I have been teaching NUEN 618 since Fall 2004. It is a PhD-level course that introduces tightly coupled multiphysics simulation techniques and their applications to typical problems arising in nuclear science and engineering (e.g., reactor dynamics and safety transients, conjugate heat transfer, radiative transfer, fluid-structure interaction). Applications to other engineering fields will be also considered, e.g., for the students’ projects (after instructor approval).
- Most of the numerical methods still currently in use in nuclear reactor analysis can be traced back to the 1970’s and 1980’s. At that time, multiphysics phenomena were computed and analyzed through a “divide and conquer” approach, whereby each physic component was treated using mono-disciplinary codes and coupling among the intertwined physical processes was weak and often
done a priori using envelope values.
- With advances in computer software and hardware (e.g., the message passing interface paradigm from the mid 1990’s), computer codes have been increasingly coupled to one another, so as to model reality with a higher degree of fidelity.
- However, this coupling was still performed in an explicit fashion, whereby some physic components were staggered or lagged in time, a mathematical approach known as operator-splitting that resulted in loss of accuracy, or worse, numerical instabilities.
- Over the last 2+ decades, a new approach, based on a monolithic view of the whole multiphysics problem, has successfully been applied to a wide range of problems, from plasma physics to hemodynamics. These techniques, based on a derivative-free approach to Newton’s method, are now
being applied to many problems of interest in science and engineering. Powerful software libraries, such as the MOOSE framework (https://mooseframework.inl.gov/), are based on such ideas.
- This course focuses on advanced numerical techniques for nonlinear coupled multiphysics applications: this includes a review of operator-splitting techniques and their advantages and drawbacks, a presentation of derivative-free Newton’s technique for a monolithic approach to multiphysics simulations, a description of recent trends and issues in multiphysics code development.
- First, these numerical techniques will be presented using simple examples, with coding assignments in Matlab or Python. This will allow you to better understand the inner workings of such algorithms rather than becoming users of black-box solvers.
- In the second part of the course, the world-class multiphysics object-oriented library, MOOSE
(https://mooseframework.inl.gov/) will be presented and the fundamental techniques surveyed earlier will be demonstrated using MOOSE. The use of other finite element libraries such as deal.ii (www.dealii.org) or libmesh (http://libmesh.github.io/) will be discussed.
- The course will conclude with student projects’ presentations.