Common family of numerical methods such as finite element and finite difference involve the discretization of domain into regular grids or meshes. Mesh generation and re-meshing process, however, for obtaining required accuracy are complicated and time-consuming. Recently, Mesh Free (MFree) methods have been developed to overcome the drawbacks of such conventional numerical methods. In the present work, a novel approach is developed for solving multi-group neutron transport equation in two-dimensional $X-Y$ geometry based on a mesh free scheme using the Radial Point Interpolation Method (RPIM). The $K^{+}$ principle which is an extremum variational principle for solving even parity neutron transport equation is our choice to implement RPIM. The directional dependence of even-parity angular flux is expanded by the spherical harmonic polynomials which leads to P_N method. The multi-quadrics radial basis function is used to construct the RPIM shape functions for spatial approximation of angular flux to obtain the discretized MFree weak-form of neutron transport equation. As the RPIM shape functions possess the Kronecker delta function property, essential boundary conditions is enforced as efficiently as in the finite element method (FEM). The obtained results are compared with some mesh-based methods such as conventional finite element method to evaluate the performance of the presented approach. It is demonstrated that the proposed method is robust, stable, reliable and efficient for treatment of neutron transport.

诸如有限元和有限差分之类的常用数值方法涉及将域离散化为规则的网格或网格。然而，为了获得所需的精度，网格生成和重新网格化过程是复杂且耗时的。近来，已经开发了无网格（MFree）方法来克服这种常规数值方法的缺点。在目前的工作中，开发了一种新颖的方法来求解二维中的多组中子输运方程$X--ÿ$使用径向点插值方法（RPIM）的基于无网格方案的几何图形。这${ķ}^{+}$求解奇偶中子输运方程的极值变分原理是我们实现RPIM的选择。奇偶校验角通量的方向相关性由球谐多项式扩展，得出P _N方法。使用多二次方径向基函数构造用于角通量空间近似的RPIM形状函数，以获得中子输运方程的离散MFree弱形式。由于RPIM形状函数具有Kronecker增量函数属性，因此基本边界条件的执行效率与有限元方法（FEM）相同。将获得的结果与某些基于网格的方法（例如常规有限元方法）进行比较，以评估所提出方法的性能。结果表明，所提出的方法是稳定，稳定，可靠和有效的中子输运处理方法。