On the Spectrum of an Operator Associated with the Neutron Transport Equation

1969 ◽  
Vol 17 (1) ◽  
pp. 162-171 ◽  
Author(s):  
R. B. Kellogg
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
Neutron Transport Equation ◽  
Spectrum Of An Operator

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.

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.

Sign in / Sign up

Export Citation Format

Share Document