A Multi Level Multi Domain Method for Particle In Cell Plasma Simulations

TL;DR

This paper introduces an adaptive multi-level multi-domain method for Particle In Cell plasma simulations, addressing key challenges in grid refinement, particle shape functions, and stability constraints with a novel MLMD system and implicit PIC approach.

Contribution

It presents a new adaptive technique combining MLMD and implicit PIC methods, improving stability and accuracy in plasma simulations across multiple scales.

Findings

Effective handling of grid refinement and particle shape functions.

Stable and accurate simulations demonstrated through various tests.

Particles are confined to their original levels with boundary repopulation.

Abstract

A novel adaptive technique for electromagnetic Particle In Cell (PIC) plasma simulations is presented here. Two main issues are identified in designing adaptive techniques for PIC simulation: first, the choice of the size of the particle shape function in progressively refined grids, with the need to avoid the exertion of self-forces on particles, and, second, the necessity to comply with the strict stability constraints of the explicit PIC algorithm. The adaptive implementation presented responds to these demands with the introduction of a Multi Level Multi Domain (MLMD) system (where a cloud of self-similar domains is fully simulated with both fields and particles) and the use of an Implicit Moment PIC method as baseline algorithm for the adaptive evolution. Information is exchanged between the levels with the projection of the field information from the refined to the coarser levels and the interpolation of the boundary conditions for the refined levels from the coarser level fields. Particles are bound to their level of origin and are prevented from transitioning to coarser levels, but are repopulated at the refined grid boundaries with a splitting technique. The presented algorithm is tested against a series of simulation challenges.