A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit

Burger, R; Kroker, I; Rohde, C

Keywords: clarifier, thickener model; Finite volume method; Galerkin projection; Polynomial chaos; Uncertainty quantification

Abstract

The continuous sedimentation process in a clarifier-thickener can be described by a scalar nonlinear conservation law for the local solids volume fraction. The flux density function is discontinuous with respect to spatial position due to feed and discharge mechanisms. Typically, the feed flow cannot be given deterministically and efficient numerical simulation requires a concept for quantifying uncertainty. In this paper uncertainty quantification is expressed by a new hybrid stochastic Galerkin (HSG) method that extends the classical polynomial chaos approximation by multiresolution discretization in the stochastic space. The new approach leads to a deterministic hyperbolic system for a finite number of stochastic moments which is however partially decoupled and thus allows efficient parallelisation. The complexity of the problem is further reduced by stochastic adaptivity. For the approximate solution of the resulting high-dimensional system a finite volume scheme is introduced. Numerical experiments cover one- and two-dimensional situations.

Más información

Título según WOS: A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit
Título según SCOPUS: A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit
Título de la Revista: ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
Volumen: 94
Número: 10
Editorial: WILEY-V C H VERLAG GMBH
Fecha de publicación: 2014
Página de inicio: 793
Página final: 817
DOI:

10.1002/zamm.201200174

Notas: ISI, SCOPUS