期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 64, 期 1, 页码 41-80出版社
SIAM PUBLICATIONS
DOI: 10.1137/S0036139902408163
关键词
polydisperse suspensions; sedimentation; systems of conservation laws; strongly degenerate parabolic-hyperbolic systems; central difference approximation
We show how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments (sedimentation with compression or sedimentation- consolidation process). For N solid particle species, this theory reduces in one space dimension to an N x N coupled system of quasilinear degenerate convection- diffusion equations. Analyses of the characteristic polynomials of the Jacobian of the convective flux vector and of the diffusion matrix show that this system is of strongly degenerate parabolic-hyperbolic type for arbitrary N and particle size distributions. Bounds for the eigenvalues of both matrices are derived. The mathematical model for N = 3 is illustrated by a numerical simulation obtained by the Kurganov - Tadmor central difference scheme for convection diffusion problems. The numerical scheme exploits the derived bounds on the eigenvalues to keep the numerical diffusion to a minimum.
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