Using non-conforming triangular meshes in fluid modeling of atmospheric-pressure discharges

Accurate resolution of boundary layers near plasma-facing surfaces and the propagation of fast ionization waves are crucial for high-fidelity modeling of atmospheric-pressure discharges. To manage the computational complexity of such problems, space-adaptive numerical methods are essential for maintaining feasible simulation times. Currently, the use of space-adaptive methods in plasma modeling remains somewhat limited, with existing applications primarily relying on structured computational meshes. To better handle real-world scenarios, the use of space-adaptive methods on triangular meshes would be advantageous. In this contribution, we present the open-source finite-element package triellipt [1], which is capable of solving elliptic and parabolic PDEs on nonconforming adaptive triangular meshes and supports conservative mesh refinement. As a proof of concept, the package is applied to simulate streamer discharges in both open-space and pin-to-plane configurations. Its relationship to other simulation techniques is discussed in terms of robustness and flexibility for discharge modeling. [1] I. L. Semenov, triellipt, GitHub repository (2025), https://github.com/INP-SDT/triellipt