Fictitious domain methods for two-phase flow energy balance computations in nuclear components

Abstract

This paper is dedicated to the numerical simulation of nuclear components (cores and steam generators) by fictitious domain methods. The fictitious domain approach consists in immersing the physical domain under study in a Cartesian domain, called the fictitious domain, and in performing the numerical resolution on this fictitious domain. The calculation times are then efficiently reduced by the use of fast solvers. In counterpart, one has to handle with an immersed boundary, generally non-aligned with the Cartesian mesh, which can be non-trivial. The two fictitious domain methods compared here on industrial simulations and developed by Ramière et al. deal with an approximate immersed interface directly derived from the uniform Cartesian mesh. All the usual immersed boundary conditions (Dirichlet, Robin, Neumann), possibly mixed, are handled through a unique formulation of the fictitious problem. This kind of approximation leads to first-order methods in space that exhibit a good ratio of the precision of the approximate solution over the CPU time, which is very important for industrial simulations. After a brief recall of the fictitious domain method with spread interface (Ramière et al., CMAME 2007) and the fictitious domain method with immersed jumps (Ramière et al., JCP 2008), we will focus on the numerical results provided by these methods applied to the energy balance equation in a steam generator. The advantages and drawbacks of each method will be pointed out. Generally speaking, the two methods confirm their very good efficiency in terms of precision, convergence, and calculation time in an industrial context. Copyright © 2011 John Wiley & Sons, Ltd.