scholarly journals Diffusion Synthetic Acceleration Methods for the Diamond-Differenced Discrete-Ordinates Equations

1977 ◽  
Vol 64 (2) ◽  
pp. 344-355 ◽  
Author(s):  
R. E. Alcouffe
Keyword(s):  
Discrete Ordinates ◽  
Diffusion Synthetic Acceleration ◽  
Acceleration Methods

scholarly journals ACCELERATION OF A 2-DIMENSIONAL, 2-ENERGY GROUP NEUTRON NOISE SOLVER BASED ON A DISCRETE ORDINATES METHOD IN THE FREQUENCY DOMAIN

2021 ◽  
Vol 247 ◽  
pp. 21005
Author(s):  
Huaiqian Yi ◽  
Paolo Vinai ◽  
Christophe Demazière
Keyword(s):  
Convergence Rate ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Neutron Transport ◽  
Discrete Ordinates ◽  
Energy Group ◽  
Diffusion Synthetic Acceleration ◽  
Wide Range ◽  
Neutron Noise ◽  
System Configurations

The acceleration of the convergence rate is studied for a neutron transport solver to simulate 2-D, 2-energy-group neutron noise problems in the frequency domain. The Coarse Mesh Finite Difference (CMFD) method is compared to the Diffusion Synthetic Acceleration (DSA) method. Numerical tests are performed using heterogeneous system configurations with different boundary conditions. The CMFD scheme leads to a better convergence rate. The results also show that CMFD can accelerate neutron noise problems in a wide range of perturbation frequencies with almost equal efficiency. An unstable convergence behavior is nevertheless observed in problems with purely reflective boundary conditions. Stabilization techniques such as performing multiple transport sweeps, underrelaxing the flux update, and using the lpCMFD method are investigated and improvements can be obtained.

scholarly journals ARES: A Parallel Discrete Ordinates Transport Code for Radiation Shielding Applications and Reactor Physics Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Yixue Chen ◽  
Bin Zhang ◽  
Liang Zhang ◽  
Junxiao Zheng ◽  
Ying Zheng ◽  
...  
Keyword(s):  
Anisotropic Scattering ◽  
Radiation Shielding ◽  
Discrete Ordinates ◽  
Boltzmann Transport ◽  
Reactor Physics ◽  
Linear System Of Equations ◽  
Diffusion Synthetic Acceleration ◽  
Transport Code ◽  
Discontinuous Finite Element ◽  
Solution Methods

ARES is a multidimensional parallel discrete ordinates particle transport code with arbitrary order anisotropic scattering. It can be applied to a wide variety of radiation shielding calculations and reactor physics analysis. ARES uses state-of-the-art solution methods to obtain accurate solutions to the linear Boltzmann transport equation. A multigroup discretization is applied in energy. The code allows multiple spatial discretization schemes and solution methodologies. ARES currently provides diamond difference with or without linear-zero flux fixup, theta weighted, directional theta weighted, exponential directional weighted, and linear discontinuous finite element spatial differencing schemes. Discrete ordinates differencing in angle and spherical harmonics expansion of the scattering source are adopted. First collision source method is used to eliminate or mitigate the ray effects. Traditional source iteration and Krylov iterative method preconditioned with diffusion synthetic acceleration are applied to solve the linear system of equations. ARES uses the Koch-Baker-Alcouffe parallel sweep algorithm to obtain high parallel efficiency. Verification and validation for the ARES transport code system have been done by lots of benchmarks. In this paper, ARES solutions to the HBR-2 benchmark and C5G7 benchmarks are in excellent agreement with published results. Numerical results are presented which demonstrate the accuracy and efficiency of these methods.

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