Research On Improved Integral Variational Nodal Method And Acceleration Algorithm

With the vigorous development of fast reactor,neutron calculation codes with fast reactor simulation capabilities have become an urgent need.On the other hand,large-scale core simulation poses severe challenges to computing efficiency and computing memory.How to improve computing efficiency and reduce memory without significantly affecting computing accuracy has become a research hotspot.Aiming at the limitations and shortcomings of the variational nodal method in its application,the research on the improved integral variational nodal method and its acceleration algorithm was carried out in this paper,which will provide powerful tool support for accurate and efficient neutronics simulation of fast reactors and thermal reactors.In this paper,firstly,the hexagonal integral transport variational nodal method calculation code VITAS2.0（Variational Integral Transport Analysis Solver）was developed for hexagonal assembly structure in fast reactors.In order to avoid the complicated rotation transformation of spherical harmonic when dealing with periodic boundary conditions,the even parity variable defined on the nodal surfaces was introduced,and from this,the Ritz procedure corresponding to the hexagonal integral transport variational nodal method was derived.Based on the variational principle and employing the variable transformation approach,the response matrix equation was derived;at the same time,the quasi-reflective boundary condition（QRIC）acceleration method was proposed,which effectively improves the solution speed of the matrix equation.The verification results of the TAKEDA-4 benchmark showed that VITAS2.0could have high calculation accuracy.In addition,the QRIC method can increase the speed of response matrix construction by 3 times and the speed of solving matrix equations by 75 times.At the same time,the accuracy was not significantly reduced:the accuracy loss of k_eff is less than 12 pcm,and the accuracy loss of flux is less than 0.1%.Secondly,the angle processing method of axial surfaces was improved to solve the efficiency problem of thermal reactor neutronics simulation,and the quasi-transport integral variational nodal method calculation code VITAS-2D/1D for rectangular geometry was developed.By eliminating the axial and radial cross-derivative terms in the second-order even parity neutron transport equation,and adopting the diffusion approximation to the angular variable of the axial surfaces,the theoretical model of the quasi-transport integral variational nodal method was established.The self-designed two-dimensional core model was used to verify the correctness of the two-dimensional core calculation of the VITAS-2D/1D code;the numerical verification of the three-dimensional core problem is completed using the TAKEDA-1 benchmark.The results showed that VITAS-2D/1D code could have considerable calculation accuracy,and the calculation speed is about twice that of the VITAS code,showing the advantage of calculation efficiency.In summary,this paper established an improved integral variational nodal method,and applied acceleration method.It significantly improved the calculation efficiency and saved the calculation memory while ensuring the calculation accuracy,which provided new ideas for the development of neutronics calculation methods.