Exponential Time Differencing Schemes for Fuel Depletion and Transport in Molten Salt Reactors: Theory and Implementation

Abstract

A numerical framework for modeling depletion and mass transport in liquid-fueled molten salt reactions is presented based on exponential time differencing. The solution method involves using the finite volume method to transform the system of partial differential equations (PDEs) into a much larger system of ordinary differential equations. The key part of this method involves solving for the exponential of a matrix. We explore six different algorithms to compute the exponential in a series of progression problems that explore physical transport phenomena in molten salt reactors. This framework shows good results for solving linear parabolic PDEs with each of the six matrix exponential algorithms. For large problems, the series solvers such as Padé and Taylor have large run times, which can be mitigated by using the Krylov subspace.

Keywords:

• Molten salt reactors
• depletion
• burnup
• species transport
• exponential time differencing

Acknowledgments

This work was funded by the U.S. Department of Energy (DOE) Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation program. This paper has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the DOE.