Cell-Centered Imposed Diffusion Synthetic Acceleration for Weighted Difference Transport Methods

We compute the spectral radius for Reed’s cell-centered imposed diffusion synthetic acceleration (IDSA) method applied to a fixed-weights weighted diamond-difference (WDD) scheme. We show that Reed’s conclusion that IDSA is conditionally stable is strictly true only for very small magnitude spatial weights. For the zeroth-order nodal integral method, the step method (unit weights), and WDD methods with large enough weights (say larger than 0.5), a simple choice of the diffusion coefficient results in unconditionally stable, rapidly converging iterations. Moreover, the IDSA’s spectral radius vanishes in the limit of infinitely thick computational cells, thereby implying immediate convergence for sufficiently thick problems. We verify all these results via model and nonmodel test problems.