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Spectral WENO schemes with Adaptive Mesh Refinement for models of polydisperse sedimentation
Author(s) -
Bürger R.,
Mulet P.,
Villada L.M.
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201100189
Subject(s) - conservation law , jacobian matrix and determinant , scalar (mathematics) , nonlinear system , sedimentation , mathematics , adaptive mesh refinement , physics , statistical physics , mathematical analysis , geometry , geology , paleontology , computational science , quantum mechanics , sediment
Abstract The sedimentation of a polydisperse suspension with particles belonging to N size classes (species) can be described by a system of N nonlinear, strongly coupled scalar first‐order conservation laws. Its solutions usually exhibit kinematic shocks separating areas of different composition. Based on the so‐called secular equation [J. Anderson, Lin. Alg. Appl. 246 , 49–70 (1996)], which provides access to the spectral decomposition of the Jacobian of the flux vector for this class of models, Bürger et al. [J. Comput. Phys. 230 , 2322–2344 (2011)] proposed a spectral weighted essentially non‐oscillatory (WENO) scheme for the numerical solution of the model. It is demonstrated that the efficiency of this scheme can be improved by the technique of Adaptive Mesh Refinement (AMR), which concentrates computational effort on zones of strong variation. Numerical experiments for the cases N = 4 and N = 7 are presented.