  This paper focuses on solving coupled problems of lumped parameter models.
Such problems are of interest for the simulation of severe accidents in nuclear
reactors~: these coarse-grained models allow for fast calculations for
statistical analysis used for risk assessment and solutions of large problems
when considering the whole severe accident scenario. However, this modeling
approach has several numerical flaws. Besides, in this industrial context,
computational efficiency is of great importance leading to various numerical
constraints. The objective of this research is to analyze the applicability of
explicit coupling strategies to solve such coupled problems and to design
implicit coupling schemes allowing stable and accurate computations. The
proposed schemes are theoretically analyzed and tested within CEA's procor
platform on a problem of heat conduction solved with coupled lumped parameter
models and coupled 1D models. Numerical results are discussed and allow us to
emphasize the benefits of using the designed coupling schemes instead of the
usual explicit coupling schemes.
