Electromagnetic particle codes on unstructured grids

Abstract

The most widely used computational model of collisionless plasmas is the Lagrangian-Eulerian hybrid technique known as particle-in-cell or PIC. In the electromagnetic version, Maxwell's equations are solved on an Eulerian grid and electromagnetic forces are interpolated form the grid to particle locations. Particles are then moved in Lagrangian fashion while their currents are interpolated back onto the grid to provide sources for the fields on the next cycle.

There are many applications where one needs to model plasmas and electromagnetic waves inside regions of complicated shape. Traditional methods for solving Maxwell's equations employ finite differences on regular grids to replace differential operators. These methods are awkward for complicated boundary shapes, often replacing smoothly curved or slanted boundaries with stairsteps. The desire to incorporate realistic boundaries into plasma simulations is motivated by a host of situations in which proper representation of the boundary shape is expected to be critical.

Our approach to solving this problem is to design electromagnetic particle codes based on the use of unstructured grids. The arbitrary connectivity of unstructured grids provides the flexibility to place nodes wherever needed to fit the most complex boundary shapes. The most significant problems that must be addressed as a result of this strategy are: grid generation, field solution, and particle tracking. Our solutions to these problems, along with a few preliminary results, are presented in this paper.