Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach

• A clarifier-thickener model with several random perturbations is proposed.
• Uncertainty quantification for hyperbolic problems with several random perturbations.
• Introduction to the hybrid stochastic Galerkin (HSG) finite volume method.
• Discussion of the accuracy and computational efficiency of the HSG discretization.
• Multivariate multi-wavelets provide stochastic adaptivity of the HSG method.

Continuous sedimentation processes in a clarifier-thickener unit can be described by a scalar nonlinear conservation law whose flux density function is discontinuous with respect to the spatial position. In the applications of this model, which include mineral processing and wastewater treatment, the rate and composition of the feed flow cannot be given deterministically. Efficient numerical simulation is required to quantify the effect of uncertainty in these control parameters in terms of the response of the clarifier-thickener system. Thus, the problem at hand is one of uncertainty quantification for nonlinear hyperbolic problems with several random perturbations. The presented hybrid stochastic Galerkin method is devised so as to extend the polynomial chaos approximation by multiresolution discretization in the stochastic space. This approach leads to a deterministic hyperbolic system, which is partially decoupled and therefore suitable for efficient parallelisation. Stochastic adaptivity reduces the computational effort. Several numerical experiments are presented.