State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou, Zhejiang, China.
IEEE Trans Vis Comput Graph. 2012 Aug;18(8):1281-9. doi: 10.1109/TVCG.2011.141.
A water drop behaves differently from a large water body because of its strong viscosity and surface tension under the small scale. Surface tension causes the motion of a water drop to be largely determined by its boundary surface. Meanwhile, viscosity makes the interior of a water drop less relevant to its motion, as the smooth velocity field can be well approximated by an interpolation of the velocity on the boundary. Consequently, we propose a fast deformable surface model to realistically animate water drops and their flowing behaviors on solid surfaces. Our system efficiently simulates water drop motions in a Lagrangian fashion, by reducing 3D fluid dynamics over the whole liquid volume to a deformable surface model. In each time step, the model uses an implicit mean curvature flow operator to produce surface tension effects, a contact angle operator to change droplet shapes on solid surfaces, and a set of mesh connectivity updates to handle topological changes and improve mesh quality over time. Our numerical experiments demonstrate a variety of physically plausible water drop phenomena at a real-time rate, including capillary waves when water drops collide, pinch-off of water jets, and droplets flowing over solid materials. The whole system performs orders-of-magnitude faster than existing simulation approaches that generate comparable water drop effects.
由于在小尺度下具有较强的粘性和表面张力，水滴的行为不同于大体积的水体。表面张力使得水滴的运动主要由其边界表面决定。同时，由于粘性使得水滴内部对其运动的影响较小，因为可以通过边界上的速度插值来很好地近似平滑速度场。因此，我们提出了一种快速变形表面模型，以真实地动画化水滴及其在固体表面上的流动行为。我们的系统通过将整个液体体积的 3D 流体动力学简化为一个变形表面模型，以拉格朗日方式高效地模拟水滴运动。在每个时间步，模型使用隐式平均曲率流算子来产生表面张力效应，使用接触角算子来改变固体表面上的液滴形状，并使用一组网格连接更新来处理拓扑变化和随时间提高网格质量。我们的数值实验以实时速率展示了各种物理上合理的水滴现象，包括水滴碰撞时的毛细波、射流的收缩以及液滴在固体材料上的流动。整个系统的性能比生成可比水滴效果的现有模拟方法快几个数量级。
