A r -Adaptive Discontinuous Galerkin Method Based on Interface Conservation for Reacting Hypersonic Viscous Flows

A novel adaptive discontinuous Galerkin (DG) finite element method is presented for reacting hypersonic viscous flows on 3D arbitrary grids. The so-called r-adaptive mesh algorithm, simply consisting in repositioning mesh nodes, is used to dynamically transform an initial grid into an optimal mesh and therefore to produce the best numerical solution for a given problem. A variational formulation based on the interface conservation is introduced to obtain posteriori error estimations at mesh nodes in the r-adaptive grid method. The library Mutation++ is used to provide a flexible interface to thermodynamic closure equations and transport coefficients. Numerical experiments for thermal-chemical non-equilibrium reactive hypersonic viscous flows are conducted to validate the developed r-adaptive DG method. The obtained DG solutions are compared with experimental data and the reference solutions obtained by NASA’s state-of-the-art codes: DPLR and LAURA, when possible. Preliminary numerical results are highly promising and encouraging, demonstrating that the error indicator based on the interface conservation can reliably and efficiently detect and identify both under-resolved flow features and regions of high gradient solutions. The resultant r-adaptive DG method is able to align mesh cell interfaces with viscous shock waves and effectively offer anisotropic mesh adaption for viscous shock waves, which in turn significantly improves the accuracy of the DG solution for predicting the hypersonic heating on unstructured grids.