A positivity-preserving finite volume scheme for multi-group neutron diffusion kinetics equations with delayed neutrons. (1st January 2023) - Xu, Jinjing; Zhao, Fei; Sheng, Zhiqiang; Yuan, Guangwei
Abstract: Neutron diffusion kinetics equation contains a diffusion type equation and a set of ordinary differential equations, which form a coupled system. In this paper, we give a positivity theorem for neutron diffusion kinetics equation with delayed neutrons and propose a nonlinear positivity-preserving finite volume scheme on general star-shaped quadrilateral meshes, which can deal with discontinuous and anisotropy diffusion coefficient problems. The existence of solution for the nonlinear system is proved under certain constraint on time step size, which is independent of spatial mesh size. Three nonlinear iteration strategies are introduced to solve the nonlinear system. Numerical experiments are performed to demonstrate that the scheme is positivity-preserving and keeps approximately second order accuracy in space. The computational costs of three nonlinear iteration strategies are compared. Another example is also present to show some constraint on time step size is necessary for the convergence of the nonlinear iteration.