Mathematics Colloquia and Seminars

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Description

Idaho National Laboratory
Thermal Science & Safety Analysis
Reactor Safety Simulation Group
P.O. Box 1625
Idaho Falls, ID 83415-3840, USA
robert.nourgaliev@inl.gov

Within the ongoing renaissance in nuclear power industry, safety analysis plays a key role in ensuring success of new reactor system designs and safe operation/life extension of old reactor fleet. In the present talk, I will discuss the challenges and requirements for the development of new generation safety tools, with the focus placed on physics modeling, mathematical formulation, numerics, code architecture and algorithmic difficulties. Modern nuclear safety analysis codes involve multiphysics (including single- and multi-phase thermalhydraulics, neutronics, thermal-structural analysis, corrosion chemistry, reliability and human factors, etc.) and necessitate modeling of the whole complex reactor system in a tightly-coupled fashion. This requires the development of the code architecture and numerical algorithms which are capable of dealing with highly non-linear problems and stiff multi-scale linear algebra. At INL, we have initiated the development of the next generation system analysis code, which is envisioned to be capable of dealing with the above outlined challenges. I will describe/highlight code’s numerical capabilities, including a) high-order spatio-temporal discretization (using recovery/reconstruction Discontinuous Galerkin and fully-implicit L-stable Runge-Kutta schemes, with the accuracy up to the 12th-order in space and the 5th-order in time), b) Jacobian-free Newton-Krylov (JFNK) methodology for tight coupling multiple-time multi-physics problems, physics-based preconditioning of stiff linear algebra, c) ability of the code to interface with modern risk analysis methodologies (including static and dynamic PRA), d) uncertainty quantification (UQ), and verification and validation (V&V) practice. The challenges in physics and mathematics include homogenization of multi-physics and multi-phase/multi-component fluid flows, ensuring well-posedness of the underlying governing equations, and development of adequate closure laws, accounting for developing and nonsteady- state flows/multiphysics. A few simple demonstrations of the code application in reactor safety analysis (including Risk-Informed Safety Margin Characterization, RISMC) will be also presented.

Note that there are two Applied Math seminars this week and this one is not at the regular time.