We propose and analyze in this paper a new derivation of a phase-field model to approximate inhomogeneous multiphase perimeters. It is based on suitable decompositions of perimeters under some embeddability condition which allows not only an explicit derivation of the model from the surface tensions, but also gives rise to a Γ-convergence result. We propose a simple and robust scheme to simulate the gradient flow of the approximating energy. We illustrate the efficiency of our approach with a series of numerical simulations in 2D and 3D, and we address in particular the dynamics of droplets evolving on a fixed solid.

中文翻译：

---

非均匀最小分区的新相场模型及其在液滴动力学中的应用

我们在本文中提出并分析了相场模型的新推导，以近似非均匀多相周长。它基于在某些可嵌入性条件下对周长进行适当的分解，这不仅允许从表面张力明确推导模型，而且还产生 Γ-收敛结果。我们提出了一种简单而稳健的方案来模拟近似能量的梯度流。我们通过一系列 2D 和 3D 数值模拟来说明我们方法的效率，我们特别解决了液滴在固定固体上演化的动力学问题。