Efficient Dynamic Mesh Refinement Technique for Simulation of HPM Breakdown induced Plasma Pattern Formation

Numerical simulation of the complex plasma dynamics associated with high power, high frequency microwave breakdown at high pressures, leading to the formation of filamentary plasma structures such as self-organized plasma arrays, is a computationally challenging problem. The widely used 2D EM-plasma fluid model, which accurately captures the experimental observations, requires a run-time of several days to months to simulate standard problems due to stringent numerical requirements in terms of cell size and time step. In this paper, we present a self-aware mesh refinement algorithm which uses a coarse mesh and a fine mesh that dynamically expands based on the plasma profile topology to resolve the sharp gradients in E-fields and plasma density in the breakdown region. The dynamic mesh refinement (DMR) technique is explained in details and its performance has been evaluated using a standard benchmark microwave breakdown problem. We observe a speedup of 8 (of the order of $O(r^{3})$, when refinement factor ($r$) is 2) compared to a traditional single uniform fine mesh based simulation. The technique is scalable and performs better when problem size increases. We also present a comprehensive spatio-temporal visual analysis to explain the complex physics of HPM breakdown, leading to self-organized plasma filamentation.