Abstract:

Roots of coarse mesh, or advanced, nodal methods [1] can be traced to “exact finite difference schemes.” After a brief overview of the exact finite difference schemes, a nodal scheme will be developed for the scalar convection-diffusion PDE [2, 3]. Benefits and limitations of these coarse mesh schemes will be discussed; and ways to relax these limitations will be pointed out.  Current work to remove the restrictions on domain geometry is focused on two approaches:  1) hybrid scheme in which nodal methods are restricted to the interior of the domains and along boundaries that are parallel to the coordinate axes, while a second scheme—such as finite element, more suitable for complex boundaries—is used along curved boundaries [4]; 2) iso-parametric mapping approach to transform the hexahedral elements to a simple cube on which traditional NIM can be applied [5].

A brief overview of work, mostly carried out by undergraduate students, on the use of virtual, mixed and augmented reality for education and training will also be given.

1.            R. D. Lawrence, “Progress in Nodal Methods for the Solution of the Neutron Diffusion and Transport Equations,” Progress in Nuclear Energy, 17 (3), 271 (1986).

2.            Rizwan-uddin, “Comparison of the Nodal Integral Method and Non-Standard Finite-Difference Schemes for the Fisher Equation,” SIAM J. Scientific Computing, 22 (6), 1926-1942 (2001).

3.            Fei Wang and Rizwan-uddin, “A Modified Nodal Scheme for the Time-Dependent, Incompressible Navier-Stokes Equations,” J. Comp. Physics, 187, 168-196 (2003).

4.            Sundar Namala and Rizwan-uddin, "Hybrid Nodal Integral -Finite Element Method (NI-FEM) for 2D, Time-Dependent Burgers’ Equation in Arbitrary Geometries", Proc. of the Int. Topical Meeting on Nuclear Reactor Thermal Hydraulics, 3741-3755, Portland, OR, August 25-29, 2019.

5.            Ibrahim Jarrah and Rizwan-uddin, "Nodal Integral Method for Arbitrary Hexahedral Elements Applied to 3D Convection-Diffusion Equation", Proc. of the International Conference on Mathematics and Computational Methods applied to Nuclear Science and Engineering (M&C 2019), 1260-1269,  Portland, OR, August 25-29, 2019.

Virtual Education and Research Lab (VERL):

At VERL, we develop models to simulate physical phenomena, and solve them analytically and on high performance computers to simulate all aspects of processes taking place in and related to reactors and nuclear power plants (including neutronics, thermal hydraulics, etc). Recent focus has been on advanced numerical schemes for Computational Fluid Dynamics (CFD) as well as on multi-scale, multi-physics approaches achieved by coupling multiple codes. We also develop virtual, 3D, immersive and interactive models of facilities such as nuclear power plants, control rooms and laboratories, to help design better human-machine-interfaces, facilitate efficient design, and improve education and training. A recent addition to our portfolio is digital instrumentation and control and cyber security in the nuclear industry. This extension is being pursued in collaboration with the cyber security expertise available at the Coordinated Science Lab at the University of Illinois.

Bio:

Dr Rizwan Uddin is Professor and Head of Nuclear, Plasma, and Radiological Engineering Department; Professor of Computational Science and Engineering; and Director of Master of Engineering in Energy Systems program at the University of Illinois at Urbana-Champaign. His areas of interest include thermal hydraulics; CFD; computational methods development; coupled neutronics and thermal hydraulics; biological systems and general modeling and simulation. With guidance from his undergraduate and graduate students, he has also been exploring the use of computer- and video-games for education and training.