An Arbitrary Curvilinear Coordinate Method for Particle-In-Cell Modeling

TL;DR

This paper introduces the ACC-PIC method, a novel particle-in-cell simulation approach that operates on a uniform logical grid mapped to complex physical geometries, enabling efficient plasma modeling in arbitrary domains.

Contribution

It develops a curvilinear coordinate formulation for PIC, including a symplectic particle mover and Poisson solver, to handle complex geometries with a uniform logical grid.

Findings

Enables PIC simulations on arbitrary boundary-fitted meshes.

Preserves symplectic structure with a modified leapfrog integrator.

Simplifies charge density computation on complex geometries.

Abstract

A new approach to the kinetic simulation of plasmas in complex geometries, based on the Particle-in- Cell (PIC) simulation method, is explored. In the two dimensional (2d) electrostatic version of our method, called the Arbitrary Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are carried out in 2d on a uniform grid on the unit square logical domain, and mapped to a nonuniform boundary-fitted grid on the physical domain. As the resulting logical grid equations of motion are not separable, we have developed an extension of the semi-implicit Modified Leapfrog (ML) integration technique to preserve the symplectic nature of the logical grid particle mover. A generalized, curvilinear coordinate formulation of Poisson's equations to solve for the electrostatic fields on the uniform logical grid is also developed. By our formulation, we compute the plasma charge density on the logical grid based on the particles' positions on the logical domain. That is, the plasma particles are weighted to the uniform logical grid and the self-consistent mean electrostatic fields obtained from the solution of the logical grid Poisson equation are interpolated to the particle positions on the logical grid. This process eliminates the complexity associated with the weighting and interpolation processes on the nonuniform physical grid and allows us to run the PIC method on arbitrary boundary-fitted meshes.