Preconditioners for the Onsager-Stefan-Maxwell equations for multicomponent diffusion
This work provides a robust preconditioning strategy for solving multicomponent diffusion problems, which is important for computational fluid dynamics and electrochemical applications.
The authors propose an augmented Lagrangian preconditioner for the Onsager-Stefan-Maxwell equations, proving discretization-robustness for a Picard linearization and demonstrating robustness or mild dependence on mesh refinement and polynomial degree across several multicomponent flow applications.
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.