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Center for Nonlinear Studies |
The shape function kinetics (SFK) method, based on decomposing the mass into discrete particles using shape functions of compact support, will be presented. The particle positions and shape evolve in response to internal velocity spread and external forces. Two strategies for remapping the particles are discussed: a Barnes-Hut tree combined with a Gaussian mixture model and a mesh-based remapping using Richardson-Lucy iteration. Numerical simulations of standard test problems illustrate the advantages of the method which include very low noise compared to the standard particle-in-cell technique, inherent positivity, and large dynamic range.
In addition, a novel implicit-moment Coulomb collision algorithm for PIC codes will be described. Particle-pairing algorithms are the standard tool for including the effects of Coulomb collisions in PIC plasma simulation codes. These algorithms are restricted to resolving the characteristic collision frequency in order to maintain accuracy. Our algorithm uses recent work by Fox and co-workers to generate a discrete set of quadrature nodes representing the velocity distribution. These nodes are implicitly advanced in time using the collisional drag force. The original set of PIC particles then collides with the time-advanced nodes using the Nanbu collision algorithm. The result is a semi-implicit collision algorithm that works well for large time steps, as demonstrated in a variety of test problems.
Host: Luis Chacon