Numerical simulation of the interaction of a shock wave with a permeable deformable granulated layer

The article presents a mathematical model that describes, in a one-dimensional approximation, the interconnected processes of unsteady deformation of flat permeable granular layers. The model consists of solid particles and wave processes in pore and surrounding gas. The model is based on nonlinear equations of dynamics of two interpenetrating continua. As interfacial forces, drag forces are taken into account when gas flows around ball particles and friction forces. The numerical solution of the equations is carried out according to the modified scheme of S. K. Godunov, adapted to the problems of the dynamics of interpenetrating media. The contact surfaces of pure gas with the porous granular layer and pore gas are the surface of the fracture of porosity and permeability. The numerical implementation of contact conditions is based on the solution of the problem of disintegration of a gap at a jump in porosity. Solutions are obtained for the effects of plane shock waves on a deformable granular layer. We study the transformation of waves passing through an elastoplastic granular layer with and without taking into account changes in the permeability of the layer. When solving problems, the dependence of the change in the permeability of a layer on its compression is used, which is also obtained numerically when modeling the compression of symmetric fragments of granular layers in a spatial setting. Numerical studies of the processes of nonlinear interaction of shock waves with deformable permeable granular layers have shown that the parameters of transmitted and reflected waves substantially depend on the degree of compression of the granular layers. Assessment of the protective properties of permeable barriers when exposed to strong shock waves should be carried out taking into account changes in their permeability due to deformation layers.