A Diffusion Synthetic Acceleration Method for Block Adaptive Mesh Refinement

A multidimensional block-based adaptive mesh refinement (BAMR) method for the neutral particle transport equation with diamond and linear discontinuous spatial differencing was developed several years ago. This method was implemented in the PARallel TIme-dependent SN (PARTISN) deterministic transport code. However, the only source acceleration method available with BAMR was transport synthetic acceleration. Although the block-based adaptive mesh is orthogonal, the individual mesh cells may not be simply connected. Because of this lack of simple connectivity, development of a fully consistent diffusion synthetic acceleration (DSA) method has not been possible. This paper describes the development of a DSA method based upon an additive correction to the scalar flux iterate after a transport sweep. This DSA equation is differenced using a vertex-centered diffusion discretization that is diamond-like and may be characterized as "partially" consistent. It does not appear algebraically possible to derive a diffusion discretization that is fully consistent with diamond transport differencing on AMR meshes. The diffusion matrix is symmetric positive definite, and the DSA method is effective for most applications. This BAMR-DSA solver has been implemented and tested in two dimensions for rectangular (X-Y) and cylindrical (R-Z) geometries. As expected, results confirm that a partially consistent BAMR-DSA method will introduce instabilities for extreme cases (e.g., scattering ratios approaching 1.0 with optically thick cells), but for most realistic problems, e.g., the iron-water shielding problem, the BAMR-DSA method provides an effective acceleration method.