# A spectral deferred correction strategy for low Mach number reacting flows subject to electric fields

## TL;DR

This paper introduces a spectral deferred correction algorithm for low Mach number reacting flows with electric fields, enabling stable, second-order accurate simulations of complex electrochemical interactions.

## Contribution

It extends the MISDC framework to include electric field effects and charged species transport with a Jacobian-Free Newton Krylov approach for implicit treatment.

## Key findings

- Demonstrates second-order convergence in space and time.
- Shows stability in steady and unsteady flow problems.
- Designed for potential multidimensional applications.

## Abstract

We propose an algorithm for low Mach number reacting flows subjected to electric field that includes the chemical production and transport of charged species. This work is an extension of a multi-implicit spectral deferred correction (MISDC) algorithm designed to advance the conservation equations in time at scales associated with advective transport. The fast and nontrivial interactions of electrons with the electric field are treated implicitly using a Jacobian-Free Newton Krylov approach for which a preconditioning strategy is developed. Within the MISDC framework, this enables a close and stable coupling of diffusion, reactions and dielectric relaxation terms with advective transport and is shown to exhibit second-order convergence in space and time. The algorithm is then applied to a series of steady and unsteady problems to demonstrate its capability and stability. Although developed in a one-dimensional case, the algorithmic ingredients are carefully designed to be amenable to multidimensional applications.