Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

TL;DR

This paper introduces three numerical algorithms for simulating charge transport in PEC solar cells, combining finite element and discontinuous Galerkin methods with implicit-explicit time stepping to efficiently solve complex nonlinear PDE systems.

Contribution

The work develops and analyzes three novel numerical algorithms tailored for coupled reaction-drift-diffusion-Poisson equations in PEC solar cells, enhancing computational efficiency and accuracy.

Findings

Algorithms effectively solve nonlinear PDE systems

Simulation results show impact of parameters on charge transport

Proposed methods outperform traditional approaches

Abstract

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.