A finite volume scheme for two‐phase compressible flows

Abstract

AbstractIn gas‐particle two‐phase flows, when the concentration of the disperesed phase is low, certain assumptions may be made which simplify considerably the equations one has to solve. The gas and particle flows are then linked only via the interaction terms. One may therefore uncouple the full system of equations into two subsystems: one for the gas phase, whose homogeneous part reduces to the Euler equations; and a second system for the particle motion, whose homogeneous part is a degenerate hyperbolic system. The equations governing the gas phase flow may be solved using a high‐resolution scheme, while the equations describing the motion of the dispersed phase are treated by a donor‐cell method using the solution of a particular Riemann problem. Coupling is then achieved via the right‐hand‐side terms. To illustrate the capabilities of the proposed method, results are presented for a case specially chosen from among the most difficult to handle, since it involves certain geometrical difficulties, the treatment of regions in which particles are absent and the capturing of particle fronts.