Spectral WENO schemes with Adaptive Mesh Refinement for models of polydisperse sedimentation

Abstract

AbstractThe 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.