On A Powder Consolidation Problem

. The problem of the consolidation of an aerated fine powder under gravity is considered. The industrial relevance of the problem is discussed and a mathematical model is introduced. The mathematical structure is that of a coupled system for three unknowns, pressure, stress and height of the powder in the (axisymmetric) bunker containing it. The system itself consists of a parabolic PDE, an ODE and an integral equation determining a free boundary corresponding to the height of the powder. Existence and uniqueness of a solution is established. A numerical method based on a formulation of the semidiscretized problem as an index 1 DAE is proposed and implemented. The feasilibility of the approach is illustrated by computational results. Key words. consolidation, multiphase, parabolic, free boundary, DAE, integral equation. AMS subject classifications. 35K55, 65L80, 65M06, 76S05 1. Introduction. One important factor determining the mechanical properties of fine powders is the possible pres..