GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods

We present and study two new Lagrangian numerical methods for solving the equations of hydrodynamics, in a systematic comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture many advantages of both smoothed-particle hydrodynamics (SPH) and gridbased or adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to an arbitrarily high-order matrix gradient estimator and a Riemann solver acting over the volume “overlap.” We implement and test a parallel, second-order version of the method with coupled self-gravity & cosmological integration, in the code GIZMO:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require “artificial diffusion” terms; and allows the fluid elements to move with the flow so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages vs. SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced “particle noise” & numerical viscosity, more accurate sub-sonic flow evolution, & sharp shock-capturing. Advantages vs. non-moving meshes include: automatic adaptivity, dramatically reduced advection errors & numerical diffusion/overmixing, velocity-independence of numerical errors, accurate coupling to N-body gravity solvers, and good angular momentum conservation and elimination of “grid alignment” effects. We can, for example, follow hundreds of orbits of gaseous disks, while AMR and SPH methods break down in a few orbits. However, non-adaptive fixed meshes exhibit the lowest levels of “grid noise” among all methods we consider. All of these differences between methods are important for a wide range of astrophysical problems.