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 45 articles , 1 standard article )

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  1. Du, Qiang; Tian, Xiaochuan: Mathematics of smoothed particle hydrodynamics: a study via nonlocal Stokes equations (2020)
  2. Imoto, Yusuke: Truncation error estimates of approximate operators in a generalized particle method (2020)
  3. Jandaghian, M.; Shakibaeinia, A.: An enhanced weakly-compressible MPS method for free-surface flows (2020)
  4. Tavares da Silva, Leandro; Giraldi, Gilson Antonio: Fixed point implementation of a variational time integrator approach for smoothed particle hydrodynamics simulation of fluids (2020)
  5. Anwar, Shadab: Three-dimensional modeling of coalescence of bubbles using lattice Boltzmann model (2019)
  6. Ji, Zhe; Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.: A new multi-resolution parallel framework for SPH (2019)
  7. Mimault, Matthias; Ptashnyk, Mariya; Bassel, George W.; Dupuy, Lionel X.: Smoothed particle hydrodynamics for root growth mechanics (2019)
  8. Vela, Luis Vela; Reynolds-Barredo, J. M.; Sánchez, Raul: A positioning algorithm for SPH ghost particles in smoothly curved geometries (2019)
  9. Wenzel, E. A.; Garrick, S. C.: A point-mass particle method for the simulation of immiscible multiphase flows on an Eulerian grid (2019)
  10. 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)
  11. Petkova, Maya A.; Laibe, Guillaume; Bonnell, Ian A.: Fast and accurate Voronoi density gridding from Lagrangian hydrodynamics data (2018)
  12. Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang: Lagrangian particle method for compressible fluid dynamics (2018)
  13. Schnabel, Dirk; Özkaya, Ekrem; Biermann, Dirk; Eberhard, Peter: Modeling the motion of the cooling lubricant in drilling processes using the finite volume and the smoothed particle hydrodynamics methods (2018)
  14. Imoto, Yusuke; Tagami, Daisuke: Truncation error estimates of approximate differential operators of a particle method based on the Voronoi decomposition (2017)
  15. Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; Tartakovsky, Alexandre M.; Parks, Michael L.: Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics (2017)
  16. Sugiura, Keisuke; Inutsuka, Shu-ichiro: An extension of Godunov SPH II: application to elastic dynamics (2017)
  17. Hashemi, M. R.; Manzari, M. T.; Fatehi, R.: A SPH solver for simulating paramagnetic solid fluid interaction in the presence of an external magnetic field (2016)
  18. 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)
  19. Lind, S. J.; Stansby, P. K.; Rogers, B. D.: Incompressible-compressible flows with a transient discontinuous interface using smoothed particle hydrodynamics (SPH) (2016)
  20. Nogueira, Xesús; Ramírez, Luis; Clain, Stéphane; Loubère, Raphaël; Cueto-Felgueroso, Luis; Colominas, Ignasi: High-accurate SPH method with multidimensional optimal order detection limiting (2016)

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