Computer Programs

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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DIFFUSION-ACE | NEA-0808/01 | Tested | 03-JAN-1986 |

Machines used:

Package ID | Orig. computer | Test computer |
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NEA-0808/01 | FACOM M-200 | IBM 3081 |

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4. METHOD OF SOLUTION

Leakage iteration method is applied. For this method, a reactor is divided into several layers along the Z axis and into several rectangular channels perpendicular to the x-y plane.

A one-dimensional neutron flux calculation is performed for each channel with the radial leakage coefficient. A two-dimensional neutron flux calculation is then made for each layer with the axial leakage determined from the one-dimensional calculation.

The one- and two-dimensional leakage will be iterated until the consistency is attained between the two.

Leakage iteration method is applied. For this method, a reactor is divided into several layers along the Z axis and into several rectangular channels perpendicular to the x-y plane.

A one-dimensional neutron flux calculation is performed for each channel with the radial leakage coefficient. A two-dimensional neutron flux calculation is then made for each layer with the axial leakage determined from the one-dimensional calculation.

The one- and two-dimensional leakage will be iterated until the consistency is attained between the two.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Number of energy groups is fixed to be 2 or 3.

Maximum number of channels along X axis is 10.

Maximum number of channels along Y axis is 10.

Maximum number of blocks along Z axis is 12.

Maximum number of channels at which one-dimensional calculation is performed is 79.

Number of energy groups is fixed to be 2 or 3.

Maximum number of channels along X axis is 10.

Maximum number of channels along Y axis is 10.

Maximum number of blocks along Z axis is 12.

Maximum number of channels at which one-dimensional calculation is performed is 79.

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6. TYPICAL RUNNING TIME

Typical running time of the example case of JPDR quater core (72/4 assemblies) is 150 sec CPU with the computer FACOM-M200.

Typical running time of the example case of JPDR quater core (72/4 assemblies) is 150 sec CPU with the computer FACOM-M200.

NEA-0808/01

NEA-DB has tested the program on IBM 3081D. To execute the test case included in the package required 202 seconds of CPU time.[ top ]

7. UNUSUAL FEATURES OF THE PROGRAM

In this program, the leakage iterative method is applied which has the following characteristics: a. A fine-mesh difference approximation technique is applied only to the channels and layers. Therefore, it is not necessary to calculate the neutron fluxes at all fine-mesh points in the core and thus the computer time is reduced.

If the block which is formed by a channel and a layer, is a 12 cm cube and the mesh width is 2 cm, the number of fine-mesh points is 6x6x6=216.

In the present method, however, the number of mesh points is 6+(6x6)=42, that is about one-fifth of the former. The terms connecting the channel and layer calculations are only the neutron leakage and the neutron source, which reduce the computer memory required.

b. Since the neutron leakage from a block is calculated by a fine- mesh difference approximation, the discretization error is minimized.

c. When only one fine-mesh point is located in each block, this method becomes the same as a fine-mesh difference approximation. In this case, the iterative scheme corresponds to one of the variants of the Peaceman-Rachford iterative method. Therefore, it is possible to establish the condition under which the consistency is achieved between the axial and radial leakages in the same manner as ADI (alternative direction implicit iterative method due to Peaceman and Rachford), and it is easy to compare the results with those obtained from conventional fine-mesh difference approximation methods. The computer code can be used for calculating both the collapsed flux and the fine-mesh flux.

In this program, the leakage iterative method is applied which has the following characteristics: a. A fine-mesh difference approximation technique is applied only to the channels and layers. Therefore, it is not necessary to calculate the neutron fluxes at all fine-mesh points in the core and thus the computer time is reduced.

If the block which is formed by a channel and a layer, is a 12 cm cube and the mesh width is 2 cm, the number of fine-mesh points is 6x6x6=216.

In the present method, however, the number of mesh points is 6+(6x6)=42, that is about one-fifth of the former. The terms connecting the channel and layer calculations are only the neutron leakage and the neutron source, which reduce the computer memory required.

b. Since the neutron leakage from a block is calculated by a fine- mesh difference approximation, the discretization error is minimized.

c. When only one fine-mesh point is located in each block, this method becomes the same as a fine-mesh difference approximation. In this case, the iterative scheme corresponds to one of the variants of the Peaceman-Rachford iterative method. Therefore, it is possible to establish the condition under which the consistency is achieved between the axial and radial leakages in the same manner as ADI (alternative direction implicit iterative method due to Peaceman and Rachford), and it is easy to compare the results with those obtained from conventional fine-mesh difference approximation methods. The computer code can be used for calculating both the collapsed flux and the fine-mesh flux.

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10. REFERENCES

- Y. Naito, M. Maekawa and K. Shibuya:

"A Leakage Iterative Method for Solving the Three-Dimensional

Neutron Diffusion Equation"

Nucl. Sci. Eng. 58 (1975).

- Y. Naito, M. Maekawa and M. Toba:

"Computer code system CELL-ACE for Burn-up Dependent Averaged Few

Group Constants Over the Cell in LWR"

JAERI-M 7544 (1978).

- Y. Naito, M. Maekawa and K. Shibuya:

"A Leakage Iterative Method for Solving the Three-Dimensional

Neutron Diffusion Equation"

Nucl. Sci. Eng. 58 (1975).

- Y. Naito, M. Maekawa and M. Toba:

"Computer code system CELL-ACE for Burn-up Dependent Averaged Few

Group Constants Over the Cell in LWR"

JAERI-M 7544 (1978).

NEA-0808/01, included references:

- Y. Naito, M. Maekawa and K. Shibuya:A Three-Dimensional Neutron Diffusion Calculation Code

DIFFUSION-ACE

JAERI 1262 (July, 1979).

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NEA-0808/01

To run the test case on IBM 3081D, 792 Kbytes of main storage are required.[ top ]

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NEA-0808/01

File name | File description | Records |
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NEA0808_01.003 | INFORMATION FILE | 81 |

NEA0808_01.004 | DIFFUSION-ACE JCL USED IN TESTING | 71 |

NEA0808_01.005 | DIFFUSION-ACE FORTRAN SOURCE | 4779 |

NEA0808_01.006 | SAMPLE PROBLEM INPUT | 55 |

NEA0808_01.007 | PRINTED OUTPUT FOR SAMPLE PROBLEM | 2693 |

Keywords: diffusion equations, iterative methods, neutron diffusion equation, neutron flux, three-dimensional.