Numerical simulation of dynamic processes in the medium of fine-grained solid particles

A simplified model system of governing equations describing the motion of an ensemble of solid fine-grained particles arising in the continual description of two-phase disperse media is considered. Specific features of this system are discontinuity in the characteristic velocity of small disturbance propagation when the volume fraction equals the value of close packing and possibility of forming void regions free of particles. A modification to the Godunov method based on the exact solution to the Riemann problem and an approximate HLL-type solver is proposed for the system considered which takes into account the mentioned specific features. Verification of the methods developed is performed on a set of test problems that are analogues of well-known in gas dynamics benchmarks by Sod and Shu-Osher. The problem of decompaction of a side-wall layer of compressed particles is also considered. The mechanism of particle detachment and development of a near-wall void zone free of particles is described. The obtained numerical results are compared with the available analytical data.