We describe an Arbitrary-Lagrangian-Eulerian (ALE) method for the compressible Euler system with capillary force. The algorithm is split in two steps. First, the Lagrangian step is based on cell-centered schemes [9], [20], [46]. The surface tension force is discretized in order to exactly verify the Laplace law at the discrete level. We also provide a second-order spatial extension and a low-Mach correction, which do not break the well-balanced property of the scheme. The Lagrangian scheme is assessed on several problems, particularly on a linear Richtmyer-Meshkov instability which is the targeted application. The second step is the rezoning and remapping done thanks to a swept-region method using exact intersections near the interface. We use a Volume Of Fluid (VOF) method to track the interface. We describe the treatment of mixed-cells, and in particular the thermodynamics closure and the curvature calculation. The new scheme is used to investigate the influence of surface tension on a non-linear Richtmyer-Meshkov instability.

我们描述了具有毛细作用力的可压缩欧拉系统的任意拉格朗日欧拉（ALE）方法。该算法分为两个步骤。首先，拉格朗日步骤基于以细胞为中心的方案[9]，[20]，[46]。将表面张力离散化，以便在离散水平上精确验证拉普拉斯定律。我们还提供了二阶空间扩展和低马赫数校正，这不会破坏该方案的均衡特性。拉格朗日方案是针对几个问题进行评估的，尤其是针对线性Richtmyer-Meshkov不稳定性这一目标应用。第二步是通过使用靠近接口的精确交点的扫掠区域方法完成了重新分区和重新映射。我们使用液体体积（VOF）方法来跟踪界面。我们描述了混合细胞的治疗，尤其是热力学闭合和曲率计算。该新方案用于研究表面张力对非线性Richtmyer-Meshkov不稳定性的影响。