Preprint 2026-32
Juan Barajas-Calonge, Raimund Bürger, Pep Mulet, Luis M. Villada:
An invariant-region-preserving finite-volume-element scheme for a polydisperse model of flow and segregation in general domains
Abstract:
A spatially two-dimensional model for the flow of a mixture of a continuous phase with a disperse phase that consists of particles (or droplets) of N species in general geometries consists of a system of N conservation laws for the concentrations of particles, coupled with a Stokes-type system of equations governing the velocity of the mixture. This model is studied for the special case of sedimentation of polydisperse solid-liquid suspensions. This coupled transport-flow problem is approximated by a numerical scheme in which the Stokes equations are discretized on a primal triangular mesh using a finite element approach, while the concentration equations are approximated on a dual diamond mesh by a finite volume scheme. The resulting finite volume element (FVE) scheme is second-order accurate in space and time. The concentration vector is required to take values in a set of physically relevant states (i.e., its components are non-negative and sum to at most a prescribed maximum value). It is proven that this invariant region is preserved by the numerical solutions produced by the FVE scheme. This property is ensured by applying a pair of linear scaling limiters to a second-order MUSCL reconstruction of the concentration field. The FVE scheme is applied to simulate the settling of polydisperse suspensions in various types of vessels.
