| In this thesis,the radial basis function-finite difference RBF-FD method and the diamond difference DD method are used to solve the neutron transport equation.RBF-FD method is an extension of the classical finite difference method.It does not depend on mesh generation and is suitable for solving differential equations defined in complex geometric regions.These two algorithms will produce oscillations near the discontinuity.In this paper,Weighted essentially non-oscillatory WENO method is used to eliminate oscillations.The main purpose of this method is to achieve arbitrary high order in smooth regions and no oscillations in the vicinity of discontinuities.In Chapter 1,it describe the relevant background of the transport equation.In Chapter 2,it describes two algorithms to solve the neutron transport equation,which will produce Gibbs phenomenon for discontinuous problems,In Chapter 3 and Chapter 4,it construct WENO interpolation and WENO reconstruction to eliminate oscillations respectively.In Chapter 5,it construct RBF-WENO interpolation method to eliminate oscillations.Through the comparison of experimental data,WENO method can eliminate vibration and achieve theoretical accuracy. |
