An h/p Adaptive Discontinuous Galerkin Method for Shock Dominated High Speed Flows
Speaker: John Ekaterinaris, Embry-Riddle Aeronautical University
Presentation
Abstract
High order discontinuous Galerkin (DG) discretizations possess features making them attractive for computations of three dimensional complex flows with shocks. A key element, which could make the DG method more suitable for these computations, is application of limiting procedures that ensure accurate and crisp capturing of discontinuities for three-dimensional complex flows in domains with nontrivial geometry. A total variation bounded (TVB) limiter is constructed and applied in the canonical computational space to enable capturing of strong shocks and steep flow gradients without numerical oscillations in unstructured meshes. This unified limiting procedure for DG discretizations in unstructured meshes is well suited for h –, p –, and h/p dynamic adaptive refinement of the computed numerical solutions. The performance of the unified limiting approach is demonstrated for a number of standard high speed flow problems including strong shocks to show the potential of the method. Furthermore, hierarchical limiting of higher order expansions of the numerical solution in three–dimensional unstructured meshes is demonstrated. Increased order of expansion and adaptive mesh refinement in selected flow regions is introduced in the dynamic h/p – refinement context in order to locally enhance resolution of three–dimensional simulations that include both discontinuities and complex flow features. Enhanced resolution for transonic shocks is obtained with adaptive mesh refinement. It is furthermore demonstrated that accurate capturing of discontinuities leading to flow instabilities triggered by complex shock interactions becomes possible at a reduced computational cost. Applications of the method to chemically reactive high speed flows are shown.
Biography
Prof. John Ekaterinaris revived his Ph.D. in Aerospace Engineering at Georgia Institute of Technology in 1987. He worked at NASA–Ames Research Center, 1988-1995 through the Navy-NASA joint institute of Aeronautics with Naval Postgraduate Scholl at Monterey. He was visiting scientist at wind energy department RISOE National laboratory DK, and then Research Director at the Institute of Applied and Computational Mathematics of FORTH until 2005. In Sept. 2005 he moved into academia and joined the faculty of Mechanical and Aerospace Engineering at the University of Patras. He joined the faculty of Aerospace Engineering of Embry-Riddle Aeronautical University in August 2012. His interests are development and application of high order methods in computational mechanics (including aerodynamics, magnetogasdynamics, and computational fluid structure interaction), flow control, high speed flow transition and turbulence, multi-scale phenomena, and biomechanics. He is author of over 50 journal papers. He is associate editor for the Journal Progress in Aerospace Sciences and editor in chief for the Journal Aerospace Science and Technology.