This work develops efficient algorithms for numerically solving the neutron diffusion equation by a wavelet Galerkin method (WGM). One of the main problems encountered in solving neutron diffusion equation using WGM is the treatment of the boundary and interface conditions. In one-dimensional problems, the boundaries of the wavelet series expansions are assumed to be the analytical boundaries of the problem, and the boundary condition equations are replaced by end equations in Galerkin system. In two-dimensional problems, in order to maintain the integrity of the system, the boundaries of the wavelet series are shifted until the end is independent on any expansion coefficients of the scaling function that affect the solution within the real boundaries.Since the scaling functions are compactly supported, only a finite number of the connection coefficients are nonzero. The resultant matrix has a block diagonal structure, which can be inverted easily, therefore, enables us to extend the solution to two-dimensional heterogeneous cases and make the inner iteration efficient in the eigenvalue and multigroup problems. We tested our WGM algorithm with several diffusion problems including two-dimensional heterogeneous problems and multi-group problems. The solutions are very accurate with a proper selection of Daubechies' order and dilation order. Our WGM algorithm provides very accurate solutions for one-dimensional and two-dimensional heterogeneous problems in which the flux exhibits very steep gradients.
Defense-in-Depth is the basis of safety design of nuclear plants, and refined and strengthened year by year. Nowadays, the importance of it has been further highlighted triggered by the accident at Fukushima Daiichi Nuclear Power Station.
Accidents described previously have been shown it could not care enough to uncertainty related to design, construction, maintenance and operation has exposed. It’s the lessons learned of that is to say to reduce uncertainty of design is the use of risk informed is essential. Therefore, the establishment of the design approach that uses risk informed consideration of the Defense-in-Depth is an important theme.
Defense-in-Depth is a measure which prevents the increase of the event frequency and core damage in consideration of the degree of safety margins, redundancy, diversity and consideration of radiation safety due to core damage and security.
The plant designers and utilities have made efforts to ensure safety utilized conventional design technique, which means deterministic, and risk information, in order to incorporate Defense-in-Depth concepts.
To consider Defense-in-Depth in the design phase, various requirements should be taken into consideration. It has been coming to be able to perform more rational and quantitative judgment by utilization of risk information.
In that case, while the designers of various fields will work in cooperation to ensure safety, if there are common utilization schemes for risk information among designers, more efficient and rational design works can be advanced in consideration of Defense-in-Depth. However, conventionally, it is hard to say that such schemes have functioned in order that designers may advance design works in collaboration.
This research intends to generate the schemes which advance design works in sharing the same risk information databases, which mean various risk indications etc), in other words, the schemes which will become lingua franca for utilizing risk information, in case of nuclear plants designs.
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