In recent years, variational-formulation based high-order schemes, such as discontinuous Galerkin (DG) scheme, have demonstrated promising capabilities for CFD applications. Compared to commonly used numerical methods, these high-order schemes are particularly attractive for (i) providing high-order accurate solutions with less sensitivity to mesh topology; (ii) enforcing physical realizability on solutions to guarantee numerical nonlinear stability; and (iii) better balancing computational robustness and resolution requirement for multi-physics simulations. This talk will start by illustrating several challenges associated with modern CFD applications, followed by a short tutorial introducing DG formulation and its numerical properties. DG’s performance will be demonstrated by considering canonical flow configurations, and compared against the commonly used numerical methods.
After the tutorial, the talk will focus on the further development of DG method for predicting discontinuity-containing flows (i.e. hypersonic flows up to Mach 18). Entropy-bounded DG scheme that has provable numerical stability will be briefly discussed, which serves as the foundation for simulations with explicit time integration. The talk will then move on to elaborate the recently developed artificial-viscosity method for predicting convective heat transfer on the surfaces of hypersonic re-entry vehicles. Emphasis will be given on how to obtain zero-residual implicit calculations while preserving high-order benefits. The developed DG-based numerical capability will be tested and validated in a wide range of flow applications, from LES of canonical turbulent flows and reacting flows, to detonation and hypersonic flows.