Gremaud, Pierre A.; Kelley, C. T.; Royal, T. A.; Coffey, Kristy A. On a powder consolidation problem. (English) Zbl 0995.35086 SIAM J. Appl. Math. 62, No. 1, 1-20 (2001). 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. Reviewer: Angela Handlovičová (Bratislava) 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 Keywords:semidiscretization in space; multiphase; index 1 DAE; integral equation PDFBibTeX XMLCite \textit{P. A. Gremaud} et al., SIAM J. Appl. Math. 62, No. 1, 1--20 (2001; Zbl 0995.35086) Full Text: DOI