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 30 articles , 1 standard article )

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  1. Carberry Mogan, S. R.; Chen, D.; Hartwig, J. W.; Sahin, I.; Tafuni, A.: Hydrodynamic analysis and optimization of the Titan submarine via the SPH and finite-volume methods (2018)
  2. Petkova, Maya A.; Laibe, Guillaume; Bonnell, Ian A.: Fast and accurate Voronoi density gridding from Lagrangian hydrodynamics data (2018)
  3. Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang: Lagrangian particle method for compressible fluid dynamics (2018)
  4. Imoto, Yusuke; Tagami, Daisuke: Truncation error estimates of approximate differential operators of a particle method based on the Voronoi decomposition (2017)
  5. Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; Tartakovsky, Alexandre M.; Parks, Michael L.: Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics (2017)
  6. Sugiura, Keisuke; Inutsuka, Shu-ichiro: An extension of Godunov SPH II: application to elastic dynamics (2017)
  7. Hashemi, M. R.; Manzari, M. T.; Fatehi, R.: Evaluation of a pressure splitting formulation for weakly compressible SPH: fluid flow around periodic array of cylinders (2016)
  8. Lind, S. J.; Stansby, P. K.; Rogers, B. D.: Incompressible-compressible flows with a transient discontinuous interface using smoothed particle hydrodynamics (SPH) (2016)
  9. Tricco, Terrence S.; Price, Daniel J.; Bate, Matthew R.: Constrained hyperbolic divergence cleaning in smoothed particle magnetohydrodynamics with variable cleaning speeds (2016)
  10. Amicarelli, Andrea; Albano, Raffaele; Mirauda, Domenica; Agate, Giordano; Sole, Aurelia; Guandalini, Roberto: A smoothed particle hydrodynamics model for 3D solid body transport in free surface flows (2015)
  11. Bian, Xin; Li, Zhen; Karniadakis, George Em: Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition (2015)
  12. Iwasaki, Kazunari: Minimizing dispersive errors in smoothed particle magnetohydrodynamics for strongly magnetized medium (2015)
  13. Litvinov, S.; Hu, X. Y.; Adams, N. A.: Towards consistence and convergence of conservative SPH approximations (2015)
  14. Ramaswamy, Rajesh; Bourantas, George; Jülicher, Frank; Sbalzarini, Ivo F.: A hybrid particle-mesh method for incompressible active polar viscous gels (2015)
  15. Stasyszyn, Federico A.; Elstner, Detlef: A vector potential implementation for smoothed particle magnetohydrodynamics (2015)
  16. Violeau, Damien; Leroy, Agnès: Optimal time step for incompressible SPH (2015)
  17. Hou, Q.; Kruisbrink, A. C. H.; Pearce, F. R.; Tijsseling, A. S.; Yue, T.: Smoothed particle hydrodynamics simulations of flow separation at bends (2014)
  18. Leroy, A.; Violeau, D.; Ferrand, M.; Kassiotis, C.: Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH (2014)
  19. Puri, Kunal; Ramachandran, Prabhu: Approximate Riemann solvers for the Godunov SPH (GSPH) (2014)
  20. Puri, Kunal; Ramachandran, Prabhu: A comparison of SPH schemes for the compressible Euler equations (2014)

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