TY - GEN
T1 - Functional thin films on surfaces
AU - Azencot, Omri
AU - Vantzos, Orestis
AU - Wardetzky, Max
AU - Rumpf, Martin
AU - Ben-Chen, Mirela
N1 - Publisher Copyright: © 2015 ACM.
PY - 2015/8/7
Y1 - 2015/8/7
N2 - The motion of a thin viscous film of fluid on a curved surface exhibits many intricate visual phenomena, which are challenging to simulate using existing techniques. A possible alternative is to use a reduced model, involving only the temporal evolution of the mass density of the film on the surface. However, in this model, the motion is governed by a fourth-order nonlinear PDE, which involves geometric quantities such as the curvature of the underlying surface, and is therefore difficult to discretize. Inspired by a recent variational formulation for this problem on smooth surfaces, we present a corresponding model for triangle meshes. We provide a discretization for the curvature and advection operators which leads to an efficient and stable numerical scheme, requires a single sparse linear solve per time step, and exactly preserves the total volume of the fluid. We validate our method by qualitatively comparing to known results from the literature, and demonstrate various intricate effects achievable by our method, such as droplet formation, evaporation, droplets interaction and viscous fingering.
AB - The motion of a thin viscous film of fluid on a curved surface exhibits many intricate visual phenomena, which are challenging to simulate using existing techniques. A possible alternative is to use a reduced model, involving only the temporal evolution of the mass density of the film on the surface. However, in this model, the motion is governed by a fourth-order nonlinear PDE, which involves geometric quantities such as the curvature of the underlying surface, and is therefore difficult to discretize. Inspired by a recent variational formulation for this problem on smooth surfaces, we present a corresponding model for triangle meshes. We provide a discretization for the curvature and advection operators which leads to an efficient and stable numerical scheme, requires a single sparse linear solve per time step, and exactly preserves the total volume of the fluid. We validate our method by qualitatively comparing to known results from the literature, and demonstrate various intricate effects achievable by our method, such as droplet formation, evaporation, droplets interaction and viscous fingering.
KW - Flows on curved surfaces
KW - Free surface flows
KW - Thin films
UR - http://www.scopus.com/inward/record.url?scp=84956631469&partnerID=8YFLogxK
U2 - https://doi.org/10.1145/2786784.2786793
DO - https://doi.org/10.1145/2786784.2786793
M3 - Conference contribution
T3 - Proceedings - SCA 2015: 14th ACM SIGGRAPH / Eurographics Symposium on Computer Animation
SP - 137
EP - 146
BT - Proceedings - SCA 2015
A2 - Spencer, Stephen N.
T2 - 14th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, SCA 2015
Y2 - 7 August 2015 through 9 August 2015
ER -