An improvement to the spatial discretisation in the Astrophysical Weighted Particle Hydrodynamics method
The study introduces new approximations for node weights and centroids in Astrophysical Weighted Particle Hydrodynamics (AWPH) to enhance spatial discretization accuracy. By deriving these approximations from Taylor-series expansions of the kernel function and support function, the authors propose a more accurate method than previously used ones. The findings suggest that while these improvements are significant for the cubature rule itself, their impact on the final physical solution depends on node clustering.