A Dissipative Filter for DG Discretizations with Sub-cell Discontinuity Resolution
Speaker: John Ekaterinaris, Embry-Riddle Aeronautical University
Presentation
Abstract
The filter designed by Yee et al. (JCP Vol. 150, 1999) and extensively used in the development of low dissipative well-balanced high order accurate finite difference schemes is adapted to the finite element context of DG discretizations. The filter operator is constructed in the canonical computational domain for the standard cubical element where it can be applied in a direction per direction basis, and then extended for all element types in unstructured meshes using collapsed coordinate transformations. The performance of the proposed dissipative mechanism is demonstrated and evaluated for different orders of expansions for one-dimensional and multidimensional problems with exact solutions. It is shown that for higher order discretizations sub-cell discontinuity resolution is obtained and the design order of accuracy is preserved even for flow including discontinuities. The filtering operator is applied for a number of standard inviscid flow test problems including strong shocks interactions to demonstrate that the proposed dissipative mechanism for DG discretizations yields superior results compared to the results obtained with the TVB limiter, high-order hierarchical limiting, or application of adaptive mesh refinement. The proposed approach is well suited for h/p-type adaptive computations in order to locally enhance resolution for three dimensional flow simulations that include both discontinuities and complex flow features such as high speed compressible turbulence.
Biography
Prof. John Ekaterinaris received his Ph.D. 1987 from Georgia Institute of Technology. Between the years 1987–1995, he worked at the Numerical Aerodynamics Simulation (NAS) branch of NASA Ames Research Center at Moffett Field, and at the same time he was faculty at the Naval Postgraduate School at Monterey, CA. He took a Senior Research Scientist position at RISOE National Laboratory in Denmark between the years 1995–1997. He returned to California and worked at Nielsen Engineering and Research between 1997–2000. In 2000 he joined the faculty of Mechanical and Aerospace Engineering at the University of Patras and the Institute of Applied and Computational Mathematics at FORTH. In 2012, he joined Embry-Riddle Aeronautical University, where he presently teaches and conducts research with his students.
His interests are computational mechanics (including aerodynamics, magnetogasdynamics, flow control, flow transition, turbulence research, and flow structure interaction), multi-scale phenomena, stochastic PDEs, and biomechanics. He is the author of over 60 journal papers. He is an associate editor for the journal Progress in Aerospace Sciences and editor-in-chief for the journal Aerospace Science and Technology.