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Free surface tension in incompressible smoothed particle hydrodynamcis (ISPH)

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A Letter to this article was published on 28 December 2021


In this work a Dirichlet pressure boundary condition for incompressible Smoothed Particle Hydrodynamics (SPH) is presented for free surfaces under surface tension. These free surfaces occur when the surrounding phase in simulations is neglected for computational reasons while the effects of the surface tension shall remain. We demonstrate capabilities of the boundary condition by comparing it to an approach from the literature. The simulations show that our approach provides a higher stability to the free surface, being capable of capturing static and transient processes as much as bubble coalescence. Furthermore a new approach is presented to compute the curvature more exactly for three-dimensional cases in order to stabilize the simulation, which is applicable for weakly compressible SPH and incompressible SPH simulations.

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Correspondence to Jan-Philipp Fürstenau.

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1.1 Square bubble

See Fig. 17.

Fig. 17
figure 17

Plots of the square bubble test case after 0.01, 0.03, 0.05, 0.07, 0.09   s, simulated with our own approach with the lowest and highest resolution [right] and simulated with the approach according to Hirschler with the lowest and the highest resolution [right]

1.2 3D bubble collision

See Fig. 18.

Fig. 18
figure 18

Plots of the three dimensional bubble shapes for the centric bubble collision at \(\tau = 0, 0.3125, 0.725, 1.3125\) and 2 [left] and for the eccentric bubble collision at \(\tau = 0, 0.375, 0.5625, 0.875\) and 2.8125 [right]

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Fürstenau, JP., Weißenfels, C. & Wriggers, P. Free surface tension in incompressible smoothed particle hydrodynamcis (ISPH). Comput Mech 65, 487–502 (2020).

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