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A Matrix-Free Discontinuous Galerkin Method for Nonequilibrium Hypersonic Flow
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In this work we extend a matrix-free DG method developed for high-speed ideal gas problems to high-enthalpy regimes where nonequilbrium effects are important. The efficiency of our approach relies on the use of a Jacobian-Free Newton--Krylov method and a low-memory preconditioner built from reduced basis approximations of the Jacobian. We analyze the performance of these solvers on nonequilibrium flow problems and explore techniques to improve convergence behavior and robustness when encountering stiff chemical kinetics and multiscale features. Particular attention is paid to problems with shocks and the interaction of the solvers with artificial viscosities adapted for nonequilibrium flow.
