Preprint 2025-23
Eider Aldana, Ricardo Oyarzúa, Jesús Vellojín:
Numerical analysis of a three-field formulation for a reverse osmosis model
Abstract:
In this work, we study a coupled Navier-Stokes/convectiondiffusion model arising in the description of reverse osmosis membrane processes. The model accounts for the incompressible viscous flow of a saline solution and the transport of solute concentration, including appropriate interface conditions that capture the membrane permeability and rejection effects. We propose and analyze a variational formulation of the stationary problem, establishing existence, uniqueness, and positivity of solutions under suitable assumptions on the data. To approximate the problem numerically, we introduce a conforming finite element discretization and prove discrete stability estimates, as well as the well-posedness of the resulting nonlinear system. Furthermore, we develop a fixed-point strategy to handle the nonlinear coupling and provide error estimates for the discrete scheme. Numerical experiments are presented to confirm the theoretical results and to illustrate the performance of the method in relevant test cases for desalination applications.
