Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows

• Published in: Journal of computational physics 2019-01, Vol.376, p.54-75
• Main Authors: Ching, Eric J., Lv, Yu, Gnoffo, Peter, Barnhardt, Michael, Ihme, Matthias
• Format: Article
• Language: English
• Subjects: Artificial viscosity; Computational grids; Computational physics; Cylinders; Discontinuous Galerkin method; Finite volume method; Galerkin method; Heat transfer; Hypersonic flow; Mach reflection; Mathematical analysis; Shock capturing; Stabilization; State of the art; Topology; Viscosity
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2018.09.016

•Developed a robust shock capturing method for DG schemes.•Intraelement variations are used for shock detection.•Smooth artificial viscosity is used for shock stabilization.•Benchmarked heating predictions against FV solvers in hypersonic viscous flows.•DG predictions exhibit reduced sensitivity to mesh topology and flux functions. This study is concerned with predicting surface heat transfer in viscous hypersonic flows using high-order discontinuous Galerkin (DG) methods. Currently, finite-volume (FV) schemes are most commonly employed for computing flows in which surface heat transfer is a target quantity; however, these schemes suffer from large sensitivities to a variety of factors, such as the inviscid flux function and the computational mesh. High-order DG methods offer advantages that can mitigate these sensitivities. As such, a simple and robust shock capturing method is developed for DG schemes. The method combines intraelement variations for shock detection with smooth artificial viscosity (AV) for shock stabilization. A parametric study is performed to evaluate the effects of AV on the solution. The shock capturing method is employed to accurately compute double Mach reflection and viscous hypersonic flows over a circular half-cylinder and a double cone, the latter of which involves a complex flow topology with multiple shock interactions and flow separation. Results show this methodology to be significantly less sensitive than FV schemes to mesh topology and inviscid flux function. Furthermore, quantitative comparisons with state-of-the-art FV calculations from an error vs. cost perspective are provided.