A Monolithic Multi-domain Hybridized Discontinuous Galerkin Solver for Inductively Coupled Plasma Flow

In the context of increasing interest in space exploration, having a reliable means of predicting the behaviour of thermal protection material during atmospheric re-entry is of capital importance. Inductively coupled plasma facilities have been designed to fulfill this demand, producing a high quality plasma and simulating accurately the re-entry conditions. In parallel, they motivated the development of dedicated efficient numerical solvers in order to better understand the experiments. However, these solvers have several drawbacks, such as slow convergence due to a staggered solution approach between the Maxwell and Navier-Stokes equations, and their use of multi-block high-quality structured mesh. In this work, we develop a novel multi-domain monolithic high-order hybridized discontinuous Galerkin (HDG) solver for inductively coupled plasma. We show that HDG method alleviates the mesh restrictions considerably, except in the boundary layer, where the mesh still needs to be structured. Moreover, we prove that the monolithic aspect of the solver allows for a fast convergence to the steady-state starting from initial data far from the solution. Using a manufactured solution, it is shown that the order of convergence of the monolithic HDG method is p + 1 in the L2 norm, with p the degree of the approximation space. Finally, a comparison of the HDG code with a finite volume code (COOLFluiD) and experimental data are performed, showing a good agreement.