Anti-symmetric plasma moment equations with conservative discrete counterparts

Abstract

We derive a set of fluid moment equations with inherent consistency and numerical stability, conceived by exploiting the anti-symmetric nature of the plasma flow operator (∇·v+v·∇). The obtained equations can be interpreted as an alternative to the traditional Eulerian and Lagrangian representations—one in which plasma flows generate infinitesimal rotations of generalized fluid moments n, nv, and p. The continuous model has a discrete analog with exact mass, momentum, and energy conservation, which is achieved by construction through vanishing integrals of the anti-symmetric flow terms. Positivity preservation is obtained through the use of the generalized moment quantities. The conservation properties of the approach are illustrated in simulations of seeded blob propagation, where we verify numerical conservation to machine accuracy.