Development of a fully-implicit ODE-solver for containment analysis code Provisionally Accepted

Jun Huang^1* Jinggang Li¹ Yinxiang Ma^1*

• ¹China Guangdong Nuclear Research Institute Co., Ltd., China

The thermal-hydraulic dynamics in containment are governed by a system of stiff ordinary differential equations (ODEs). A fully implicit discretization scheme is adopted to discretize these ODEs in order to mitigate the effects of stiffness. In comparison with explicit or semi-implicit discretization schemes that are subject to Courant limits on time steps, the fully implicit discretization scheme is more suitable for a containment analysis code that focuses on predicting both short term and long-term thermal-hydraulic parameters after an accident. This paper introduces a general-purpose ODE solver for the containment analysis code. The outline of the solver is as follows: The fully implicit discrete equations lead to a large set of nonlinear equations that need to be solved using Newton's iterative method. The partial derivative components in the Jacobi matrix are calculated by perturbation method using the finite difference approximation, which avoids the complicated derivation of partial derivatives. The scaling modification technique is incorporated into this ODE solver to deal with significant differences in unknow variable magnitudes and the line search method is introduced to address the difficulty of obtaining an accurate root estimate with Newton's method when the initial guess is far from the actual root. This proposed ODE solver was applied to two typical stiff ODE problem to test its stiffnesssuppressed ability and to demonstrate that this proposed solver can perform calculation with very large time step. Then, the CASSIA code, containment analysis code developed by CNPRI, equipped with this ODE solver was applied to CNSI benchmark problem and CVTR test 3 problem to preliminarily demonstrate the proposed ODE solver can perform containment thermal-hydraulic analysis correctly. This paper could provide references for the development of a home-made containment analysis code.