Numerical Simulation of Dynamic Processes in a Medium of Fine-Grained Solid Particles

• Published in: Mathematical models and computer simulations Vol. 15; no. 2; pp. 210 - 226
• Main Authors: Nemtsev, M. Y., Menshov, I. S., Semenov, I. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2023; Springer Nature B.V
• Subjects: Exact solutions; Gas dynamics; Godunov method; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Propagation velocity; Simulation and Modeling; two-phase dispersed media; Godunov method; continuum model of ensemble of solid particles; Riemann problem
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048223020138

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 dispersed media is considered. The specific features of this system consist of a discontinuity in the characteristic velocity of the propagation of small disturbances when the volume fraction equals the value of dense packing and the 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 Harten–Lax–van Leer (HLL)-type solver, which takes into account the mentioned specific features, is proposed for the system considered. The methods developed are verified on a set of test problems that are analogs of the benchmarks by Sod and Shu–Osher, which are well-known in gas dynamics. 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 numerical results are compared with the available analytical data.