Preconditioners for the Onsager-Stefan-Maxwell equations for multicomponent diffusion

TL;DR

This paper introduces a robust preconditioning strategy for solving the Onsager-Stefan-Maxwell equations in multicomponent diffusion, applicable to diverse physical settings and verified through multiple application examples.

Contribution

It proposes an augmented Lagrangian preconditioner combined with multigrid and Schwarz methods, ensuring discretization-robust solutions for complex multicomponent flow models.

Findings

Preconditioner shows robustness across mesh refinements and polynomial degrees.

Effective in modeling cross-diffusion, nonideal mixing, and electrochemical effects.

Applicable to various real-world multicomponent flow problems.

Abstract

The Onsager-Stefan-Maxwell (OSM) equations are an important model of mass transport in multicomponent flows with multiple chemical species. They describe the coupling of diffusive fluxes between species, accounting for their interactions through frictional and thermodynamic driving forces. In this work we propose an augmented Lagrangian preconditioner and prove its discretization-robustness for a Picard linearization of the stationary OSM equations in the isobaric, isothermal, ideal gaseous setting. For the Newton linearization we employ the augmented Lagrangian preconditioner as a block diagonal smoother inside a monolithic geometric multigrid iteration and combine with vertex star Schwarz methods. This strategy is shown to be applicable in a wide variety of settings which incorporate cross-diffusion, nonideal mixing, thermal, pressure, convective, and electrochemical effects. We demonstrate robustness or mild dependence with respect to mesh refinement and polynomial degree of the proposed monolithic preconditioning strategy for different types of multicomponent flows in several applications: cross-diffusion in the human airways, separation of gases under a temperature gradient, nonideal mixing of benzene and cyclohexane, and electrolytic transport in a Hull cell undergoing electroplating.