The numerical simulation of surface tension is an active area of research in many different fields of application and has been attempted using a wide range of methods. Our contribution is the derivation and implementation of an implicit cohesion force based approach for the simulation of surface tension effects using the Smoothed Particle Hydrodynamics (SPH) method. We define a continuous formulation inspired by the properties of surface tension at the molecular scale which is spatially discretized using SPH. An adapted variant of the linearized backward Euler method is used for time discretization, which we also strongly couple with an implicit viscosity model. Finally, we extend our formulation with adhesion forces for interfaces with rigid objects.

Existing SPH approaches for surface tension in computer graphics are mostly based on explicit time integration, thereby lacking in stability for challenging settings. We compare our implicit surface tension method to these approaches and further evaluate our model on a wider variety of complex scenarios, showcasing its efficacy and versatility. Among others, these include but are not limited to simulations of a water crown, a dripping faucet, and a droplet toy.

表面张力的数值模拟是许多不同应用领域的一个活跃的研究领域，并且已经使用多种方法进行了尝试。我们的贡献是推导和实现基于隐式内聚力的方法，用于使用平滑粒子流体动力学 (SPH) 方法模拟表面张力效应。我们定义了一种连续配方，其灵感来自分子尺度表面张力的特性，并使用 SPH 进行空间离散。线性化后向欧拉方法的改进变体用于时间离散化，我们还与隐式粘度模型强耦合。最后，我们用与刚性物体的界面的粘附力来扩展我们的公式。

计算机图形学中现有的表面张力 SPH 方法大多基于显式时间积分，因此在具有挑战性的设置下缺乏稳定性。我们将隐式表面张力方法与这些方法进行比较，并在更广泛的复杂场景中进一步评估我们的模型，展示其有效性和多功能性。其中包括但不限于水冠、滴水水龙头和水滴玩具的模拟。