Numerical simulation of the interaction of a deformable gas permeable fragment of a granular layer with a shock wave in a three-dimensional formation

The numerical method developed by the authors earlier for solving three-dimensional problems of dynamic interaction of deformable bodies and media in Eulerian variables based on the high-precision Godunov scheme is applied to solve problems of interaction of a deformable gas-permeable fragment of a granular layer with shock waves. The modeling is based on a unified modified Godunov's numerical method both for calculating gas motion and for calculating the dynamic deformation of elastic-plastic elements of a permeable granular layer. The increase in accuracy is achieved by merging the domains of influence of the numerical and differential problems. It is assumed that the sandy granular layer consists of a set of identical spherical deformable quartz particles representing a cubic packing. The space between the particles is filled with compressible gas medium (air). A symmetrical packaging element is highlighted in the form of a sequence of spherical particles. To demonstrate the numerical methodology, it is assumed that a multilayer granular medium in the direction of propagation of a planar shock wave consists of three layers of particles in a square-section channel with rigid walls. The study is conducted following the methodology with explicit identification of moving Lagrangian contact surfaces using multigrid algorithms. The results of numerical studies of the shock wave propagation process in a granular layer taking into account the movement of its deformable elements are presented. It is shown that for the given task parameters, the influence of deformation processes is insignificant. The shock wave passing through the layer forms a gas dynamic flow close to one-dimensional behind the barrier. The agreement of the results of the numerical solution with known experimental results regarding the parameters of the shock wave passing through the layer indicates the adequacy of the applied mathematical and numerical models.