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.

中文翻译：

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核反应堆严重事故平台集中参数模型耦合问题的求解

本文重点解决集总参数模型的耦合问题。这些问题对于模拟核反应堆中的严重事故很有意义~：这些粗粒度模型允许在考虑整个严重事故情景时快速计算用于风险评估和大问题解决方案的统计分析。然而，这种建模方法有几个数值缺陷。此外，在这个工业环境中，计算效率非常重要，导致各种数值约束。本研究的目的是分析显式耦合策略在解决此类耦合问题中的适用性，并设计允许稳定和准确计算的隐式耦合方案。所提出的方案在 CEA' 中进行了理论分析和测试 使用耦合集总参数模型和耦合一维模型解决热传导问题的 procor 平台。讨论了数值结果，并允许我们强调使用设计的耦合方案而不是通常的显式耦合方案的好处。