High fidelity simulations of the multi-species Vlasov-Maxwell system with the Numerical Flow Iteration

TL;DR

This paper presents a novel iterative-in-time numerical method for high-fidelity simulations of the multi-species Vlasov-Maxwell system, overcoming computational challenges of traditional approaches by reconstructing phase-space dynamics from electromagnetic field history.

Contribution

It extends an existing electrostatic method to the full Vlasov-Maxwell system using Hamiltonian splitting for structure preservation and reduced memory usage.

Findings

Enables high-resolution simulations below phase-space grid scale.

Maintains structure-preserving properties in the numerical scheme.

Reduces memory requirements compared to traditional methods.

Abstract

Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its six-dimensional phase-space dynamics, strong filamentation, and multi-scale structure make direct numerical simulation extremely demanding. Particle-In-Cell (PIC) methods remain the standard for ion-scale studies, yet their memory cost and intrinsic noise hinder accurate electron-scale simulations. In this paper, we introduce an alternative method based on an iterative-in-time approximation of characteristics. The approach reconstructs the phase-space dynamics from the time history of the electromagnetic fields and the initial distribution functions, enabling extremely high effective resolution far below the phase-space grid scale without storing or advecting high-dimensional data. Earlier work demonstrated this capability for the multi-species electrostatic Vlasov system. Here we discuss an extension of the method to the full Vlasov-Maxwell equations using a Hamiltonian splitting to advance the solution in a structure-preserving way while retaining the reduced memory footprint.