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.
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