Over recent years a set of high-order discontinuous schemes have gradually emerged as a new cornerstone for enabling high-fidelity CFD applications. The discontinuous Galerkin (DG) method, as a representative, has been successfully applied to a number of challenging problems and demonstrated superior capabilities over the conventional finite-different and finite-volume schemes. Specifically, DG method is able to provide high-order discretization on unstructured meshes, utilizes a compact discretization, and is well suited for advanced refinement strategies. This talk will start with a short introduction to the recent progress on scheme innovation, and its implication on the next-generation CFD technique. However, it has been recognized that high-order DG approximations suffer robustness issues when applied to solving nonlinear conservation laws. These nonlinear numerical instabilities may arise from physical discontinuities, geometrical singularities, and under-resolved turbulence structures. To address these issues, the present study is concerned with the development of a realizable and stable high-order DG method, by embedding the entropy principle to the discretization and thereby imposing physical-constraints on local-cell solution representations. After outlining the mathematical formulation and the proof of stability, the performance of the novel DG method is evaluated by considering a series of test cases involving shocks, turbulence, and chemical reactions. The last part of this talk focuses on the DG-based simulations of high Reynolds-number wall-bounded flows, which have direct relevance to the aerodynamics optimization and design of efficient turbomachinery. The major challenge in this regard is that the fine near-wall turbulence structures make fully resolved CFD simulations computationally prohibitive. The present effort will introduce a wall-modeled large-eddy simulation (WMLES) technique based upon the physics-enriched DG formulation, in which the solution basis in the wall-adjacent region is augmented by the law of the wall. The capability of the physics-enriched DG WMLES will be demonstrated in the successful prediction of the NASA transonic bump configuration (Rec = 2.8 million).
Dr. Yu Lv
Assistant Professor of the Aerospace Engineering Department at Mississippi State University. Dr. Lv received his PhD in 2016 from Stanford University. He worked in the Center for Turbulence Research, at Stanford University, as a Postdoc Fellow, before joining Mississippi State University in 2017. He received his Master’s and Bachelor’s degrees from the University of Michigan and Zhejiang University, respectively.