Meshless Analysis for Solving Multigroup Neutron Diffusion Equations

The multigroup neutron diffusion equation is fundamental to nuclear reactor analysis. The age diffusion is sufficient to describe the neutron behavior of a very large class of non-thermal reactors (except those with dimensions comparable to the neutron mean free path). Therefore, a suitable tool for obtaining an accurate solution to this equation is very useful for general reactor calculations. The meshfree methods, which are predicated on a discretization concerning dispersed nodal points or particles, are effective tools in the computational sciences that do not require mesh constraints. Unlike conventional Moving Least Squares (MLS), the Generalized Moving Least Squares (GMLS) method approximates functionals (e.g., differential operators) directly, reducing computational cost and improving accuracy. In this work, we present a semi-numerical analytical solution using the direct meshless approach for the steady-state multigroup neutron diffusion equations. The steady-state multigroup equations are reduced to a linear algebraic system and solvability is proved via block matrix inversion. Numerical benchmarks, convergence analysis and comparisons with traditional finite element and finite difference methods are provided.

کلیدواژه ها:

Point kinetics equations ، meshless methods ، Direct meshless local Petrov-Galerkin ، diffusion ، Multigroup method ، MLS ، GMLS