Shock-capturing Methods for High-Order Discontinuous Galerkin Schemes
Speaker: Yu Lv, Center of Turbulence Research, Stanford University
Presentation
Abstract
High-order discontinuous Galerkin (DG) schemes have demonstrated promising performance in many CFD applications, especially computational aerodynamics. However, capturing shocks in DG-schemes remains an open problem. This talk discusses recent developments of two artificial-viscosity (AV) formulations for high-order DG schemes that are suited for implicit and explicit numerical predictions. For explicit calculations, the design of the AV scheme is guided by the CFL stability constraint; while for implicit and time-dependent simulations, the AV scheme is designed to be able to achieve machine-zero solution-residuals. The discussion also covers the shock-detector based on an entropy-residual function, which forms another key ingredient of the new shock-capturing capability. The implementation is built on our entropy-bounded DG-scheme that imposes physical realizability of numerical solutions, thereby guaranteeing the robustness of the scheme.. Several examples, including applications to hypersonic-flows and chemically reacting flows, will be presented to demonstrate the performance of these shock-capturing approaches.
Biography
Yu Lv is a postdoc researcher working at the Center of Turbulence Research at Stanford University. He got his Ph.D. degree from the Mechanical Engineering department at Stanford University (2016) and his Master’s degree form the Aeronautics department at the University of Michigan (2013). He studied at Zhejiang University, China, for his Bachelor’s degree in thermal physics. His Ph.D. and postdoc advisor is Prof. Matthias Ihme, and his dissertation topic is on the development of entropy-bounded high-order schemes. Lv’s current research interests are in numerical analysis, high-order schemes, and high-speed flows.