The Lagrangian hydrodynamics code magma2

S Rosswog

doi:10.1093/mnras/staa2591

Abstract

ABSTRACTWe present the methodology and performance of the new Lagrangian hydrodynamics code magma2, a smoothed particle hydrodynamics (SPH) code that benefits from a number of non-standard enhancements. By default it uses high-order smoothing kernels and wherever gradients are needed, they are calculated via accurate matrix inversion techniques, but a more conventional formulation with kernel gradients has also been implemented for comparison purposes. We also explore a matrix inversion formulation of SPH with a symmetrization in the particle indices that is not frequently used. We find interesting advantages of this formulation in some of the tests, for example, a substantial reduction of surface tension effects for non-ideal particle setups and more accurate peak densities in Sedov blast waves. magma2 uses artificial viscosity, but enhanced by techniques that are commonly used in finite-volume schemes such as reconstruction and slope limiting. While simple to implement, this approach efficiently suppresses particle noise, but at the same time drastically reduces dissipation in locations where it is not needed and actually unwanted. We demonstrate the performance of the new code in a number of challenging benchmark tests including, for example, multidimensional vorticity creating Schulz–Rinne-type Riemann problems and more astrophysical tests such as a collision between two stars to demonstrate its robustness and excellent conservation properties.

Highlights

A Lagrangian formulation of hydrodynamics is a natural choice for many astrophysical problems
The Arepo code (Springel 2010a), for example, tesselates space into Voronoi cells and evolves the hydrodynamic equations via a Riemann solver-based finite volume strategy. Such finite volume approaches are not bound to Voronoi or other meshes and can be applied to hydrodynamic schemes which use particles. Several such finite volume particle schemes have been suggested in the applied mathematics literature (Ben Moussa et al 1999; Vila 1999; Hietel et al 2000; Junk 2003), but they have only recently found their way into astrophysics (Gaburov & Nitadori 2011; Hopkins 2015; Hubber et al 2018) where they have delivered accurate results
In this paper we describe the new Lagrangian hydrodynamics code MAGMA2, an Smooth Particle Hydrodynamics (SPH) code that benefits from many improvements compared to more traditional SPH methods

Summary

Introduction

A Lagrangian formulation of hydrodynamics is a natural choice for many astrophysical problems. Smoothed Particle Hydrodynamics (SPH) (Lucy 1977; Monaghan 1977) is the most wide-spread Lagrangian method in astrophysics It is entirely mesh-free and the equations can be symmetrised in a way so that mass, energy, momentum and angular momentum are conserved by construction. These blips cause surface tension effects that can suppress weakly triggered fluid instabilities (Agertz et al.2007; McNally et al 2012) Such effects can be counterbalanced by a careful setup of initial conditions with consistent smoothness, by alternative expressions for SPH volume elements (Ritchie & Thomas 2001; Saitoh & Makino 2013; Hopkins 2013; Rosswog 2015a; Cabezon et al 2017) or by adding artificial conductivity terms to smooth out sharp transitions in the internal energy (Price 2008; Valdarnini 2012).

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