Convergence of AMR and SPH simulations - I. Hydrodynamical resolution and convergence tests

Abstract

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.

19 pages, 9 figures, 1 table, accepted for publication in MNRAS

References in corpus (8)

• Smoothed Particle Hydrodynamics and Magnetohydrodynamics
• Modeling Collapse and Accretion in Turbulent Gas Clouds: Implementation and Comparison of Sink Particles in AMR and SPH
• Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
• A new Jeans resolution criterion for (M)HD simulations of self-gravitating gas: Application to magnetic field amplification by gravity-driven turbulence
• A test suite for quantitative comparison of hydrodynamics codes in astrophysics
• On the Origin of Cores in Simulated Galaxy Clusters
• Protostellar collapse: A comparison between SPH and AMR calculations
• Generation of density inhomogeneities by magnetohydrodynamic waves in two dimensions

Cited by in corpus (27)

• First results from the IllustrisTNG simulations: A tale of two elements -- chemical evolution of magnesium and europium
• Theoretical Challenges in Galaxy Formation
• Phantom: A smoothed particle hydrodynamics and magnetohydrodynamics code for astrophysics
• The energy and momentum input of supernova explosions in structured and ionised molecular clouds
• SPHGal: Smoothed Particle Hydrodynamics with improved accuracy for Galaxy simulations
• Clumps and triggered star formation in ionised molecular clouds
• Boosting the accuracy of SPH techniques: Newtonian and special-relativistic tests
• Protoplanetary disc evolution affected by star-disc interactions in young stellar clusters
• Grand challenges in protoplanetary disc modelling
• Magnetic field amplification in accretion discs around the first stars: implications for the primordial IMF
• Numerical convergence of hydrodynamical simulations of galaxy formation: the abundance and internal structure of galaxies and their cold dark matter haloes
• A switch to reduce resistivity in smoothed particle magnetohydrodynamics
• The AGORA High-resolution Galaxy Simulations Comparison Project. III: Cosmological zoom-in simulation of a Milky Way-mass halo
• nIFTY galaxy cluster simulations III: The Similarity & Diversity of Galaxies & Subhaloes
• Understanding `galaxy groups' as a unique structure in the universe
• Galaxy cluster mergers as triggers for the formation of jellyfish galaxies: case study of the A901/2 system
• Comparing Simulations of AGN Feedback
• The Kelvin-Helmholtz instability and smoothed particle hydrodynamics
• Calibrating cosmological simulations with implicit likelihood inference using galaxy growth observables
• No double detonations but core carbon ignitions in high-resolution, grid-based simulations of binary white dwarf mergers
• Modeling the Lyman-$\alpha$ forest with Eulerian and SPH hydrodynamical methods
• Sheets, filaments and clumps - high resolution simulations of how the thermal instability can form molecular clouds
• Simulating stellar winds in AMUSE
• Interactions of a shock with a molecular cloud at various stages of its evolution due to thermal instability and gravity
• The interaction of hydrodynamic shocks with self-gravitating clouds
• Shocking interactions of supernova remnants with atomic and molecular clouds -- the interplay between shocks, thermal instability and gravity in the large cloud regime
• pyro: A teaching code for computational astrophysical hydrodynamics