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

A mathematical model and numerical method for solving problems of the flow of two-phase mixtures of gas and fine solid particles are considered. The particles are assumed to be absolutely rigid, incompressible, and nondeformable. As the initial model, the continuum model of R.I. Nigmatulin is considered. The model has two drawbacks: it is not strictly hyperbolic (i.e., it degenerates into an elliptical one under certain flow regimes) and has a nonconservative form, which makes it difficult to solve numerically. This paper proposes a method for regularizing Nigmatulin’s model at a discrete level, which makes it possible to eliminate these shortcomings and develop a numerical model that is well-conditioned for evolutionary problems of the flow of gas-dispersed mixtures with nondeformable solid particles. The regularization method is based on splitting the original system into two subsystems, each of which is strictly hyperbolic and has a conservative form. Difference schemes of the Godunov type are developed for the numerical solution of these subsystems. Testing of the proposed model and implemented methods includes checking the preservation of a homogeneous solution and the formation of shock waves and rarefaction waves in a gas, as well as compaction and decompaction waves in the particle phase. The results of the numerical simulation of the interaction of a shock wave in a gas with a near-wall layer of particles are also presented.