This paper will present a high fidelity solution algorithm for a model of a nuclear reactor core barrel. This model consists of a system of nine nonlinearly coupled partial differential equations. The coolant is modeled with the 1-D six-equation two-phase flow model of RELAP5. Nonlinear heat conduction is modeled with a single 2-D equation. The fission power comes from two 2-D equations for neutron diffusion and precursor concentration. The solution algorithm presented will be the physics-based preconditioned Jacobian-free Newton-Krylov (JFNK) method. In this approach all nine equations are discretized and then solved in a single nonlinear system. Newtons method is used to iterate the nonlinear system to convergence. The Krylov linear solution method is used to solve the matrices in the linear steps of the Newton iterations. The physics-based preconditioner provides an approximation to the solution of the linear system that accelerates the Krylov iterations. Results will be presented for two algorithms. The first algorithm will be the traditional approach used by RELAP5. Here the two-phase flow equations are solved separately from the nonlinear conduction and neutron diffusion. Because of this splitting of the physics, and the linearizations employed this method is first order accurate in time. A second algorithm will be the JFNK method solved second order in time accurate. Results will be presented which compare these two algorithms in terms of accuracy and efficiency.

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