Transport equation response matrix block diagonalization method based on symmetric group theory

Abstract

The invention discloses a transport equation response matrix block diagonalization method based on a symmetric group theory. The method comprises the steps that 1, a whole reactor core solving region is divided according to regular geometry to obtain regular blocks, a universal function is established for a neutron transport equation based on a block variation method, and a weak solution form of the transport equation is constructed; a spherical harmonic function and an orthogonal polynomial are adopted to perform discrete processing on neutron angular flux density, and the spherical harmonic function and the spatial orthogonal polynomial jointly form a primary function of flux; 2, all symmetric groups of the blocks subjected to symmetric transformation are determined according to geometrical shapes of the blocks, and projection operators of the symmetric groups are utilized to project the primary function so as to construct an irreducible symmetric primary function; and 3, the irreducible symmetric primary function is used to substitute the spherical harmonic function and the spatial orthogonal polynomial in the step 1, a new primary function is adopted to perform discrete processing on variables, and a new response matrix is a matrix of diagonal blocks. By the adoption of the method, the floating point operation amount of the matrix is greatly lowered, and a calculation memory needed for storing the response matrix is greatly reduced.

Description

technical field [0001] The invention relates to the technical field of nuclear reactor core design and safety, in particular to a block diagonalization method of a transport equation response matrix based on symmetric group theory. Background technique [0002] The calculation of the whole core transport segment is of great significance in the calculation of neutronics. In the solution of the neutron transport equation, if the response relation of the neutron entry and exit jet at the inner boundary of the nodal block can be constructed in advance, then the midpoint of the nodal block can be obtained by scanning and iterating the nodal block until convergence according to the response relation. neutron leakage, so as to solve the neutron flux distribution in each node. This approach is called the response matrix approach. The angle term of the transport equation is usually discretized by using spherical harmonics. If the expansion of the angle term takes the first N-order...

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Problems solved by technology

In addition, if calculations such as fuel consumption and transient state are performed, the cross-sections of each block are different, so each block needs to calculate its own response matrix separately, which poses a great challenge to computing memory and computing efficiency

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