Nonlinear Diffusion Acceleration in Voids for the Weighted Least-Square Transport Equation

Abstract The nonlinear diffusion acceleration (NDA) is an effective scheme to increase convergence for highly diffusive problems. However, for second order transport equations, the scheme is not yet defined in voids. In this paper we derive modifications to the NDA to handle problems containing void regions. A Fourier analysis shows that the newly developed modifications accelerates unconditionally for scattering ratios smaller than one. Numerical test with Reed’s problem showed that the NDA scheme results in a non-constant flux shape in the void regions. Further investigations revealed that this coarse mesh problem is caused by the interface coupling between void and material regions.