【Lecture】Improved Shock capturing with high-order discontinuous Galerkin discretizations using adaptive mesh refinement and sub-cell discontinuity resolution


Time: Wednesday, May 16, 2018 9:00-11:00 am

Venue: RM A114, Aerospace Building

Lecturer:  Professor John. A. Ekaterinaris

                 Embry-Riddle Aeronautical University

                Editor in Chief of the Journal Aerospace Science and Technology (AESCTE)


Education Background:

Ph.D. - Doctor of Philosophy in Aerospace Engineering, Georgia Institute of Technology

M.S. - Master of Science in Mechanical Engineering, Georgia Institute of Technology

Academic Background

1988 - 1995      Research Scientist, NASA/Ames Research Center, CA.

1990 - 1992      Assistant Research Professor, Naval Postgraduate School.

1992 - 1995      Associate Research Professor, Naval Postgraduate School.

1995 - 1997      Senior Research Scientist, RISOE National Laboratory, DK.

1997 - 2000      Senior Research Scientist, NIELSEN Engineering and Research.

2000 - 2005      Research Director, Institute of Appl. and Computational Math. (IACM), Foundation for Research and Technology Hellas (FORTH), Crete, Greece, collaborating professor with FORTH/IACM.

2005 - 2012      Professor School of Mechanical and Aerospace Engineering, University of Patras, Greece.

2012-Present     Embry-Riddle Aeronautical University

Research Areas:

Development and application of CFD methods,

Design and development of high order accurate methods for structured and unstructured meshes,

Development and application of finite element methods for fluid dynamics, structural dynamics and electromagnetis,

Applications of computational mechanics to biomechanics and bioengineering.


Discontinuous Galerkin (DG) discretizations possess features making them attractive for high-resolution computations in three-dimensional flows that include strong discontinuities and embedded complex flow features. Key elements, which could make the DG method more suitable for computations of such time-dependent flows in complex domains, is use of adaptive mesh refinement (AMR) and application of limiting procedures that ensure sharp and accurate capturing of discontinuities for unstructured mixed-type meshes. A unified limiting approach suitable for increased order of expansion and adaptive mesh refinement is introduced in the context of it h/p-adaptivity in order to locally enhance resolution for three-dimensional flow simulations that include discontinuities and embedded complex flow features. Furthermore, a nonlinear filter is employed in the finite element context of discontinuous DG discretizations to achieve low dissipative, well-balanced, high-order discontinuity capturing. It is shown that for higher order discretizations discontinuity resolution within the cell is achieved and the design order of accuracy is preserved. The filter 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 and higher-order hierarchical limiting. The proposed approach is suitable for p–adaptivity in order to locally enhance resolution of three-dimensional flow simulations that include discontinuities and complex flow features.

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