Enhancing lpCMFD Acceleration with Successive Overrelaxation for Neutron Transport Source Iteration

We present the new iterative method lpCMFD-SOR, which combines the linear prolongation coarse-mesh finite difference (lpCMFD) scheme with the method of successive overrelaxation (SOR) for neutron transport source iteration (SI). The lpCMFD method is the latest coarse-mesh finite difference (CMFD)–type acceleration scheme and is unconditionally stable and more effective than the standard CMFD method. The SOR method is a variant of the Gauss-Seidel method for solving a linear system of equations, resulting in faster convergence. The idea is to update the scattering source with overrelaxation to speed up the coupled transport-diffusion SI. Fourier analysis shows that the lpCMFD-SOR method converges for a relaxation parameter in the range of . It becomes less effective when underrelaxed (i.e., ) and increasingly more effective as increases above 1 until reaching the optimal overrelaxation value, which is, however, problem dependent. The optimal overrelaxation parameter increases with both the scattering ratio and the optical thickness of the problem. Numerical experiments have confirmed the Fourier analysis results. In general, the SOR method can further enhance the convergence rate of the lpCMFD method by more than 40% for neutron transport problems.