We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying surface energies. These variations typically arise from surface energy dependence on temperature and/or concentration. Furthermore, since the surface energy is an interfacial property depending on the types of materials on either side of an interface, spatial variation is required for modeling the contact angle at the triple junction between a liquid, solid and surrounding air. Our discretization is based on the surface energy itself, rather than on the associated traction condition most commonly used for discretization with particle methods. Our energy based approach automatically captures surface gradients without the explicit need to resolve them as in traction condition based approaches. We include an implicit discretization of thermomechanical material coupling with a novel particle-based enforcement of Robin boundary conditions associated with convective heating. Lastly, we design a particle resampling approach needed to achieve perfect conservation of linear and angular momentum with AffineParticle-In-Cell (APIC) [Jiang et al. 2015]. We show that our approach enables implicit time stepping for complex behaviors like the Marangoni effect and hydrophobicity/hydrophilicity. We demonstrate the robustness and utility of our method by simulating materials that exhibit highly diverse degrees of surface tension and thermomechanical effects, such as water, wine and wax.

中文翻译：

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具有空间梯度的表面能的保持动量的隐式物质点方法

我们提出了一种新颖的材料点法（MPM）离散化由空间变化的表面能引起的表面张力。这些变化通常来自表面能对温度和/或浓度的依赖性。此外，由于表面能是界面性质，取决于界面两侧的材料类型，因此需要空间变化来模拟液体，固体和周围空气之间的三重连接处的接触角。我们的离散化是基于表面能本身，而不是基于粒子方法离散化最常使用的关联牵引条件。我们基于能量的方法可以自动捕获表面梯度，而无需像基于牵引条件的方法那样明确地解决它们。我们包括热力学材料的隐式离散化，以及与对流加热有关的基于Robin的新型Robin边界条件的基于粒子的强制执行。最后，我们设计了一种粒子重采样方法，该方法需要使用AffineParticle-In-Cell（APIC）来实现线性和角动量的完美守恒[Jiang等。2015]。我们证明了我们的方法可以使诸如Marangoni效应和疏水性/亲水性之类的复杂行为的隐式时间步进。我们通过模拟表现出高度不同程度的表面张力和热机械效应的材料（例如水，酒和蜡）来证明我们方法的鲁棒性和实用性。我们设计了一种粒子重采样方法，该方法需要使用AffineParticle-In-Cell（APIC）来实现线性和角动量的完美守恒[Jiang等。2015]。我们证明了我们的方法可以使诸如Marangoni效应和疏水性/亲水性之类的复杂行为的隐式时间步进。我们通过模拟表现出高度不同程度的表面张力和热机械效应的材料（例如水，酒和蜡）来证明我们方法的鲁棒性和实用性。我们设计了一种粒子重采样方法，该方法需要使用AffineParticle-In-Cell（APIC）来实现线性和角动量的完美守恒[Jiang等。2015]。我们证明了我们的方法可以使诸如Marangoni效应和疏水性/亲水性之类的复杂行为的隐式时间步进。我们通过模拟表现出高度不同程度的表面张力和热机械效应的材料（例如水，酒和蜡）来证明我们方法的鲁棒性和实用性。