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Description
In high power vacuum arcs, the physics of the plasma and the surrounding surfaces can be strongly coupled both thermally and materially by energy deposition from the plasma to the materials and by gas-phase species emitted from the materials into the plasma, respectively. The former can also produce surface geometry modifications which then feed back to the electric field. The first step in capturing such couplings beginning with a Particle-In-Cell (PIC) approach to modeling the plasma is to model heat conduction within the electrode(s) with thermal fluxes corresponding to a combination of impacting particles and heat loss to particle emission. However, numerical constraints of these two models, especially when modeling the plasma using semi-implicit PIC (SIPIC) [1], are at odds with one another. Specifically, the time step size is constrained by the CFL requirement for electrons in the near-surface elements while the mesh element size is constrained by the high thermal gradients in the solid. Constraining the time step size and the mesh size to the most restrictive requirements leads to excessive temporal refinement in the electrodes and spatial refinement in the plasma which together require several orders of increased and unnecessary computational costs.
In this work we present an algorithm for decoupling the spatial discretizations in finite element PIC simulations from the material discretization, allowing larger elements in the plasma domain and a corresponding larger overall time step in the simulations. Specifically, a preprocessing step constructs a mapping across non-conformal surface meshes at the electrode-plasma interface that allows efficient and conservative two-way data transfers of fluxes between the domains. Results are presented for thermal conduction in an electrode driven by impacting particles. We demonstrate that the non-conformal surface mesh data transfers produce results with accuracy and numerical convergence consistent with matching spatial discretizations but at significantly reduced computational cost using element sizes in the plasma over two orders of magnitude larger than that required for matching surface meshes. Together with the allowed increase in time step in the plasma domain, this approach enables production simulations that would otherwise be intractable.
References
[1] D. C. Barnes, “Improved C1 shape functions for simplex meshes”, J. Comp. Phys, 424, 109852, 2021.
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
