Numerical Solution of Stiff Burnup Equation with Short Half Lived Nuclides by the Krylov Subspace Method

Abstract

The Krylov subspace method is applied to solve nuclide burnup equations used for lattice physics calculations. The Krylov method is an efficient approach for solving ordinary differential equations with stiff nature such as the nuclide bunrup with short lived nuclides. Some mathematical fundamentals of the Krylov subspace method and its application to burnup equations are discussed. Verification calculations are carried out in a PWR pin-cell geometry with UO2 fuel. A detailed burnup chain that includes 193 fission products and 28 heavy nuclides is used in the verification calculations. Shortest half life found in the present burnup chain is approximately 30 s (106Rh). Therefore, conventional methods (e.g., the Taylor series expansion with scaling and squaring) tend to require longer computation time due to numerical stiffness. Comparison with other numerical methods (e.g., the 4-th order Runge-Kutta-Gill) reveals that the Krylov subspace method can provide accurate solution for a detailed burnup chain used in the present study with short computation time.