This paper presents an overview and introduction to Smoothed Particle Hydrodynamics and Magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several `urban myths' regarding SPH, in particular the idea that one can simply increase the `neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the NDSPMHD SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.

SPLASH (formerly SUPERSPHPLOT) visualizes output from (astrophysical) simulations using the Smoothed Particle Hydrodynamics (SPH) method in one, two and three dimensions. Written in Fortran 90, it uses the PGPLOT graphics subroutine library for plotting. It is based around a command-line menu structure but utilizes the interactive capabilities of PGPLOT to manipulate data interactively in the plotting window. SPLASH is fully interactive; visualizations can be changed rapidly at the touch of a button (e.g. zooming, rotating, shifting cross section positions etc). Data is read directly from the code dump format giving rapid access to results and the visualization is advanced forwards and backwards through timesteps by single keystrokes. SPLASH uses the SPH kernel to render plots of not only density but other physical quantities, giving a smooth representation of the data.

Written in Fortran, DUSTYWAVE computes the exact solution for linear waves in a two-fluid mixture of gas and dust. The solutions are general with respect to both the dust-to-gas ratio and the amplitude of the drag coefficient.

Phantom is a smoothed particle hydrodynamics and magnetohydrodynamics code focused on stellar, galactic, planetary, and high energy astrophysics. It is modular, and handles sink particles, self-gravity, two fluid and one fluid dust, ISM chemistry and cooling, physical viscosity, non-ideal MHD, and more. Its modular structure makes it easy to add new physics to the code.

Solar-MACH (Solar MAgnetic Connection HAUS) derives and visualizes the spatial configuration and solar magnetic connection of different observers (i.e., spacecraft or planets) in the heliosphere at different times. It provides publication-ready figures for analyzing Solar Energetic Particle events (SEPs) or solar transients such as Coronal Mass Ejections (CMEs). Solar-MACH is available as a Python package; a Streamlit-enabled tool that runs in a browser is also available (solar-mach.github.io)