An Investigation of the Temporal Subdomain Method for Solving the Finite Element Formulation of the Space-Time Reactor Kinetics Equations
| Autor: | Haluk Utku, John M. Christenson |
|---|---|
| Rok vydání: | 1994 |
| Předmět: |
Computer simulation
Series (mathematics) 010308 nuclear & particles physics Space time Mathematical analysis 0211 other engineering and technologies 02 engineering and technology 01 natural sciences Finite element method law.invention Alternating direction implicit method Nuclear Energy and Engineering law 0103 physical sciences Cartesian coordinate system 021108 energy Condition number Algorithm Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Nuclear Science and Engineering. 116:55-66 |
| ISSN: | 1943-748X 0029-5639 |
| DOI: | 10.13182/nse94-a21481 |
| Popis: | The temporal subdomain method (TSM), based on a spatial finite element formulation, is investigated as a method for the solution of the space-time-dependent multigroup neutron dynamics equations. The spatial aspect of the problem was formulated as an array of finite elements by using a two-dimensional rectangular coordinate system subdivided into contiguous triangular elements. Within each element and within each neutron group, the flux was represented by a linear polynomial. Numerical experiments using a computer program developed during the course of the investigation demonstrated that the method is straightforward to implement and that it produces stable calculations for a wide range of time steps. The stability of the method has been tested for sinusoidal, ramp, and step-changed reactivity insertions. The results show that the TSM outperforms most alternating direction implicit methods in the sense that a similar degree of accuracy can be achieved with larger time steps using the same number of nodes. System condition number calculations as a function of node number were also carried out for a series of static eigenvalue calculations to determine the likelihood of error propagation and the difficulty of inverting the global system matrices during the time-dependent calculations. |
| Databáze: | OpenAIRE |
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