Charla 178: A second-order invariant-region-preserving scheme for a transport-flow model of polydisperse sedimentation

Conferencista: Raimund Bürger, $\mbox{CI}^2\mbox{MA}$ & Departamento de Ingeniería Matemática. Universidad de Concepción, Chile

Fecha: Lunes 15 de septiembre de 2025, 2:00 am.

Lugar: C-119A

Resumen: A polydisperse suspension, consisting of N species of solid particles with varying sizes or densities, sediments in a viscous fluid due to gravity. This process leads to the segregation of species and fluid flow driven by density differences. In two dimensions, for particles differing only in size, this phenomenon is modeled by a coupled transport-flow system. This system includes a hyperbolic system of N nonlinear conservation laws for the solid particle volume fractions and a Stokes system for the mixture’s average flow.
A high-order numerical scheme is formulated on a Cartesian grid. This scheme combines a finite-difference approximation for the Stokes system with a finite-volume (FV) scheme for the transport equations. The FV scheme employs a central weighted essentially non-oscillatory (CWENO) reconstruction applied to a first-order local Lax-Friedrichs (LLF) numerical flux.
The invariant region preserving (IRP) property of the FV scheme is demonstrated by using scaling limiters on the CWENO reconstruction polynomials and leveraging the discretely divergence-free (DDF) velocity field generated by the Stokes solver. The IRP property ensures that the solids volume fractions remain non-negative and their sum does not exceed a specified maximum value. Numerical examples are provided to illustrate the model, the scheme, and its properties.