Hierarchical Divergence-Free Bases and Their Application to Particulate Flows

[+] Author and Article Information
V. Sarin

Department of Computer Science, Texas A&M University, College Station, TX 77843e-mail: sarin@cs.tamu.edu

A. H. Sameh

Department of Computer Science, Purdue University, West Lafayette, IN 47907e-mail: sameh@cs.purdue.edu

J. Appl. Mech 70(1), 44-49 (Jan 23, 2003) (6 pages) doi:10.1115/1.1530633 History: Received July 02, 2001; Revised April 09, 2002; Online January 23, 2003
Copyright © 2003 by ASME
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Hestenes,  M. R., and Stiefel,  E., 1952, “Methods of Conjugate Gradients for Solving Linear Systems,” J. Res. Natl. Bur. Stand., 49, pp. 409–436.
Saad,  Y., and Schultz,  M. H., 1986, “GMRES: A Generalized Minimum Residual Algorithm for Solving Nonsymmetric Linear Systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput., 7, pp. 856–869.
Meijerink,  J. A., and Van der vorst,  H. A., 1977, “An Iterative Solution Method for Linear Equation Systems of Which the Coefficient Matrix is a Symmetric M-Matrix,” Math. Comput., 31, pp. 148–162.
Gustafson,  K., and Hartman,  R., 1983, “Divergence-Free Bases for Finite Element Schemes in Hydrodynamics,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 20(4), pp. 697–721.
Hall,  C. A., Peterson,  J. S., Porsching,  T. A., and Sledge,  F. R., 1985, “The Dual Variable Method for Finite Element Discretizations of Navier-Stokes Equations,” Int. J. Numer. Methods Eng., 21, pp. 883–898.
Golub, G. H., and Van Loan, C. F., 1996, Matrix Computations 3rd Ed., Johns Hopkins University Press Ltd., London.
Sarin,  V., and Sameh,  A. H., 1998, “An Efficient Iterative Method for the Generalized Stokes Problem,” SIAM J. Sci. Comput. (USA), 19(1), pp. 206–226.
Sameh,  A. H., and Sarin,  V., 2002, “Parallel Algorithms for Indefinite Linear Systems,” Parallel Comput., 28, pp. 285–299.
Sarin, V., 1997, “Efficient Iterative Methods for Saddle Point Problems,” Ph.D. thesis, University of Illinois, Urbana-Champaign.
Dembo,  R. S., Eisenstat,  S. C., and Steihaug,  T., 1982, “Inexact Newton Methods,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 19(2), pp. 400–408.
Eisenstat,  S. C., and Walker,  H. F., 1996, “Choosing the Forcing Terms in an Inexact Newton Method,” SIAM J. Sci. Comput. (USA), 17(1), pp. 16–32.
Hu, H., 1996, “Direct Simulation of Flows of Solid-Liquid Mixtures,” Int. J. Multiphase Flow, 22 .
Smith, B. F., Gropp, W. D., McInnes, L. C., and Balay, S., 1995, “Petsc 2.0 Users Manual,” Technical Report TR ANL-95/11, Argonne National Laboratory.
Gropp, W. D., Lusk, E., and Skjellum, A., 1994, Using MPI: Portable Parallel Programming With the Message Passing Interface, M.I.T. Press, Cambridge, MA.
Shewchuk, J. R., 1996. “Triangle: Engineering a 2D Quality Mesh Generator and Delaunary Triangulator,” First Workshop on Applied Computational Geometry, ACM, Philadelphia, PA, pp. 124–133.
Karypis, G., and Kumar, V., 1996. “Parallel Multilevel k-Way Partitioning Scheme for Irregular Graphs,” Technical Report 96-036, University of Minnesota.
Knepley, M. G., Sarin, V., and Sameh, A. H., 1998. “Parallel Simulation of Particulate Flows,” Proc. of the 5th Intl. Symp., IRREGULAR ’98, LNCS 1457, Springer, Berlin, pp. 226–237.


Grahic Jump Location
The coarsening of a 4×4 mesh to a 2×2 mesh
Grahic Jump Location
Sedimentation of multiple particles: (a) mesh with 8689 elements and 6849 nodes, and (b) partitioning into eight domains. Only the region of interest is shown.
Grahic Jump Location
Sedimentation of a single particle: (a) mesh with 2461 elements and 1347 nodes, (b) partitioning into eight domains. The gravitational force pulls the particles towards the right.
Grahic Jump Location
Particles moving in a periodic channel



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