题 目：Progress of Reconstructed Discontinuous Galerkin Methods for Computational Fluid Dynamics
报 告 人：罗 宏 教授 （North Carolina State University）
时 间：2018年12月13日（周四）9：30
地 点：延长校区应用数学和力学所东会议室
摘 要：The current status for the efficient simulation and analysis of flow problems using a second-order finite volume (FV) method on unstructured grids is briefly reviewed. It is concluded that all major areas required in the analysis cycle - grid generation, flow solvers, and visualization – have seen major advances in recent years, allowing us to produce high-quality solutions for a variety of flow problems around complex geometries in a matter of hours. The presentation will then be focused on the development of a higher-order reconstructed discontinuous Galerkin (DG) method for computational fluid dynamics (CFD). The idea behind rDG methods is to combine the efficiency of the reconstruction methods in FV methods and the accuracy of the DG methods to obtain a better numerical algorithm in CFD. The beauty of the resulting rDG methods is that they provide a unified formulation for both FV and DG methods, and contain both classical FV and standard DG methods as two special cases of the rDG methods, and thus allow for a direct efficiency comparison. Different reconstruction methods will be presented and discussed. In our latest work, a rDG method based on a Hierarchical WENO reconstruction, termed HWENO(P1P2), designed not only to enhance the accuracy of DG methods but also to ensure the nonlinear stability of the rDG method, is presented to solve compressible flow problems at all speeds on hybrid grids. The developed HWENO(P1P2) method is used to compute a variety of flow problems on hybrid meshes to demonstrate its accuracy, robustness, and non-oscillatory property. The numerical experiments indicate that the HWENO(P1P2) method is able to capture shock waves within one cell without any spurious oscillations, and achieve the designed thirdorder of accuracy: one order accuracy higher than the underlying DG method, indicating the potential of this rDG method to become a viable, competitive, and perhaps superior DG method over existing FV and DG methods for CFD. Extension of the rDG methods to the incompressible flows, multi-phase flows, hyperbolic diffusion equation, Lagrangian hydrodynamics, Magnetohydrodynamics, and the porting of the rDG methods on GPUs will also be presented and discussed.
