Two very different mhd codes for astrophysics: Athena and GIZMO. Scope and limitations Leire Beitia Antero AEGORA Research Group Univesidad Complutense de Madrid 22 Ma rch, 2018 Equations of ideal magnetohydrodynamics (MHD) Basic equations to solve ∂ρ Equation of mass continuity +∇⋅(ρ v)=0 ∂t ∂ρ v Equation of motion +∇⋅(ρ v v−B B+P)=0 ∂t ∂ E Equation of energy +∇⋅((E+ P)v−B(B⋅v))=0 ∂t ∂ B Induction equation −∇×(v×B)=0 ∂t B⋅B P ρ(v⋅v) B⋅B hydro P=P + E= + + hydro 2 γ−1 2 2 (No microscopic dissipation) 2 Solving the equations of MHD Smooth Particle (magneto)Hydrodynamics SPH, SPMHD Grid-based codes Finite differences Godunov methods (finite volumes) Moving mesh/mesh-free + Godunov methods 3 SPH & SPMHD Lagrangian approach Neighbouring particles Particle a Since 1977 (Lucy, 1977; Gringold & Monaghan, 1977) Fluid seen as a set of particles of mass m that are moved with the local fluid velocity v ∑ ρ = m W (|r −r |, h ) a b a b a b Sum over neighbouring particles inside R h 4 kern SPH & SPMHD Lagrangian approach Neighbouring particles Particle a PHANTOM (Price et al. 2017) SPMHD code https://phantomsph.bitbucket.io/ Last stable release: 13/03/2018 Developed over the last decade, Fortran 90 5 Grid-based codes Eulerian approach Volume discretised into cells Fluid equations solved across the area/volume elements Finite-volume Godunov schemes 6 Grid-based codes: Athena ATHENA (Stone et al., 2008) C language Publicly available. Latest version (v4.2) from 2013 https://princetonuniversity.github.io/Athena-Cversion/AthenaDocsDownLd Documentation https://princetonuniversity.github.io/Athena-Cversion/ Mass, momentum and energy fluxes: Magnetic fields: Finite volumes finite areas 7 Moving meshes Hybrid approach Non-regular mesh Cells move and deform continuously Lagrangian + Finite-volume Godunov methods 8 Moving meshes: GIZMO GIZMO (Hopkins, 2015) C language Publicly available. Latest version 18/02/2018 https://bitbucket.org/phopkins/gizmo-public Documentation: http://www.tapir.caltech.edu/~phopkins/Site/GIZMO_files/gizmo_documentation.h tml Lagrangian/Eulerian code Meshless Finite Volume (MFV) and Meshless Finite Mass (MFM) methods 9