Exact and Locally Implicit Source Term Solvers for Multifluid-Maxwell Systems

TL;DR

This paper introduces exact and locally implicit source term solvers for multifluid-Maxwell systems, enabling efficient, energy-conserving simulations of complex plasma phenomena by overcoming rapid kinetic process resolution challenges.

Contribution

It develops a locally implicit algorithm for source term updates in multifluid-Maxwell models, combining analytical solutions and efficient matrix inversion to handle fast kinetic scales.

Findings

The locally implicit solver conserves energy exactly.

It is efficient and robust for large-scale plasma simulations.

The method can incorporate additional local sources like collisions.

Abstract

Recently, a family of models that couple multifluid systems to the full Maxwell equations draw a lot of attention in laboratory, space, and astrophysical plasma modeling. These models are more complete descriptions of the plasma than reduced models like magnetohydrodynamic (MHD) since they naturally retain non-ideal effects like electron inertia, Hall term, pressure anisotropy/nongyrotropy, etc. One obstacle to broader application of these model is that an explicit treatment of their source terms leads to the need to resolve rapid kinetic processes like plasma oscillation and electron cyclotron motion, even when they are not important. In this paper, we suggest two ways to address this issue. First, we derive the analytic forms solutions to the source update equations, which can be implemented as a practical, but less generic solver. We then develop a time-centered, locally implicit algorithm to update the source terms, allowing stepping over the fast kinetic time-scales. For a plasma with $S$ species, the locally implict algorithm involves inverting a local $3S+3$ matrix only, thus is very efficient. The performance can be further elevated by using the direct update formulas to skip null calculations. Benchmarks illustrated the exact energy-conservation of the locally implicit solver, as well as its efficiency and robustness for both small-scale, idealized problems and large-scale, complex systems. The locally implicit algorithm can be also easily extended to include other local sources, like collisions and ionization, which are difficult to solve analytically.