Guillaume Chiavassa, María Carmen Martí, Pep Mulet:
Hybrid WENO schemes for polydisperse sedimentation models
Polydisperse sedimentation models can be described by a strongly coupled system of conservation laws for the concentration of each species of solids. Typical solutions for the sedimentation model considered for batch settling in a column include stationary kinematic shocks separating layers of sediment of different composition. This phenomenon, known as segregation of species, is a specially demanding task for numerical simulation due to the need of accurate numerical simulations. Very high-order accurate solutions can be constructed by incorporating characteristic information, available due to the hyperbolicity analysis made in [R. Donat and P. Mulet, A secular equation for the Jacobian matrix of certain mul- tispecies kinematic flow models, Numer. Methods Partial Differential Equations, 26 (2010), pp. 159–175.] But characteristic-based schemes, see [R. B¨urger, R. Donat, P. Mulet, and C. A. Vega, On the implementation of WENO schemes for a class of polydisperse sedimentation models, J. Comput. Phys., 230 (2011), pp. 2322–2344], are very expensive in terms of computational time, since characteristic information is not readily available, and they are not really necessary in constant areas, where a less complex method can obtain similar results. With this idea in mind, in this paper we develop a hybrid finite difference WENO scheme that only uses the characteristic information of the Jacobian matrix of the system in those regions where singularities exist or are starting to develop, while it uses a component-wise approximation of the scheme in smooth regions
This preprint gave rise to the following definitive publication(s):
Guillaume CHIAVASSA, María Carmen MARTí, Pep MULET: Hybrid WENO schemes for polydisperse sedimentation models. International Journal of Computer Mathematics, vol. 93, 11, pp. 1801-1817, (2016).