Research On Variational Integral Transport Nodal Method And Fast Solving Algorithm

In order to save the computational time overhead of the program and improve the calculation accuracy,based on the traditional variational nodal method,this paper proposes an variational integral nodal method that improves P_N expansion order.The nodal method program mainly consists of two parts:the construction of the response matrix and the solution of the response matrix equation.The process of constructing the response matrix involves the inversion of a large-scale matrix,and the solution time of the inverse matrix is proportional to the cube of the matrix dimension.The integral method implicitly writes the angle dependence into the expansion moment when the even-parity flux is discrete,and transforms the large-dimensional matrix into a finite number of small-dimensional matrices,thereby effectively reducing the program's solution time.When the P_N expansion order is high,the dimensions of each expansion moment in the response matrix equation are very large.This paper will use the Partitioned Matrix Algorithm to decompose the response matrix into high-order and low-order moments.The low-order moments iteratively solve the equation to convergence,and use high-order moments to correct,reducing the solution matrix response time.Due to the parallelism of the response matrix construction and the solution of the response matrix equations in the nodal method,a parallel algorithm based on MPI communication is developed in this paper.Through the region decomposition strategy,the solution domain is divided into several non-overlapping subdomains and distributed to multiple computing processors for parallel computing,reducing the calculation time of the total program.For the hexagonal core problem,the 60°periodic condition can be used to convert the full core to 1/6 core,which reduces the number of nodes in the core and reduces the program calculation time.The calculation of the rectangular and hexagonal nodal geometric benchmarks verifies the correctness of the traditional variational nodal method and the variational integral nodal method.The calculation results of rectangular geometry show that compared with the traditional method,the variational integral nodal method has higher calculation accuracy when the low-order angle expansion is performed;when the angle expansion order is increased,the time cost of the integration method is much smaller than the traditional method,shows good computational accuracy and time advantage.When the angle expansion order is 3 and the number of computing processors is 105,the total parallel efficiency of both methods reaches about90%,and the implemented parallel algorithm shows good parallel performance.In the hexagonal geometry calculation,based on the integration method,the full core geometry is simplified to a 1/6 core problem,and the parallel calculation of the program is realized.The results show that:1/6 cores can greatly improve the calculation efficiency of the program under the premise of ensuring the same calculation accuracy;when the number of parallel computing cores is 18,compared to full core serial calculation,when the expansion order of 1/6 core is P₁,P₃,or P₅,the total calculation time overhead can be reduced by about dozens of times,and a fast solution to the hexagonal block geometry is realized.