FPM Simulations of a High-Speed Water Jet Validation with CFD and Experimental Results

  • Christian VessazEmail author
  • Ebrahim Jahanbakhsh
  • François Avellan
Part of the Springer Hydrogeology book series (SPRINGERHYDRO)


The present chapter reports the development of finite particle method (FPM) in the framework of a high-speed water jet simulation. The FPM kernel is used to improve the consistency of standard SPH for non-uniform particle distribution. The time integration is performed with a modified Verlet scheme. At the end of each time step, a particle shifting method is applied to mitigate the particle clustering issue by restoring a uniform particle spacing. The influence of particle spacing and maximum CFL number are investigated in the case of a high-speed water jet impinging on a flat plate. The influence of the impinging angle is analyzed for three different angles: 90°, 60°, and 30°. The time history of the pressure coefficient is recorded on the flat plate to compare the FPM simulations with available measurements and grid-based CFD simulations. The validation of the results is based on the comparison of the averaged pressure coefficient profile as well as the comparison of the free-surface location for the three different impinging angles.


Smoothed particle hydrodynamics Finite particle method Impinging jet Particle shifting 


\( c \)

Color function [–]

\( C \)

Absolute velocity [m s−1]

\( \overrightarrow {C} \)

Absolute velocity vector [m s−1]

\( f \)

Arbitrary function [–]

\( h \)

Smoothing length [m]

\( m \)

Mass [kg]

\( \overrightarrow {n} \)

Normal vector [–]

\( N \)

Number of particle [–]

\( p \)

Static pressure [Pa]

\( \overrightarrow {R} \)

Shifting vector [m]

\( t \)

Time [s]

\( V \)

Volume [m3]

\( W \)

Kernel [m−3]

\( \tilde{W} \)

Renormalized kernel [m−3]

\( X,Y,Z \)

Cartesian coordinate [m]

\( \rho \)

Density [kg m−3]

\( \alpha ,\beta \)

Cartesian coord

\( (i),(j) \)


\(\text{max} \)

Maximum value

\( {\text{ref}} \)

Reference value



The authors would like to thank particularly the Ark, the foundation for innovation of Valais Canton, which is financially supporting within the Project HydroVS the research leading to the results presented in this chapter and ALSTOM Hydro for their financial support and technical assistance to the development of the SPHEROS software.


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Copyright information

© Springer Science+Business Media Singapore 2014

Authors and Affiliations

  • Christian Vessaz
    • 1
    Email author
  • Ebrahim Jahanbakhsh
    • 1
  • François Avellan
    • 1
  1. 1.EPFL—LMHLausanneSwitzerland

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