A New Residual Distribution Hydrodynamics Solver for Astrophysical
  Simulations
  A wide array of astrophysical systems can only be accurately modelled when
the behaviour of their baryonic gas components is well understood. The residual
distribution (RD) family of partial differential equation (PDE) solvers can be
used to solve the fluid equations, which govern this gas. We present a new
implementation of the RD method to do just this. The solver efficiently and
accurately calculates the evolution of the fluid, to second order accuracy in
both time and space, across an unstructured Delaunay triangulation, built from
an arbitrary distribution of vertices, in either 2D and 3D. We implement a
novel new variable time stepping routine, which applies a drifting mechanism to
greatly improve the computational efficiency of the method. We conduct
extensive testing of the new implementation, demonstrating its innate ability
to resolve complex fluid structures, even at very low resolution. Our
implementation can resolve complex fluid structures with as few as 3-5
resolution elements, demonstrated by Kelvin-Helmholtz and Sedov blast tests. It
includes three residual calculation modes, the LDA, N and blended schemes, each
designed for different scenarios. These range from smooth flows (LDA), to
extreme shocks (N), and scenarios where either may be encountered (blended). We
compare our RD solver results to state-of-the-art solvers used in other
astrophysical codes, demonstrating the competitiveness of the new approach,
particularly at low resolution. This is of particular interest in large scale
astrophysical simulations, where important structures, such as star forming gas
clouds, are often resolved by small numbers of fluid elements.
