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PySPH: a Python-based SPH framework

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PySPH is an open source framework for Smoothed Particle Hydrodynamics (SPH) simulations. It is implemented in Python <>_ and the performance critical parts are implemented in Cython <>_ and PyOpenCL_.

PySPH allows users to write their high-level code in pure Python. This Python code is automatically converted to high-performance Cython or OpenCL which is compiled and executed. PySPH can also be configured to work seamlessly with OpenMP, OpenCL, and MPI.

The latest documentation for PySPH is available at <>_.

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Here are videos <>_ of some example problems solved using PySPH.

.. _PyOpenCL: .. _PyZoltan:


  • Flexibility to define arbitrary SPH equations operating on particles in pure Python.
  • Define your own multi-step integrators in pure Python.
  • High-performance: our performance is comparable to hand-written solvers implemented in FORTRAN.
  • Seamless multi-core support with OpenMP.
  • Seamless GPU support with PyOpenCL_.
  • Seamless parallel support using Zoltan <>_ and PyZoltan_.

SPH formulations

PySPH ships with a variety of standard SPH formulations along with basic examples. Some of the formulations available are:

  • Weakly Compressible SPH (WCSPH) <>_ for free-surface flows (Gesteira et al. 2010, Journal of Hydraulic Research, 48, pp. 6--27)
  • Transport Velocity Formulation <>_ for incompressilbe fluids (Adami et al. 2013, JCP, 241, pp. 292--307)
  • SPH for elastic dynamics <>_ (Gray et al. 2001, CMAME, Vol. 190, pp 6641--6662)
  • Compressible SPH <>_ (Puri et al. 2014, JCP, Vol. 256, pp 308--333)
  • Generalized Transport Velocity Formulation (GTVF) <>_ (Zhang et al. 2017, JCP, 337, pp. 216--232)
  • Entropically Damped Artificial Compressibility (EDAC) <>_ (Ramachandran et al. 2019, Computers and Fluids, 179, pp. 579--594)
  • delta-SPH <>_ (Marrone et al. CMAME, 2011, 200, pp. 1526--1542)
  • Dual Time SPH (DTSPH) <>_ (Ramachandran et al. arXiv preprint)
  • Incompressible (ISPH) <>_ (Cummins et al. JCP, 1999, 152, pp. 584--607)
  • Simple Iterative SPH (SISPH) <>_ (Muta et al. arXiv preprint)
  • Implicit Incompressibel SPH (IISPH) <>_ (Ihmsen et al. 2014, IEEE Trans. Vis. Comput. Graph., 20, pp 426--435)
  • Gudnov SPH (GSPH) <>_ (Inutsuka et al. JCP, 2002, 179, pp. 238--267)
  • Conservative Reproducible Kernel SPH (CRKSPH) <>_ (Frontiere et al. JCP, 2017, 332, pp. 160--209)
  • Approximate Gudnov SPH (AGSPH) <>_ (Puri et al. JCP, 2014, pp. 432--458)
  • Adaptive Density Kernel Estimate (ADKE) <>_ (Sigalotti et al. JCP, 2006, pp. 124--149)
  • Akinci <>_ (Akinci et al. ACM Trans. Graph., 2012, pp. 62:1--62:8)

Boundary conditions from the following papers are implemented:

  • Generalized Wall BCs <>_ (Adami et al. JCP, 2012, pp. 7057--7075)
  • Do nothing type outlet BC <>_ (Federico et al. European Journal of Mechanics - B/Fluids, 2012, pp. 35--46)
  • Outlet Mirror BC <>_ (Tafuni et al. CMAME, 2018, pp. 604--624)
  • Method of Characteristics BC <>_ (Lastiwaka et al. International Journal for Numerical Methods in Fluids, 2012, pp. 35--46)
  • Hybrid BC <>_ (Negi et al. arXiv preprint)

Corrections proposed in the following papers are also the part for PySPH:

  • Corrected SPH <>_ (Bonet et al. CMAME, 1999, pp. 97--115)
  • hg-correction <>_ (Hughes et al. Journal of Hydraulic Research, pp. 105--117)
  • Tensile instability correction' <>_ (Monaghan J. J. JCP, 2000, pp. 2990--311)
  • Particle shift algorithms (Xu et al <>. JCP, 2009, pp. 6703--6725), (Skillen et al <>. CMAME, 2013, pp. 163--173)

Surface tension models are implemented from:

  • Morris surface tension_ (Morris et al. Internaltional Journal for Numerical Methods in Fluids, 2000, pp. 333--353)
  • Adami Surface tension formulation <>_ (Adami et al. JCP, 2010, pp. 5011--5021)

.. _Morris surface tension:<333::AID-FLD11>3.0.CO;2-7


Up-to-date details on how to install PySPH on Linux/OS X and Windows are available from here <>_.

If you wish to see a working build/test script please see our shippable.yml <>. For Windows platforms see the appveyor.yml <>.

Running the examples

You can verify the installation by exploring some examples. A fairly quick running example (taking about 20 seconds) would be the following::

$ pysph run elliptical_drop

This requires that Mayavi be installed. The saved output data can be viewed by running::

$ pysph view elliptical_drop_output/

A more interesting example would be a 2D dam-break example (this takes about 30 minutes in total to run)::

$ pysph run dam_break_2d

The solution can be viewed live by running (on another shell)::

$ pysph view

The generated output can also be viewed and the newly generated output files can be refreshed on the viewer UI.

A 3D version of the dam-break problem is also available, and may be run as::

$ pysph run dam_break_3d

This runs the 3D dam-break problem which is also a SPHERIC benchmark Test 2 <>_

.. figure:: :width: 550px :alt: Three-dimensional dam-break example

PySPH is more than a tool for wave-body interactions:::

$ pysph run cavity

This runs the driven cavity problem using the transport velocity formulation of Adami et al. The output directory cavity_output will also contain streamlines and other post-processed results after the simulation completes. For example the streamlines look like the following image:

.. figure:: :width: 550px :alt: Lid-driven-cavity example

If you want to use PySPH for elastic dynamics, you can try some of the examples from the pysph.examples.solid_mech package::

$ pysph run solid_mech.rings

Which runs the problem of the collision of two elastic rings:

.. figure:: :width: 550px :alt: Collision of two steel rings

The auto-generated code for the example resides in the directory ~/.pysph/source. A note of caution however, it's not for the faint hearted.

There are many more examples, they can be listed by simply running::

$ pysph run


PySPH is primarily developed at the Department of Aerospace Engineering, IIT Bombay <>_. We are grateful to IIT Bombay for their support. Our primary goal is to build a powerful SPH based tool for both application and research. We hope that this makes it easy to perform reproducible computational research.

To see the list of contributors the see github contributors page <>_

Some earlier developers not listed on the above are:

  • Pankaj Pandey (stress solver and improved load balancing, 2011)
  • Chandrashekhar Kaushik (original parallel and serial implementation in 2009)


If you have any questions or are running into any difficulties with PySPH, please email or post your questions on the pysph-users mailing list here:

Please also take a look at the PySPH issue tracker <>_.

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