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 mat hematical model is introduced. The mathematical structure is that of a coup led system for three unknowns, pressure, stress, and height of the powder i n the ( axisymmetric) bunker containing it. The system itself consists of a parabolic PDE, an ODE, and an integral equation determining a free boundar y corresponding to the height of the powder. Existence and uniqueness of a solution is established. A numerical method based on a formulation of the s emidiscretized problem as an index 1 DAE is proposed and implemented. The f easibility of the approach is illustrated by computational results.