In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid model, our new framework includes diffusion, friction, and surface tension. We show that surface tension can be added in an energy-conserving manner, and that diffusion and friction have a strictly dissipative effect on the energy.

中文翻译：

---

一维二维流体模型的能量稳定离散

在本文中，我们使用一维二维流体模型提出了一个完整的框架，用于通道中分层不可压缩流的能量稳定模拟。我们的新框架建立在早期关于基本双流体模型的节能工作的基础上，包括扩散、摩擦和表面张力。我们证明表面张力可以以能量守恒的方式添加，并且扩散和摩擦对能量具有严格的耗散效应。