Research On Calculation Method Of Neutron Transport Using Curved-Edge Isoparametric FEM

Discussions on the calculation methods for neutron transport equation have always been a critical topic in the field of reactor physics.The finite element method has been widely recognized by the public since its introduction into the field of neutron transport calculations in the 1970s.For the past few years,computerized tools have become more advanced.According to the existing requirements,deterministic approaches should describe geometric shapes related to a problem to be solved in a more accurate way.Depending on the diversified shapes of mesh elements,the finite element method shows its flexibility in mesh density and node quantity variations in the event that a particular region is geometrically divided,giving it a set of unique advantages.However,most of the existing research attaches great importance to both the selection of a variational principle and combination between the finite element method and various angular discretization approaches.In terms of other scholars,they have made an attempt to probe into self-adaptive meshes,etc.,mostly made based on variations in the number of mesh elements within a fixed area.In this context,the concept of curved-edge isoparametric finite elements was introduced in order to solve neutron transport equations in this paper.Instead of approximating the boundary of a curved edge problem by increasing the number of straight-edge elements habitually,spatial discretization was directly carried out at the curved-edge elements,targeting the problems to be solved.The ultimate purpose is to combine the finite element method using curved edge isoparametric elements with the discrete ordinate method to calculate the first-order neutron transport equation in the two-dimensional Cartesian coordinate system.In addition,discussing whether it can help with the accuracy or speed of existing calculations.In the C++language framework,coding was fulfilled for the calculation program ISFENTES written for the curved-edge isoparametric finite-element-based neutron transport equation.With regard to a pre-processing module of this program,it is able to read relevant parameters,such as cross sections of a material.Additionally,a curved-edge mesh auto-generating module was independently compiled in accordance with the commonly-encountered shapes of grid cells and Assemblies.As far as the solving module is concerned,its overall framework is still based on the classical source iteration method.This primarily covers the generation and storage of a stiffness matrix that corresponds to a least-squares-method-based system of variational equations,introduction of coercive boundary conditions,and solving of a matrix equation using a conjugate gradient method.After that,on the one hand,this program was utilized to calculate benchmarks at levels of grid cells and assemblies with diverse materials,energy groups,boundary conditions,and geometries.On the other hand,relevant parameters were also principally analyzed with the help of this program,including its effective multiplication factor,neutron-flux density and power distribution.The calculation results show that when S₈discrete order is adopted,The calculated absolute error of effective multiplication factor of benchmark cell is generally less than50pcm and the maximum relative error is less than two thousandths benchmark.The relative error of normalized neutron flux density in dense mesh calculation is less than one thousand.The results of the assembly-level benchmark were compared with those of other programs,and the absolute deviation of effective multiplication factor was between 20 and80pcm.The Minimum relative deviation of normalized power distribution of each lattice in the assembly is less than one thousandth,and the biggest is not more than three over one thousand.And increasing the number of direction angles before using S₈discrete order has a significant effect on improving the calculation accuracy.The calculation accuracy of the above benchmark problems by using the sparse curved mesh has been satisfactory.Only the accuracy of the neutron flux distribution is improved slightly by continuing to encrypt the grid.