Speaker
Description
The Poisson–Nernst–Planck–Navier–Stokes (PNP–NS) system describes the transport of charged species in a fluid under the influence of electric fields, coupled with fluid flow dynamics. Although the classical PNP–NS framework provides a fundamental model, it faces limitations in accurately capturing complex electrokinetic phenomena, motivating the development of enhanced formulations. In this context, a Landau–Ginzburg-type continuum theory for room-temperature ionic liquids (RTILs) is considered, leading to a modified fourth-order PNP–NS system.
A fully discrete numerical scheme based on a conforming Virtual Element Method (VEM) is presented. The spatial discretization employs an H2-conforming virtual element space for the Poisson equation, an H1-conforming space for the Nernst–Planck equations, and divergence-free conforming spaces for the Navier–Stokes system. Temporal discretization is carried out using the backward Euler method, ensuring stability and robustness.
Well-posedness of the fully discrete scheme is established, together with a priori error estimates. Numerical experiments confirm optimal convergence rates in suitable Bochner spaces and demonstrate robustness in regimes characterized by low viscosity and small permittivity parameters. Furthermore, the scheme preserves key structural and physical properties of the model, including mass, energy, and entropy, at the discrete level, for both smooth and non-smooth initial data.