The primary aim is to develop numerical methods of high numerical and physical fidelity for ion transport, crucial for producing physically accurate solutions. By means of detailed numerical simulations, the scientific focus is on understanding and enhancing the selectivity of ion transport through transient nanopores. This involves investigating the interactions between various ion transport mechanisms within electrically conductive, functionalized nanopores to determine the factors that govern ion selectivity. One of the main objectives of the method development in B3 is to design a robust finite-volume method for the coupled solution of the Poisson-Nernst-Planck-Navier-Stokes equations and to devise a consistent formulation of the electrokinetic coupling in a hybrid atomistic-continuum approach for ion mixtures.