Toward exascale: Large eddy simulation and direct numerical simulation of nuclear reactor flows with the spectral element method

Numerical simulation has been an intrinsic part of nuclear engineering research supporting the design of nuclear power plants. With the advent of Petascale computing (i.e., computers capable of more than 1 PFlop), the simulation of portions of reactor components with turbulence-resolving techniques is now possible. These simulations can provide invaluable insight into the flow dynamics, which is difficult or often impossible to obtain with experiments alone. The spectral element method in particular has emerged as a powerful method to deliver massively parallel calculations at high fidelity by using Large Eddy Simulation or Direct Numerical Simulation. In this work we review the fundamentals of the method and the reasons it is compelling for the simulation of nuclear engineering flows. Moreover, we review a series of Petascale simulations, including the simulations of helical coil steam generators, fuel assemblies and pebble beds. Even with Petascale computing, however limitations for nuclear modeling and simulation tools remain. In particular he size and scope of turbulence-resolving simulations are still limited by computing power and resolution requirements, which scale with the Reynolds number. In the final part of this manuscript we discuss the future of the field, including recent advancements in emerging architectures such as GPU-based supercomputers.