scholarly journals Numerical Approximation for Fractional Neutron Transport Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhengang Zhao ◽  
Yunying Zheng
Keyword(s):  
Transport Equation ◽  
Nuclear Reactor ◽  
Neutron Transport ◽  
Transport Processes ◽  
Neutron Transport Equation ◽  
Spatial Direction ◽  
Fully Discrete ◽  
Discrete Methods ◽  
Fifth Order ◽  
Different Order

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.

scholarly journals Solution methods of neutron transport equation in nuclear reactors

2013 ◽  
Vol 14 (2) ◽  
pp. 59
Author(s):  
Mohamad Ali Shafii
Keyword(s):  
Monte Carlo ◽  
Transport Equation ◽  
Nuclear Reactor ◽  
Nuclear Reactors ◽  
Neutron Transport ◽  
Collision Probability ◽  
Computer Memory ◽  
Neutron Transport Equation ◽  
Solution Methods ◽  
Transport Approximation

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

On the stochastic nonlinear neutron transport equation

1992 ◽  
Vol 121 (3-4) ◽  
pp. 253-272 ◽  
Author(s):  
Mustapha Mokhtar-Kharroubi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Transport Equation ◽  
Nuclear Reactor ◽  
Neutron Transport ◽  
Neutron Transport Equation ◽  
Chain Reaction ◽  
Partial Differential ◽  
Model Case

SynopsisThe probability that a neutron leads to a divergent chain reaction in a nuclear reactor is governed by a nonlinear integro-partial-differential equation [1]. A model case of this equation was completely analysed by Pazy and Rabinowitz [2,3]. The purpose of this paper is to extend their results to the general case and to tackle some related topics.

High-Dimensional Model Representations for the Neutron Transport Equation

2014 ◽  
Vol 177 (3) ◽  
pp. 350-360 ◽  
Author(s):  
Zhengzheng Hu ◽  
Ralph C. Smith ◽  
Jeffrey Willert ◽  
C. T. Kelley
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
High Dimensional ◽  
Dimensional Model ◽  
Neutron Transport Equation

scholarly journals Note on the Solution of Transport Equation by Tau Method and Walsh Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Transport Equation ◽  
Legendre Polynomials ◽  
Neutron Transport ◽  
Three Dimensional ◽  
Walsh Function ◽  
Dimensional Case ◽  
Angular Variable ◽  
Tau Method ◽  
Algebraic Equations ◽  
Neutron Transport Equation

We consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved that it is a good approximate to exact solutions. This method is based on expansion of the angular flux in a truncated series of Walsh function in the angular variable. The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.

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