It would take a long time to solve the point kinetics equations by using full implicit Runge-Kutta (FIRK) for the strong stiffness. Diagonally implicit Runge-Kutta (DIRK) is a useful tool like FIRK to solve the stiff differential equations, while it could greatly reduce the computation compared to FIRK. By embedded low-order Runge-Kutta, DIRK is implemented with the time step adaptation technique, which improves the computation efficiency of DIRK. Through four typical cases with step, ramp sinusoidal and zig-zag reactivity insertions, it shows that the results obtained by DIRK are in perfect agreement with other available results and DIRK with adaptive time step technique has more efficiency than DIRK with the fixed time step.
- Nuclear Engineering Division
A Numerical Solution to the Point Kinetic Equations Using Diagonally Implicit Runge Kutta Method
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Zhang, Z, & Cai, Y. "A Numerical Solution to the Point Kinetic Equations Using Diagonally Implicit Runge Kutta Method." Proceedings of the 2016 24th International Conference on Nuclear Engineering. Charlotte, North Carolina, USA. June 26–30, 2016. V001T02A001. ASME. https://doi.org/10.1115/ICONE24-60011
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