Smoothed particle hydrodynamics and magnetohydrodynamics. 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.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Ramaswamy, Rajesh; Bourantas, George; Jülicher, Frank; Sbalzarini, Ivo F.: A hybrid particle-mesh method for incompressible active polar viscous gels (2015)
  2. Leroy, A.; Violeau, D.; Ferrand, M.; Kassiotis, C.: Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH (2014)
  3. Puri, Kunal; Ramachandran, Prabhu: Approximate Riemann solvers for the Godunov SPH (GSPH) (2014)
  4. Puri, Kunal; Ramachandran, Prabhu: A comparison of SPH schemes for the compressible Euler equations (2014)
  5. Violeau, Damien; Leroy, Agnès: On the maximum time step in weakly compressible SPH (2014)
  6. Adami, S.; Hu, X.Y.; Adams, N.A.: A transport-velocity formulation for smoothed particle hydrodynamics (2013)
  7. Ghasemi V.A.; Firoozabadi, B.; Mahdinia, M.: 2D numerical simulation of density currents using the SPH projection method (2013)
  8. Kiara, Areti; Hendrickson, Kelli; Yue, Dick K.P.: SPH for incompressible free-surface flows. Part I: Error analysis of the basic assumptions (2013)
  9. Kiara, Areti; Hendrickson, Kelli; Yue, Dick K.P.: SPH for incompressible free-surface flows. II: Performance of a modified SPH method (2013)
  10. Peeters, Bob; Oliver, Marcel; Bokhove, Onno; Molchanov, Vladimir: On the rate of convergence of the Hamiltonian particle-mesh method (2013)
  11. Souto-Iglesias, Antonio; Macià, Fabricio; González, Leo M.; Cercos-Pita, Jose L.: On the consistency of MPS (2013)
  12. Sun, Xiaosong; Sakai, Mikio; Yamada, Yoshinori: Three-dimensional simulation of a solid-liquid flow by the DEM-SPH method (2013)
  13. Lind, S.J.; Xu, R.; Stansby, P.K.; Rogers, B.D.: Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves (2012)
  14. Price, Daniel J.: Smoothed particle hydrodynamics and magnetohydrodynamics (2012)