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On a powder consolidation problem. (English) Zbl 0995.35086

The problem of the consolidation of an aerated fine powder under gravity is investigated in this paper. An appropriate mathematical model is proposed. This model consists of a system of parabolic partial differential equations, an ordinary differential equation and an integral equation determining a free boundary corresponding to the height of powder. The solution of this system has three unknowns: pressure, stress and height of powder in the axisymmetric bunker containing the powder. Existence and uniqueness of a solution is proved. A numerical method using semidiscretization in space and then a semidiscretized problem as an index 1 DAE is presented. Efficiency and the feasibility of proposed numerical method is illustrated and discussed on some computational results.

MSC:

35R35 Free boundary problems for PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
35K55 Nonlinear parabolic equations
65L80 Numerical methods for differential-algebraic equations
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