Clarissa Astuto

Clarissa Astuto

In this paper, we investigate the correlated diffusion of two ion species governed by a Poisson-Nernst-Planck (PNP) system. Here we further validate the numerical scheme recently proposed in \cite{astuto2025asymptotic}, where a time discretization method was shown to be Asymptotic-Preserving (AP) with respect to the Debye length. For vanishingly Debye lengths, the so called Quasi-Neutral limit can be adopted, reducing the system to a single diffusion equation with an effective diffusion coefficient \cite{CiCP-31-707}. Choosing small, but not negligible, Debye lengths, standard numerical methods suffer from severe stability restrictions and difficulties in handling initial conditions. IMEX schemes, on the other hand, are proved to be asymptotically stable for all Debye lengths, and do not require any assumption on the initial conditions. In this work, we compare different time discretizations to show their asymptotic behaviors.

Clarissa Astuto, Giovanni Russo

In this paper, we propose and validate a two-species Multiscale model for a Poisson-Nernst-Planck (PNP) system, focusing on the correlated motion of positive and negative ions under the influence of a trap. Specifically, we aim to model surface traps whose attraction range, of length $δ$, is much smaller then the scale of the problem. The physical setup we refer to is an anchored gas drop (bubble) surrounded by a flow of charged surfactants {(composed by positive and negative ions) that diffuses in water. When the diffusing surfactants reach the surface of the trap, the negative ions are adsorbed because of their hydrophobic tail that is attracted by the air bubble}. As in our previous works, the effect of the attractive potential is replaced by a suitable boundary condition derived by mass conservation and asymptotic analysis. The novelty of this work is the extension of the model proposed in \cite{astuto2023multiscale}, now incorporating the influence of both carriers -- positive and negative ions -- simultaneously, which is often neglected in traditional approaches that treat ion species independently. The two carriers interact through the Coulomb potential, that is computed by a Poisson equation. [...]

Hridya Dilip, Clarissa Astuto, Armando Coco et al.

We develop a new numerical technique for approximating solutions of the Navier-Stokes equations on moving domains. The method aims at simulating an incompressible fluid past an object whose motion is assigned a priori using a level-set function. The proposed approach relies on a space discretization based on the ghost finite element method (ghost-FEM), which allows computations on unfitted meshes and avoids costly remeshing as the domain evolves in time. Time integration is performed using an IMplicit-EXplicit (IMEX) scheme to address the nonlinearity of the convective term, ensuring high-order accuracy for incompressible flows. The error introduced by the geometrical approximation is handled using the Shifted Boundary Method, which allows higher order approximations of boundary conditions on unfitted meshes. Dirichlet boundary conditions are imposed weakly by means of Nitsche's method. The associated stabilization parameter is chosen by solving a generalized eigenvalue problem, ensuring stability and accuracy of the numerical scheme. We present a series of numerical experiments designed to validate the accuracy of the proposed method, as well as comparisons with established benchmark problems involving moving boundaries.