Variable-moment fluid closures with Hamiltonian structure

TL;DR

This paper introduces a flexible framework for creating fluid moment closures of the Vlasov-Poisson system that maintain Hamiltonian structure, applicable in any dimension and adaptable via data-driven methods.

Contribution

It provides a general, Hamiltonian-preserving method for fluid closures involving arbitrary moments, extending previous ideas to higher dimensions and data-driven adjustments.

Findings

Framework preserves Hamiltonian structure in fluid closures

Applicable in any space dimension

Allows data-driven customization of closures

Abstract

Based on ideas due to Scovel-Weinstein, I present a general framework for constructing fluid moment closures of the Vlasov-Poisson system that exactly preserve that system's Hamiltonian structure. Notably, the technique applies in any space dimension and produces closures involving arbitrarily-large finite collections of moments. After selecting a desired collection of moments, the Poisson bracket for the closure is uniquely determined. Therefore data-driven fluid closures can be constructed by adjusting the closure Hamiltonian for compatibility with kinetic simulations.