions are discussed, including the need to incorporate viscous effects, real-gas thermodynamics, and fluid–structure interaction for confined or complex geometries.