Improvements and validation of the linear surface characteristics scheme

In this paper we present the last improvements of the recently proposed linear surface (LS) characteristics scheme for unstructured meshes. First we introduce a new numerical tracking technique, specifically adapted to the LS method, which tailors transverse integration weights to take into account the geometrical discontinuities that appear along the pipe affected to every trajectory in classical characteristics schemes. Another development allows using the volumetric flux variation of the LS method to re-compute step-wise constant fluxes to be used in other parts of a computational scheme. This permits to take greater advantage of the higher precision of the LS method without necessarily conceiving specialized theories for all the modular functionalities of a spectral code such as APOLLO2. Moreover we present a multi-level domain decomposition method for solving the synthetic acceleration operator that is used to accelerate the free iterations for the LS method. We discuss all these new developments by illustrating some benchmarks results obtained with the LS method. This is done by detailed comparisons with Monte-Carlo calculations. In particular we show that the new method can be used not only as a reference tool, but also inside a suitable industrial calculation scheme.