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pressure only applies in the normal direction). Since air pressure is zero
in our free surface model, we have that the pressure at the surface of the
water is
p
=
γ
∇·∇
φ.
It turns out that that
κ
=
φ
is termed the
mean curvature
of the sur-
face, a well-studied geometric quantity that measures how curved a surface
is.
∇·∇
This property has been incorporated into the ghost fluid pressure dis-
cretization by Kang et al. [Kang et al. 00]. Here, we take the ghost pressures
in the air so that we linearly interpolate to
γκ
at the point where
φ
=0,
rather than interpolating to zero. The mean curvature
κ
can easily be
estimated at that point by using the standard central difference for the
Laplacian, on trilinearly interpolated values of
φ
. Though not immediately
apparent, there is also a fairly severe stability restriction on the time step,
Δ
t
O
(Δ
x
3
/
2
ρ/γ
), since this is essentially an explicit treatment of the
surface-tension forces. Things are also rather more complicated at triple
junctions between water, solid, and air; we refer to Wang et al. [Wang
et al. 05] for more on this.
≤
