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The two-dimensional shallow-water equations (SWEs) are widely used to approximate flows for a wide range of rapidly (and slowly) varying free-surface flows, such as dam breaks, river flooding, and tidal flows including storm surge and wave overtopping causing inundation in estuaries and coastal regions. Grid-based solvers are now widely available. Although accurate and robust wetting and drying routines have been developed, grid-based solvers are limited in simulating multi-phase effects, most importantly flows with rapid distortion in flood modelling.
Here, the SPHysics numerical scheme, originally developed to solve Navier-Stokes Equations has been extended to shallow water equations.

Developers: Dr Renato Vacondio, Dr Benedict Rogers, Prof. Peter Stansby, Prof. Paolo Mignosa

Key code features:

  • Inlet-Outlet open boundaries
  • Modified Virtual Boundary Particle (MVBP) to represent solid boundaries
  • Particle splitting to provide finer resolution
  • Particle splitting and variable h
  • Water depth (or density evaluation)
  • Bed Topography Representation
  • Viscosity & Stabilisation terms

The code comes with the following test cases:

1-D Test Cases

  • 1-D Wet-bed Dam break
  • 1-D Dry-bed Dam break
  • 1-D Flow over hump with Inflow-Outflow

1 D DamBreak W250px.png

2-D Test Cases

  • 2-D Thacker Basin – rotating surface
  • Tsunami Wave with Inflow-Outflow Boundary Conditions
  • 2-D Dry-Bed Dam Break with Particle Splitting
  • 2-D CADAM Case with 45° Channel

2 D DamBreak paraview H200px.jpg

Released March 2013

SWE-SPHYSICS_1D_v1.0 March 2013

SWE-SPHYSICS_2D_v1.0 March 2013

Documentation of the shallow water equation (SWE) code:

SWE-SPHysics v1.0.00.pdf March 2013

How to reference: How to reference SWE-SPHysics.


  1. Vacondio R, Rogers B D, Stansby P K, Mignosa P. "A correction for balancing discontinuous bed slopes in two-dimensional smoothed particle hydrodynamics shallow water modeling". International Journal for Numerical Methods in Fluids. Vol. 71. Issue 7. pp 850-872. March. DOI: 10.1002/fld.3687, 2013.
  2. Vacondio R, Rogers B D, Stansby P K, Mignosa P. "Shallow water SPH for flooding with dynamic particle coalescing and splitting". Advances in Water Resources. Vol. 58. pp 10-23. August. DOI: 10.1016/j.advwatres.2013.04.007, 2013.
  3. Vacondio R., Rogers B.D., Stansby P.K.. In Press. "Accurate particle splitting for SPH in shallow water with shock capturing". International Journal for Numerical Methods in Fluids, Vol. 69. Issue 8. pp 1377-1410. DOI: 10.1002/fld.2646, 2012.
  4. Vacondio R., Rogers B.D., Stansby P.K. "Smoothed Particle Hydrodynamics: approximate zero-consistent 2-D boundary conditions and still shallow water tests". International Journal for Numerical Methods in Fluids, Vol. 69. Issue 1. pp 226-253. DOI: 10.1002/fld.2559, 2011.