An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
An analysis of 1-D smoothed particle hydrodynamics kernels
Journal of Computational Physics
Journal of Computational Physics
A switch to reduce SPH viscosity
Journal of Computational Physics
Journal of Computational Physics
Conduction modelling using smoothed particle hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
SPH without a tensile instability
Journal of Computational Physics
A positive conservative method for magnetohydrodynamics based on HLL and Roe methods
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A note on magnetic monopoles and the one-dimensional MHD Riemann problem
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
Conservative and orthogonal discretization for the Lorentz force
Journal of Computational Physics
Solidification using smoothed particle hydrodynamics
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
A multi-phase SPH method for macroscopic and mesoscopic flows
Journal of Computational Physics
Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
Journal of Computational Physics
Constrained hyperbolic divergence cleaning for smoothed particle magnetohydrodynamics
Journal of Computational Physics
A transport-velocity formulation for smoothed particle hydrodynamics
Journal of Computational Physics
A comparison of SPH schemes for the compressible Euler equations
Journal of Computational Physics
On the maximum time step in weakly compressible SPH
Journal of Computational Physics
Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH
Journal of Computational Physics
Continuous representation of projected attribute spaces of multifields over any spatial sampling
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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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.