Abstract
A second-order “Time-Dependent Multiple Balance” (TDMB) method for solving neutron transport problems is introduced and investigated. TDMB consists of solving two coupled equations: (i) the original balance equation (the transport equation integrated over a time step) and (ii) the “balance-like” auxiliary equation (an approximate neutron balance equation). Simple analysis shows that TDMB is second-order accurate and robust (unconditionally free from spurious oscillation). A source iteration (SI) method with diffusion synthetic acceleration (DSA) is formulated to solve these equations. A Fourier analysis reveals that the convergence rates of the proposed iteration schemes for TDMB are similar to those of the common (SI + DSA) schemes for Backward Euler (BE); however, TDMB requires about twice the computational effort per iteration. To demonstrate the theory—accuracy, robustness, and convergence rate—and investigate the efficiency of TDMB, we present results from a discrete ordinates (Sn) research code. Results are discussed, and future work is proposed.
Highlights
In solving the time-dependent neutron transport equation, time dependency is usually discretized, and an auxiliary equation is required to close the system of equations
The proposed TDMB-source iteration (SI) and TDMB-diffusion synthetic acceleration (DSA) iteration schemes have been implemented into an Sn research code
To avoid false convergence during iteration, convergence criterion is set as shown in Eq (16), where εtol is the specified relative error tolerance, and the spectral radius ρ is approximated as the ratio of the consecutive “residuals”
Summary
In solving the time-dependent neutron transport equation, time dependency is usually discretized, and an auxiliary equation is required to close the system of equations. Varying auxiliary equations are available, and each comes with different accuracy and stability. Widely-used standard methods include Forward Euler (FE), Crank-Nicholson (CN, a.k.a trapezoid rule), and Backward Euler (BE). FE is simple but inappropriate for typically stiff problems. CN is favorable because of its higher (second) order of accuracy. BE remains the favorite method in practice, due to its robustness; it is free from producing spuriously oscillating solutions regardless of time step size
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.
