Speaker： Hong luo, 美国北卡罗莱纳州立大学(North Carolina State University)
Our recent progress on the development of higher-order reconstructed discontinuous Galerkin (rDG) methods for computational fluid dynamics (CFD) will be presented. The idea behind rDG methods is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting rDG methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the rDG methods, and thus allow for a direct efficiency comparison. In our latest work, a reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction, termed HWENO(P1P2), designed not only to enhance the accuracy of discontinuous Galerkin 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 third-order 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 computational fluid dynamics. Extension of the rDG methods to the incompressible flows, hyperbolic diffusion equation, and the porting of the rDG methods on GPUs will also be presented and discussed.
Dr. Hong Luo is a professor in the Department of Mechanical and Aerospace Engineering at North Carolina State University. He received his Ph.D. in Applied Mathematics from Pierre and Marie Curie University (University of Paris 6) in France in 1989. Prior to joining NC State in 2007, he worked as a post-doctoral research associate at Purdue University from 1989 to 1991and as a senior research scientist at Science Applications International Corporation from 1991 to 2007. His current research interests include: Computational Fluid Dynamics, Computational Aeroacoustics, and Computational magnetohydrodynamics; Reconstructed Discontinuous Galerkin Methods on Unstructured Hybrid Grids; High Performance Computing on Hybrid CPU/GPU Architectures; Moving Boundary Problems and Fluid-Structure Interaction; Large Eddy Simulation of Turbulent Flows; Multi-phase Flows and Chemically Reactive Flows; Geometry Modeling, Unstructured Grid Generation, and Grid Adaptation. His research activities have been and are supported by NASA, AFSOR, DOE, Idaho National Laboratory, Navy, Army, NSF, DTRA, and others. Prof. Luo has over 200 papers to his credit. Currently, he leads a research group of 2 postdoctoral researchers, 6 PhD graduates, and 2 MS students at NC State.