An Eulerian version of geometrical blast dynamics for 3D simulations

Geometrical blast dynamics is a simplified model for blast wave propagation, based on geometrical shock dynamics (GSD). This new model, first developed in a Lagrangian framework, has proven useful to obtain quite accurate results at a moderate CPU cost, but is currently limited to two-dimensional configurations. In this work, we demonstrate the ability of an Eulerian fast-marching-like algorithm to deal with complex geometrical configurations. The level-set formalism avoids most of the numerical difficulties encountered with Lagrangian methods in 3D. The algorithm is described in detail, mainly for the integration of the recent extension of GSD to low Mach numbers, which includes a transverse term. The behavior of the resulting method is illustrated on various situations and compared to experimental data when available. This Eulerian approach makes accessible 3D simulations of blast waves in a complex environment at a reduced cost.