Divergence conforming finite element methods for flow-transport coupling with osmotic effects
CoRR(2024)
摘要
We propose a model for the coupling of flow and transport equations with
porous membrane-type conditions on part of the boundary. The governing
equations consist of the incompressible Navier–Stokes equations coupled with
an advection-diffusion equation, and we employ a Lagrange multiplier to enforce
the coupling between penetration velocity and transport on the membrane, while
mixed boundary conditions are considered in the remainder of the boundary. We
show existence and uniqueness of the continuous problem using a fixed-point
argument. Next, an H(div)-conforming finite element formulation is proposed,
and we address its a priori error analysis. The method uses an upwind approach
that provides stability in the convection-dominated regime. We showcase a set
of numerical examples validating the theory and illustrating the use of the new
methods in the simulation of reverse osmosis processes.
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