Exact moment models for conservation laws in phase space

TL;DR

This paper introduces exact moment models for conservation laws in phase space, enabling efficient plasma, gas, and liquid simulations that incorporate kinetic effects with fewer degrees of freedom.

Contribution

It develops a novel parameterization of the distribution function that yields exact solutions to hyperbolic conservation laws, extending to both non-relativistic and relativistic Vlasov--Maxwell equations.

Findings

Exact moment models solve hyperbolic conservation laws precisely.

Application to non-relativistic and relativistic Vlasov--Maxwell equations demonstrated.

Reduced computational complexity while capturing kinetic effects.

Abstract

Moment equations offer a compelling alternative to the kinetic description of plasmas, gases, and liquids. Their simulation requires fewer degrees of freedom than phase space models, yet it can still incorporate kinetic effects to a certain extent. To derive moment equations, we use a parameterization of the distribution function using centered moments, as proposed by Burby. This yields moment equations for which the parameterized distribution function exactly solves the hyperbolic conservation law. Similarly, a particle model is derived based on a parametrization of the distribution function using phase space moments. Finally, we present the application of the method to the non-relativistic and relativistic Vlasov--Maxwell equations.