Woodruff School of Mechanical Engineering
NRE 8011/8012 and MP 6011/6012 Seminar
Nuclear & Radiological Engineering and Medical Physics Programs
Accuracy of Spatial Discretization Schemes for Solving the Discrete Ordinates Approximation of the Transport Equation
Dr. Yousry Azmy
North Carolina State University
Thursday, January 22, 2015 at 11:00:00 AM
Boggs Building, Room 3-47
Dr. Farzad Rahnema
Research activities in NC State's Nuclear Computational Science Group span a broad range of topics from the theoretical to the applied. After a brief review of the group's current research portfolio two topics will be elaborated. First is the unified Finite Elements Method (FEM) framework for a wide variety of high spatial expansion order discrete ordinates methods. Benefits of the unified framework include: (1) reconciling traditional transport methods (e.g. Nodal) with modern numerical methods (e.g. Discontinuous Galerkin FEM); (2) reducing the difference between these methods to the selection of the function spaces; (3) enabling accurate intra-cell interpolation; and (4) employing FEM machinery for error estimation. Second is a comparison between the accuracy of a wide variety of methods utilizing a suite of 3D Method of Manufactured Solutions. In addition to varying the methods' spatial expansion order and the norm in which the error is measured we also examine the effect on accuracy of solution irregularity. As anticipated we find that no one method preforms best across the board but that high order methods more generally are more accurate and more computationally efficient than low order methods. The one exception to this observation is the case of problems with discontinuous solutions where a new approach of tracking the discontinuity along the singular characteristic using a simple step approach yields solutions that converge in the L_inf norm to the reference solution with mesh refinement while high order methods fail to do so.
Dr. Yousry Azmy received his Ph.D. in Nuclear Engineering from University of Illinois at Urbana-Champaign, in 1985. Upon graduating, he took a 1 year position as Research Assistant Professor at the University of Virginia, Charlottesville. In 1986 he joined the research staff of the Computational Physics and Engineering Division of Oak Ridge National Laboratory (ORNL). Over the following 16 years he ascended the ranks of the research ladder focusing his research on nuclear computational science, particularly on aspects of the numerical solution of the neutron transport equation. These include advanced numerical methods, numerical error estimation and analysis, iterative acceleration schemes, and parallel solution algorithms. In July 2002 he became Prof. of Nuclear Engineering in the Department of Mechanical and Nuclear Engineering at Penn State University. Starting June 1, 2008, Dr. Azmy was appointed Professor and Head of the Department of Nuclear Engineering at North Carolina State University. Dr. Azmy is member of the American Nuclear Society (ANS), SIAM, American Mathematical Society, and the American Society for Engineering Education. He was elected ANS Fellow in 2002, and won ANSí 1995 Young Member Engineering Achievement Award, and ANSí Mark Mills Award in 1986, among other honors and awards. He is active in ANS serving on Board of Directors, and has chaired the Technical Journals Committee, 2011-2014, and the Nuclear Engineering Department Heads Organization (NEDHO), 2011-12, among several other services to ANS over the past 13 years. Since 1995, he has been member of the Organization for Economic Cooperation and Developmentís Experts Group on Three Dimensional Transport Methods and Codes. In 2012 Dr. Azmy was elected to a 3-year term on the Board of Directors of the Nuclear Energy Institute. He is Director of the Consortium for Nonproliferation Enabling Capabilities, a 5-year, $/yr, 7 university plus 3 national lab collaboration sponsored by the US National Nuclear Security Administration (NNSA). In January 2015 he was named Co-Editor of the international journal Progress in Nuclear Energy. Dr. Azmy serves as consultant to a variety of domestic and international, academic and governmental organizations.