Neutron transport equation processing method based on discontinuous finite element and computer program product

Abstract

The invention provides a neutron transport equation processing method based on discontinuous finite elements and a program product. The processing method comprises the following steps: constructing a shape function and a conversion matrix of an interval B spline wavelet unit; on the basis of the discrete longitudinal standard neutron transport equation, deducing the discrete longitudinal standard neutron transport equation of the conventional discontinuous finite element; on the basis of a discrete longitudinal standard neutron transport equation of a conventional discontinuous finite element, deriving a discrete longitudinal standard neutron transport equation of an interval B-spline wavelet discontinuous finite element according to the constructed shape function and the transformation matrix of the interval B-spline wavelet unit; solving a discrete longitudinal standard neutron transport equation of interval B spline discontinuous finite elements; and guiding the design of the nuclear reactor according to a solving result. The technical problems that when a neutron transport equation is solved through a conventional discontinuous finite element at present, calculation is time-consuming if the number of grids is large, and calculation precision is not high and convergence speed is low if the number of grids is small can be solved.

Description

technical field [0001] The invention relates to the field of numerical simulation for solving neutron transport equations in nuclear engineering, in particular to a neutron transport equation processing method and a computer program product based on discontinuous finite elements. Background technique [0002] The neutron transport equation is the basis and key of small complex reactor design and shielding calculation, and its solution is also an important parameter for reactor and shielding calculation design. The neutron transport equation is an integral-differential equation with 7 independent variables (including 3 spatial position independent variables, 2 angle independent variables, 1 energy independent variable and 1 time independent variable). However, it is basically impossible to solve this equation precisely, even in steady state, it is still very difficult to solve the neutron transport equation. With the development of computers, numerical calculations have been...

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Problems solved by technology

[0005] In order to overcome the current discontinuous finite element method used to deal with neutron transport equations in the construction of small and complex reactors, there are low-order linear discontinuous finite elements that require more calculation meshes than high-order discontinuous finite elements, and high-order discontinuous finite element phases. Compared with the linear discontinuous finite element, it takes more calculation time on each unit, and the numerical "Runge" oscillation phenomenon may occur, which affects the accuracy of the calculation. Compared with the continuous finite element, the discontinuous finite element method requires more The degree of freedom reduces the computational efficiency. Although the interval B-spline wavelet function has many advantages, it lacks the technical problems of research and application in the solution of discontinuous finite elements and neutron transport equations. It provides a method based on discontinuous finite The neutron transport equation processing method and computer program products of the element can greatly improve the calculation accuracy and fast convergence speed when there are few grids. Even if there are many grids, it can be calculated quickly and takes less time.

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