A novel adaptive mesh free approach for even- parity neutron transport equation. (15th September 2022)

• Record Type: Journal Article
• Authors: Alizadeh, A.; Abbasi, M.; Minuchehr, A.; Zolfaghari, A.
• Is Part Of: Annals of nuclear energy. Volume 175(2022)
• Publication Date: 2022-09-15
• Subjects: Mesh free method -- Adaptive approach -- Even-parity neutron transport equation -- Residual based error indicator -- Radial point interpolation method; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; 621.4805
• DOI: 10.1016/j.anucene.2022.109253
• Languages: English
• ISSNs: 0306-4549

Abstract

Highlights: A novel spatially adaptive mesh free approach is presented to solve the even-parity neutron transport equation. A residual based error indicator is proposed and used in an adaptive scheme for error estimation. A RPIM mesh free method, based on MQ-RBF, which combine with a step-by-step local node refinement, is implemented. A computer program is developed with applying an adaptive node-refinement scheme to solve neutron transport problems. Abstract: In this paper, a novel spatially adaptive Mesh free approach using local nodes and radial basis functions, based on weak-form formulation is presented to solve the even-parity neutron transport equation. A residual based error indicator is proposed and used in an adaptive scheme for error estimation. The local balance of neutrons is used as an indicator to determine the appropriate regions of problem for node refinement. In this regard our previous computer program, MFreent, is upgraded for solving neutron transport equation using K + variational principle in an adaptive scheme for two-dimensional X - Y geometry. The multi-quadrics radial basis function is used to construct the radial point interpolation shape functions for spatial approximation of even-parity angular flux. Also, the angular part of flux is implemented via spherical harmonics expansion. Some numerical test cases are investigated to evaluate the performance of the locally adaptive node-refinement approach for both fixed source and eigenvalue problems solution. The obtained results confirm the solution accuracy and efficiency of the proposed method.