Stochastic Theory of Neutron Transport in Nuclear Reactor

Author(s):  
R. Yu. Nesterenko
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhengang Zhao ◽  
Yunying Zheng

Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition.


2020 ◽  
Vol 149 ◽  
pp. 107799
Author(s):  
Yue Sun ◽  
Junhe Yang ◽  
Yahui Wang ◽  
Zhuo Li ◽  
Yu Ma

A probability balance equation is formulated for the number of particles present in a cascade resulting from multiple births at each collision. Janossy’s regeneration point method is used and it leads to an integro differential equation for the generating function from which statistical information can readily be extracted. The technique is applied to the interpretation of radiation damage cascades in a homogeneous, amorphous medium in which two particles are ‘born’ per collision. The history of a single chain is followed and equations for the mean and variance are obtained as well as for individual probabilities. It is further shown how the backward and forward forms of the Boltzmann equation are related via the Green function of the system. Additional study shows that the variance also obeys a forward type of equation although its solution is not obtained as conveniently as that of the corresponding backward equation. Several analogies are made with other branches of particle physics; in particular, cosmic rays and neutron transport.


2013 ◽  
Vol 37 (23) ◽  
pp. 9747-9767 ◽  
Author(s):  
Vishwesh A. Vyawahare ◽  
P.S.V. Nataraj

2018 ◽  
Vol 112 ◽  
pp. 693-714 ◽  
Author(s):  
John R. Tramm ◽  
Kord S. Smith ◽  
Benoit Forget ◽  
Andrew R. Siegel

1998 ◽  
Vol 31 (3-4) ◽  
pp. 265-293 ◽  
Author(s):  
M. Mokhtar-Kharroubi ◽  
K. Jarmouni-Idrissi

Author(s):  
Yu Liu ◽  
Michael Nishimura ◽  
Marat Seydaliev ◽  
Markus Piro

Recent trends in nuclear reactor performance and safety analyses increasingly rely on multiscale multiphysics computer simulations to enhance predictive capabilities by replacing conventional methods that are largely empirically based with a more scientifically based methodology. Through this approach, one addresses the issue of traditionally employing a suite of stand-alone codes that independently simulate various physical phenomena that were previously disconnected. Multiple computer simulations of different phenomena must exchange data during runtime to address these interdependencies. Previously, recommendations have been made regarding various approaches for piloting different design options of data coupling for multiphysics systems (Seydaliev and Caswell, 2014, “CORBA and MPI Based “Backbone” for Coupling Advanced Simulation Tools,” AECL Nucl. Rev., 3(2), pp. 83–90). This paper describes progress since the initial pilot study that outlined the implementation and execution of a new distribution framework, referred to as “Backbone,” to provide the necessary runtime exchange of data between different codes. The Backbone, currently under development at the Canadian Nuclear Laboratories (CNL), is a hybrid design using both common object request broker architecture (CORBA) and message passing interface (MPI) systems. This paper also presents two preliminary cases for coupling existing nuclear performance and safety analysis codes used for simulating fuel behavior, fission product release, thermal hydraulics, and neutron transport through the Backbone. Additionally, a pilot study presents a few strategies of a new time step controller (TSC) to synchronize the codes coupled through the Backbone. A performance and fidelity comparison is presented between a simple heuristic method for determining time step length and a more advanced third-order method, which was selected to maximize configurability and effectiveness of temporal integration, saving time steps and reducing wasted computation. The net effect of the foregoing features of the Backbone is to provide a practical toolset to couple existing and newly developed codes—which may be written in different programming languages and used on different operating systems—with minimal programming effort to enhance predictions of nuclear reactor performance and safety.


2013 ◽  
Vol 14 (2) ◽  
pp. 59
Author(s):  
Mohamad Ali Shafii

A few numerical methods that usually used to solve neutron transport equation in nuclear reactor are SN dan PN method, Monte Carlo, Collision Probability and Methods of Characteristics . First two methods have been developed using diffusion approach, and last three methods suitable are applicated for transport approximation. Those of three methods have important role in the desain of nuclear reactors. In addition to follow the development of advanced reactor designs, the three methods were chosen because they do not use diffusion approach these are more accurate methods, as well as less need considerable computer memory. Of all the existing methods, the CP method has several advantages among the others. Keywords : Neutron transport, SN, PN, CP, MOC, MC


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