Secondary circulation in granular flow through nonaxisymmetric hoppers

SIAM Journal on Applied Mathematics

Volumn 64, Issue 2, 2004, Pages 583-600

  Gremaud, Pierre A ^a   Matthews, John V ^b   Schaeffer, David G ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b DUKE UNIVERSITY   (United States)

Author keywords

Granular; Perturbation theory; Similarity solution

Indexed keywords

GRANULAR; PERTUBRATION THEORY; SIMILARITY SOLUTIONS;

COMPRESSIVE STRESS; EIGENVALUES AND EIGENFUNCTIONS; GRANULAR MATERIALS; HOPPERS; PERTURBATION TECHNIQUES; RAW MATERIALS; TENSORS;

FLOW OF FLUIDS;

EID: 2542439783     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139903415124     Document Type: Article

References (13)

1. S. AGMON, A. DOUGLIS, AND L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), pp. 35-92.
2. U.M. ASCHER AND L.R. PETZOLD, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, 1998.
3. C.M. BENDER AND S.A. ORSZAG, Advanced Mathematical Methods for Scientists and Engineers, International Series in Pure and Applied Mathematics, McGraw-Hill, New York, 1978.
4. K.E. BRENAN, S.L. CAMPBELL, AND L.R. PETZOLD, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Classics Appl. Math. 14, SIAM, Philadelphia, 1996.
5. K.D. CLARK AND L.R. PETZOLD, Numerical solution of boundary value problems in differential-algebraic systems, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 915-936.
6. P.A. GREMAUD, J.V. MATTHEWS, AND M. SHEARER, Similarity solutions for granular materials in hoppers, in Nonlinear PDE's, Dynamics, and Continuum Physics, Contemp. Math., 255, J. Bona, K. Saxton and R. Saxton, eds., AMS, Providence, RI, 2000, pp. 79-95.
7. A.W. JENIKE, Gravity flow of bulk solids, Bulletin 108, Utah Eng. Expt. Station, University of Utah, Salt Lake City, 1961.
8. T.M. KNOWLTON, J.W. CARSON, G.E. KLINZING, AND W.C. YANG, The importance of storage, transfer and collection, Chem. Eng. Prog., 90 (1994), pp. 44-54.
9. E.W. MERROW, A quantitative assessment of R&D requirements for solids processing technology, Publication R-3216-DOE/PSSP, Rand Corporation, Santa Monica, CA, 1986.
10. R.M. NEDDERMAN, Static and Kinematic of Granular Materials, Cambridge University Press, Cambridge, UK, 1992.
11. N. REGE, Computational Modeling of Granular Materials, Ph.D. thesis, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 1996.
12. D.G. SCHAEFFER, Instability in the evolution equations describing incompressible granular flow, J. Differential Equations, 66 (1987), pp. 19-50.
13. J.R. WILLIAMS AND N. REGE, The development of circulation cell structures in granular materials undergoing compression, Powder Technol., 90 (1997), pp. 187-194.