New set of fluid moment equations describes plasma behavior with greater numerical stability

Traditionally, plasma behavior can be modeled by two different representations of the flow field. The Lagrangian representation looks at fluid motion by taking the frame of an individual fluid parcel as it moves through space and time. The Eulerian representation, on the other hand, takes a laboratory frame in which the observer watches the fluid pass by.

However, both Lagrangian and Eulerian descriptions tend to result in numerically unstable simulations unless a large diffusion is added. A new article published in Physics of Plasmas introduces a new set of plasma moment equations that exhibit numerical stability from first principles. The approach provides a novel reference frame that is an intermediate alternative to Lagrangian and Eulerian representations.

Author Federico Halpern studies turbulence in tokamaks with computer simulations and became frustrated with the traditional equations he had been using, since they would often cause his code to crash. He began to search for better, more reliable equations to describe complex plasma behavior.

Taking cues from the field of fluid dynamics, Halpern and co-author Ronald E. Waltz derived a new anti-symmetric form of the standard plasma moment approach. Instead of using the traditional approach, they described the plasma evolution using forms that have exact analogs in computers. The resulting set of fluid moment equations have inherent consistency and numerical stability out-of-the-box.

To verify their model, the Halpern and Waltz simulated the motion of a single-seeded 2-D plasma blob, finding that it indeed propagates as expected with the correct velocity. The model showed total mass, momentum and energy conservation to machine precision, demonstrating the potential advantages of the new moment representation for low dissipation supercomputer simulations of plasma phenomena.

Source: “Anti-symmetric plasma moment equations with conservative discrete counterparts,” by Federico D. Halpern and Ronald E. Waltz, Physics of Plasmas (2018). The article can be accessed at http://doi.org/10.1063/1.5038110 .