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Spectral WENO schemes with adaptive mesh refinement for models of polydisperse sedimentation. (English) Zbl 1277.76115
Summary: 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, Linear Algebra Appl. 246, 49–70 (1996; Zbl 0861.15006)], which provides access to the spectral decomposition of the Jacobian of the flux vector for this class of models, R. Bürger et al. [J. Comput. Phys. 230, No. 6, 2322–2344 (2011; Zbl 1391.76465)] 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.

MSC:
76T20 Suspensions
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76S05 Flows in porous media; filtration; seepage
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