NOTE: Later starting time than usual.

35th NIA CFD Seminar

Topic: A Reconstructed Discontinuous Galerkin Method Based on a Hierarchical WENO Reconstruction for Compressible Flows on Hybrid Grids

Date: Tuesday, May 28, 2013

Time:12:30pm-01:30pm (EST),

Location: NIA room 101

Speaker: Hong Luo

Biography: 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.

Abstract: Recently, reconstructed discontinuous Galerkin (DG) methods have been developed to solve compressible flow problems. 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 reconstructed discontinuous Galerkin (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 this presentation, a reconstructed discontinuous Galerkin (RDG) 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 for solving the compressible Navier-Stokes equations on hybrid grids. In this HWENO(P1P2) method, a quadratic polynomial solution (P2) is first reconstructed using a Hermite WENO reconstruction from the underlying linear polynomial (P1) discontinuous Galerkin solution to ensure the linear stability of the RDG method and to improve the efficiency of the underlying DG method. By taking advantage of handily available and yet invaluable information, namely the derivatives in the DG formulation, the stencils used in the reconstruction involve only von Neumann neighborhood (adjacent face-neighboring cells) and thus are compact. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the nonlinear stability of the RDG method. 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 DG methods for the solution of the compressible Navier-Stokes equations.

Additional information, including the webcast link, can be found at the NIA CFD Seminar website, which is temporarily located at

http://www.hiroakinishikawa.com/niacfds/