Abstract
In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the first recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution.
Highlights
Our starting point is the neutron space kinetics equation considering the fast and thermal groups and with six delayed neutron precursor groups
The basic idea of the method consists in expanding the scalar neutron flux and concentration of delayed neutron precursors in a double Taylor series in the spatial and temporal variable, substitution of these expansions in the space kinetic equation and construction of a linear algebraic system that allows to calculate the coefficients of the expansion in series, by the application of the boundary conditions and continuity of flux and neutron current in the interfaces of the mesh
The methodology consists of expanding the scalar neutron flux and the concentration of delayed neutron precursors in Taylor series in the spatial variable (applying the methodology discussed in (CEOLIN, 2014), where the temporal dependence is incorporated in the coefficients of that series, that allows to decompose the original problem into a recursive system of time-dependent ordinary differential equations
Summary
Our starting point is the neutron space kinetics equation considering the fast and thermal groups and with six delayed neutron precursor groups. The basic idea of the method consists in expanding the scalar neutron flux and concentration of delayed neutron precursors in a double Taylor series in the spatial and temporal variable, substitution of these expansions in the space kinetic equation and construction of a linear algebraic system that allows to calculate the coefficients of the expansion in series, by the application of the boundary conditions and continuity of flux and neutron current in the interfaces of the mesh. The methodology consists of expanding the scalar neutron flux and the concentration of delayed neutron precursors in Taylor series in the spatial variable (applying the methodology discussed in (CEOLIN, 2014), where the temporal dependence is incorporated in the coefficients of that series, that allows to decompose the original problem into a recursive system of time-dependent ordinary differential equations. The fact that the time evolution in the solution is calculated recursively for in principle all times does not impose any restrictions such as convergence limitations that are typically present in progressive time step approaches, used by the methods cited above and elsewhere
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
