Visual Simulation of Glazed Frost
Tomokazu Ishikawa ∗Yonghao Yue

Taichi Watanabe

Kei Iwasaki

Tokyo University of Technology

Columbia University / JSPS

Tokyo University of Technology

Wakayama University / UEI Research

Yoshinori Dobashi

Masanori Kakimoto

Kunio Kondo

Tomoyuki Nishita

Hokkaido University /JST CREST

Tokyo University of Technology

Tokyo University of Technology

UEI Research / Hiroshima Shudo University(a) 1,000 timesteps(b) 4,000 timesteps(c) 7,000 timesteps(d) 10,000 timesteps

Figure 1: Simulation and rendering results of generation of glazed frost.

1Introduction

Glazed frost is a crystal clear ice and formed from supercooled raindrops that freeze when they hit object surfaces such as the groundand branches of trees. Simulation methods for formation of ice
crystal, such as frost, on the surface of objects have been proposedby Kim et al. [Kim et al. 2004]. However, a supercooling state has
to be considered for simulating freezing rain, and fluid simulationis required for reproducing the effect of raindrops running down on
the ice surfaces. To our best knowledge, there has been no researchpresenting glazed frost by using a fluid simulation. We use the fluidsimulation based on FLIP method [Zhu and Bridson 2005]. Hence,
raindrops and obstacles are represented by particles which are used
to calculate the advection term, and the update of velocity field arecalculated by using grids except for advection term. We propose
a method to create an animation of glazed frost formation by taking into account the heat transfer between particles and the outsidegrids.

2

Our Simulation Method

The heat transfer from a particle to the grid is calculated by using
the FLIP method similar to the velocity field. The heat transfer between particles and grids is calculated according to the Fourier’slaw. Heat transfer is not calculated between particles, but calculated between grids. Heat transfer between grids is calculated bysolving heat transfer equations. After calculating heat transfer, theheat is distributed to the particles. To update the velocity field, atime step is set according to the CFL conditions. We employ theCrank-Nicolson method to solve the heat conduction equation (1).
∂T
∂2T
=a 2,(1)∂t∂xwhere T is a temperature, t is time, a is a thermal diffusivity andx is position vector. We decide the time to freeze by considering
the heat flux on the surface of the raindrop. Amount of heat flux is
calculated until freezing from the adhesion on the obstacles. The
speed for freezing is decided by the following sum of heat flux.
Q = Qs + Ql + Qf(2)It is known that the smaller the sum of flux Q in negative valueis, the faster the freezing speed is [Jones 1996]. So we use as thecondition for freezing or not whether the time integral of Qs and Ql∗ e-mail: ishikawatm@stf.teu.ac.jp

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SIGGRAPH 2013, July 21 – 25, 2013, Anaheim, California.
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ACM 978-1-4503-2261-4/13/07(a) Simulation result of glazed frost (b) Simulation result of glazed frost
taking into account the windof icicle shape

Figure 2: Simulation results of generating glazed frost.
which have negative value exceeds the required amount of heat Qf .
The integration calculation is limited to the time during the water
drop adheres on the obstacles, and we assume that, in case the water
drop does not adhere on the glazed frost or obstacles because of theinfluence of gravity or other raindrops, it does not freeze.

3 Results and Conclusion
Figure 2 shows two simulation results of generating glazed frost.
We can represent that supercooled water in some cases freezes instantly after collision, and in some cases gradually condensates in
the process of running down on objects. This is the result by considering heat flux and can be reproduced like this because of calculation of the time to freezing. By this effect, ice covering tree
branches, as typically seen in glazed frost, can be reproduced.
We have proposed a technique which is highly compatible for FLIP
method to solve the heat conduction equation and we have reproduced formation of glazed frost.

References
J ONES , K. F. 1996. Ice accretion in freezing rain. Tech. rep., DTICDocument.
K IM , T., H ENSON , M., AND L IN , M. C. 2004. A hybrid algorithm
for modeling ice formation. In Proceedings of the 2004 ACM
SIGGRAPH/Eurographics symposium on Computer animation,
SCA ’04, 305–314.
Z HU , Y., AND B RIDSON , R. 2005. Animating sand as a fluid.
ACM Trans. Graph. 24, 3 (July), 965–972.