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

• Published in: Combustion theory and modelling Vol. 24; no. 2; pp. 194 - 220
• Main Authors: Esclapez, Lucas, Ricchiuti, Valentina, Bell, John B., Day, Marcus S.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.03.2020; Taylor & Francis Ltd
• Subjects: Algorithms; Charging; Conservation equations; Dielectric relaxation; Dimensional stability; electric field; Electric fields; Jacobian Free Newton Krylov (JFNK); low Mach number combustion; Mach number; Preconditioning; Reacting flow; spectral deferred correction (SDC); Transport
• ISSN: 1364-7830; 1741-3559
• DOI: 10.1080/13647830.2019.1668060

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 multi-dimensional applications.