  We compare the results for a set of hydrodynamical tests performed with the
AMR finite volume code, MG and the SPH code, SEREN. The test suite includes
shock tube tests, with and without cooling, the non-linear thin-shell
instability and the Kelvin-Helmholtz instability. The main conclusions are :
(i) the two methods converge in the limit of high resolution and accuracy in
most cases. All tests show good agreement when numerical effects (e.g.
discontinuities in SPH) are properly treated. (ii) Both methods can capture
adiabatic shocks and well-resolved cooling shocks perfectly well with standard
prescriptions. However, they both have problems when dealing with
under-resolved cooling shocks, or strictly isothermal shocks, at high Mach
numbers. The finite volume code only works well at 1st order and even then
requires some additional artificial viscosity. SPH requires either a larger
value of the artificial viscosity parameter, alpha_AV, or a modified form of
the standard artificial viscosity term using the harmonic mean of the density,
rather than the arithmetic mean. (iii) Some SPH simulations require larger
kernels to increase neighbour number and reduce particle noise in order to
achieve agreement with finite volume simulations. However, this is partly due
to the need to reduce noise that can corrupt the growth of small-scale
perturbations. In contrast, instabilities seeded from large-scale perturbations
do not require more neighbours and hence work well with standard SPH
formulations and converge with the finite volume simulations. (iv) For purely
hydrodynamical problems, SPH simulations take an order of magnitude longer to
run than finite volume simulations when running at equivalent resolutions, i.e.
when they both resolve the underlying physics to the same degree. This requires
about 2-3 times as many particles as the number of cells.

Instrumentation and Methods for Astrophysics