A three-dimensional S_N high-order diamond differencing discretization with a consistent acceleration scheme

The extension of the diamond differencing scheme to high-order spatial approximation is described in the context of a regular, three-dimensional (3D) discrete ordinates method. This spatial discretization keeps the advantages of the well-known linear diamond differencing (DD) scheme in terms of rigorousness and simplicity of derivation, while extending it to high-order solutions. Along with the implementation of high-order diamond differencing comes the search for a consistent acceleration method for the S_N source iteration. The proposed method relies on a Diffusion Synthetic Acceleration (DSA) scheme, combined with a Krylov Subspace Algorithm, GMRES. This two-level acceleration scheme has been proven efficient in case of realistic problems at any order. Numerical results are provided on 2D/3D legacy benchmarks and establish good properties of our solver.