Application of Rosenbrock Methods to Tightly Coupled Multiphysics Simulations in Nuclear Science and Engineering
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Recently, researchers have investigated the implementation of accurate high order time discretization techniques in large-scale nonlinear multiphysics simulations using Implicit Runge-Kutta (IRK) methods. For a given time step, IRK methods require the iterative solution of a nonlinear system of equations using Newton’s method. Rosenbrock methods, a variant of IRK methods, avoid this issue by linearizing this system of equations, so only one Newton iteration is required at each stage. Because Rosenbrock methods may achieve this without loss of accuracy order or stability, Rosenbrock methods have the potential to generate accurate solutions more efficiently. This research investigates these claims by applying Rosenbrock methods to two representative multiphysics problems found in nuclear science and engineering: (1) the Point Reactor Kinetics Equations (PRKE) with temperature-induced reactivity feedback, and (2) non-equilibrium radiation diffusion. To assess the merits of Rosenbrock methods, a measure of accuracy per computational cost was compared between Rosenbrock methods and IRK methods, and Rosenbrock methods were found to achieve a smaller computational cost for a given level of accuracy than IRK methods of the same convergence order.
Hansel, Joshua 1989- (2011). Application of Rosenbrock Methods to Tightly Coupled Multiphysics Simulations in Nuclear Science and Engineering. Honors and Undergraduate Research. Available electronically from