Document Type : Research Article

**Author**

MASNA engineering company, P.O. Box 1439951113, Tehran, Iran

**Abstract**

Numerical solution of the multi-group static forward and adjoint neutron diffusion equation (NDE) using the Finite Elements Method (FEM) is investigated in detail. A finite element approach based on the generalized least squares method is applied for the spatial discretization of the NDE in 3D-XYZ geometry. A computer code called GELES was also developed based on the described methodology covering linear or quadratic tetrahedral elements generated via the mesh generator for an arbitrary shaped system. A number of test cases are also studied to validate the proposed approach. Moreover, to assess the output dependency to the number of elements, a sensitivity analysis is carried out at the end.

**Highlights**

- Multi-group static 3-D neutron diusion equation is solved using the nite element method.
- Generalized least squares FEM, through a variational approach is applied for solving the NDE.
- GELES code is developed based on the tetrahedral elements for an arbitrary shaped system.
- To validate the approach, output of GELES were compared against the DONJON computer code.

Acceptable accuracy for the neutron multiplication factor and the power distribution was achieved.

**Keywords**