Computational analysis demonstrates stable convergence of a mixed finite element scheme for reverse-osmosis desalination, highlighting accurate modeling of nonlinear membrane transport.
Key Points
To develop and analyze a fully discrete mixed finite element method in a Banach space framework for nonstationary coupled Brinkman–Forchheimer flow and transport equations in reverse-osmosis desalination.
Coupled an unsteady p-type convective Brinkman–Forchheimer model with transport equations across a semipermeable membrane using a pseudostress-velocity and concentration-gradient formulation.
Formulated continuous well-posedness in Banach spaces via fixed-point arguments and differential-algebraic system theory.
Constructed a fully discrete Galerkin scheme using lowest-order Raviart–Thomas elements, piecewise constants, linear boundary multipliers, and backward Euler time-stepping.
Proved well-posedness, stability, and optimal convergence rates for the fully discrete mixed formulation.
Validated theoretical error estimates through numerical experiments, demonstrating the framework's effectiveness in modeling coupled flow and membrane transport dynamics.