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Center for Nonlinear Studies |
A brief review of the current capabilities and outstanding issues for the efficient simulation and analysis of the flow problems using a second order state-of-the-art finite volume method on unstructured grids is given. 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 many engineering problems around complex geometries in a matter of hours, and that yet there are a wide range of flow problems where the second order methods can simply not deliver the required engineering accuracy. The presentation will be focused on the development and application of a discontinuous Galerkin method for computational fluid dynamics on arbitrary grids. Unlike the traditional discontinuous Galerkin methods, where either standard Lagrange finite element or hierarchical mode-based basis functions are used to represent numerical polynomial solutions in each element, this DG formulation represents the numerical polynomial solutions using a Taylor series expansion at the centroid of the cell. Consequently, this formulation is able to offer the insight why the DG methods are a better approach than the finite volume methods based on either TVD/MUSCL reconstruction or essential non-oscillatory (ENO)/weighted essential non-oscillatory (WENO) reconstruction, and has a number of distinct, desirable, and attractive features, which can be effectively used to address some of shortcomings of the DG methods. The developed method has been used to compute a variety of both steady-state and time-accurate flow problems from low Mach number to hypersonic on arbitrary meshes. The numerical results demonstrate the superior accuracy of this discontinuous Galerkin method in comparison with a second order finite volume method and a third order WENO method, indicating its promise and potential to become not just a competitive but simply a superior approach than its finite volume and ENO/WENO counterparts for solving flow problems of scientific and industrial interest. Bio: Prof. Luo has over twenty years of experience in developing numerical methods and computing algorithms for Computational Fluid Dynamics, Computational Aero-acoustics, and Computational Electromagnetics. His research area covers a wide range of spectrum: discontinuous Galerkin methods, finite element methods, finite volume methods, Cartesian grid methods, gridless methods, fluid-structure interaction, multi-material flows, reactive flows, unstructured grid generation methods, hp-adaptation methods, and parallel computing. He has over 100 papers to his credit. His current main interests are in developing parallel hp-adaptive higher-order discontinuous Galerkin method for computing compressible and incompressible Flows, acoustics and electromagnetic wave propagation, multi-material flows on arbitrary grids.
Host: Mikhail Shashkov, Hyung Taek Ahn