NAME OR DESIGNATION OF PROGRAM, COMPUTER, NATURE OF PHYSICAL PROBLEM SOLVED, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, AUXILIARIES, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED, ANY 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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SHOVAV | IAEA0826/01 | Tested | 01-DEC-1976 |

Machines used:

Package ID | Orig. computer | Test computer |
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IAEA0826/01 | IBM 370 series | IBM 370 series |

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3. NATURE OF PHYSICAL PROBLEM SOLVED

The space and time-dependent neutron diffusion equation is solved in slab geometry for four energy groups and six groups of delayed neutrons. The core thermodynamic equations are also solved at each mesh point for average temperatures of fuel and coolant to provide a temperature feedback for the kinetic calculations.

The space and time-dependent neutron diffusion equation is solved in slab geometry for four energy groups and six groups of delayed neutrons. The core thermodynamic equations are also solved at each mesh point for average temperatures of fuel and coolant to provide a temperature feedback for the kinetic calculations.

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4. METHOD OF SOLUTION

The Gauss-Seidel method is used for the static part of the solution of the diffusion equation. For the dynamic part, the optimal source projection method is used (3). This method uses a polynomial or exponential approximation to predict the fission source at each mesh point for the next time step. The degree of the polynomial is optimized so as to maximize the time step size and minimize the number of iterations. Temperature feedback is provided by recalculating cross sections using the appropriate temperature dependent shielding factors.

The Gauss-Seidel method is used for the static part of the solution of the diffusion equation. For the dynamic part, the optimal source projection method is used (3). This method uses a polynomial or exponential approximation to predict the fission source at each mesh point for the next time step. The degree of the polynomial is optimized so as to maximize the time step size and minimize the number of iterations. Temperature feedback is provided by recalculating cross sections using the appropriate temperature dependent shielding factors.

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6. TYPICAL RUNNING TIME

The running time is strongly dependent on the transient calculated, the number of mesh points, and the error criteria set by the user. Typically, 15 to 20 time steps are calculated per second on the IBM 370/195 for a 50 mesh point problem.

A 20 second transient resulting in a 200 percent power increase required 675 time steps with an error criteria of 10**(-6) and took 39.2 seconds of CPU time. A 2 millisecond transient resulting in a 170 percent power increase required 139 time steps with an error criteria of 10**(-6) and took 10 seconds of CPU time.

The running time is strongly dependent on the transient calculated, the number of mesh points, and the error criteria set by the user. Typically, 15 to 20 time steps are calculated per second on the IBM 370/195 for a 50 mesh point problem.

A 20 second transient resulting in a 200 percent power increase required 675 time steps with an error criteria of 10**(-6) and took 39.2 seconds of CPU time. A 2 millisecond transient resulting in a 170 percent power increase required 139 time steps with an error criteria of 10**(-6) and took 10 seconds of CPU time.

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7. UNUSUAL FEATURES OF THE PROGRAM

The optimal source projection method reduces required computer time by one to two orders of magnitude as compared to ordinary relaxation methods.

Six groups of delayed neutron data lambda-i and beta-i can be inserted for each fissile isotope.

Delayed neutron spectra for six delayed groups and four energy groups can be inserted.

Material group cross sections or regional group cross sections can be used for input data.

Mixing and shielding factors are used to calculate temperature dependent cross sections for temperature feedback.

The optimal source projection method reduces required computer time by one to two orders of magnitude as compared to ordinary relaxation methods.

Six groups of delayed neutron data lambda-i and beta-i can be inserted for each fissile isotope.

Delayed neutron spectra for six delayed groups and four energy groups can be inserted.

Material group cross sections or regional group cross sections can be used for input data.

Mixing and shielding factors are used to calculate temperature dependent cross sections for temperature feedback.

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10. REFERENCES

- D. Saphier, S. Yiftah:

A Program to Solve the Few Group Space Time Dependent Diffusion Equation with Temperature Feedback.

Israel Atomic Energy Commission IA 1217 (1971).

- D. Saphier:

Source Projection Method to Accelerate Reactor Dynamic Calculations.

Trans. Am. Nucl. Soc. 15, 2 (1972) 792.

- D. Saphier:

An Optimal Source Projection Method to Accelerate Space Time Dependent Calculations.

Trans. Am. Nucl. Soc. 16, 1 (1973) 300.

- D. Saphier, S. Yiftah:

A Program to Solve the Few Group Space Time Dependent Diffusion Equation with Temperature Feedback.

Israel Atomic Energy Commission IA 1217 (1971).

- D. Saphier:

Source Projection Method to Accelerate Reactor Dynamic Calculations.

Trans. Am. Nucl. Soc. 15, 2 (1972) 792.

- D. Saphier:

An Optimal Source Projection Method to Accelerate Space Time Dependent Calculations.

Trans. Am. Nucl. Soc. 16, 1 (1973) 300.

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11. MACHINE REQUIREMENTS

The amount of storage in k-bytes, N, is given approximately by - N=A+IP(B+0.125*IMAX), where A is 100, B is 10, IMAX is the number of meshpoints, and IP is 4 or 8 for single or double precision calculations, respectively. For a 65 meshpoints problem, executed in double precision, 245k bytes of storage should be allocated.

The amount of storage in k-bytes, N, is given approximately by - N=A+IP(B+0.125*IMAX), where A is 100, B is 10, IMAX is the number of meshpoints, and IP is 4 or 8 for single or double precision calculations, respectively. For a 65 meshpoints problem, executed in double precision, 245k bytes of storage should be allocated.

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IAEA0826/01

File name | File description | Records |
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IAEA0826_01.001 | PROGRAM SOURCE - FORTRAN IV | 3550 |

IAEA0826_01.002 | SAMPLE PROBLEM DATA | 328 |

IAEA0826_01.003 | SAMPLE PROBLEM OUTPUT | 1688 |

IAEA0826_01.004 | OVERLAY STRUCTURE | 10 |

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- F. Space - Time Kinetics, Coupled Neutronics - Hydrodynamics - Thermodynamics

Keywords: excursions, feedback, few-group, kinetics, neutron diffusion equation, slabs, space-time, thermodynamics.