报告题目：Status and Trend of Unstructured Grid Methods for Computational Fluid Dynamics
报告人：Hong Luo教授 美国North Carolina State University
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. 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 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 CFD. Extension of the rDG methods to the incompressible flows, hyperbolic diffusion equation, Magnetohydrodynamics, 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 1991 and 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 mgnetohydrodynamics; 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.
1. R. Nourgaliev, H. Luo, B. Weston, A. Anderson, S. Schofield, T. Dunn, J. P. Delplanque, Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin Method for Fluid Dynamics with Phase Change, Journal of Computational Physics, Vol. 305, pp. 964-996, 2016.
2. J. Cheng, X. Yang, X. Liu, T. Liu, and H. Luo, A Direct Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids, Journal of Computational Physics, Vol. 327, pp. 484-502, 2016.
3. B. Karami Halashi, and H. Luo, A Discontinuous Galerkin Method for Magnetohydrodynamics on Arbitrary Grids, Journal of Computational Physics, Vol. 326, pp. 258-277, 2016.
4. A. Pandare, and H. Luo, A Hybrid Reconstructed Discontinuous Galerkin and Continuous Galerkin method for Incompressible Flows on Unstructured Grids, Journal of Computational Physics, Vol. 322, pp. 491-510, 2016.
5. Y. Xia, C. Wang, H. Luo, M. Christon, and J. Bakosi, Assessment of a Hybrid Finite Element and Finite Volume Code for Turbulent Incompressible Flows, Journal of Computational Physics, Vol. 307, pp. 653-669, 2016.
6. J. Cheng, T. Liu, and H. Luo, A Hybrid Reconstructed Discontinuous Galerkin Method for Compressible Flows on Arbitrary Grids, Computers & Fluids, Vol. 139, pp. 68-79, 2016.
7. Xia, Y. Lou, J., Luo, H., Edwards, J., and Muller, F., OpenACC Acceleration of an Unstructured CFD Solver Based on a Reconstructed Discontinuous Galerkin Method for Compressible Flows, International Journal for Numerical Methods in Fluids, Vol. 78, No. 3, pp. 123-139, 2015.
8. Luo, H., Xia Y., Spiegel, S., Nourgaliev, R., Jiang, Z., A Reconstructed Discontinuous Galerkin Method Based on a Hierarchical WENO Reconstruction for Compressible Flows on Tetrahedral Grids, Journal of Computational Physics, Vol. 236, pp. 477-492, 2013.