A method is presented to solve two-phase problems involving a material quantity on an interface. The interface can be advected, stretched, and change topology, and material can be adsorbed to or desorbed from it. The method is based on the use of a diffuse interface framework, which allows a simple implementation using standard finite-difference or finite-element techniques. Here, finite-difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Interfacial flow with soluble surfactants is used as an example of the application of the method, and several test cases are presented demonstrating its accuracy and convergence.

中文翻译：

---

一种用于模拟可变形界面上材料量的传输、扩散和吸附/解吸的扩散界面方法

提出了一种解决涉及界面上材料量的两相问题的方法。界面可以平流、拉伸和改变拓扑结构，材料可以吸附到它或从中解吸。该方法基于使用漫反射接口框架，该框架允许使用标准有限差分或有限元技术进行简单实现。在这里，在块结构自适应网格上使用有限差分方法，并使用非线性多重网格方法求解得到的方程。使用可溶性表面活性剂的界面流动作为该方法应用的一个例子，并提供了几个测试案例来证明其准确性和收敛性。