Accurate modeling of moving boundaries and interfaces is a difficulty present in many situations of computational mechanics. We use the eXtreme Mesh deformation approach (X-Mesh) to simulate the interaction between two immiscible flows using the finite element method, while maintaining an accurate and sharp description of the interface without remeshing. In this new approach, the mesh is locally deformed to conform to the interface at all times, which can result in degenerated elements. The surface tension between the two fluids is added by imposing the pressure jump condition at the interface, which, when combined with the X-Mesh framework, allows us to have an exactly sharp interface. If a numerical scheme fails to properly balance surface tension and pressure gradients, it leads to numerical artefacts called spurious or parasitic currents. The method presented here is well balanced and reduces such currents down to the level of machine precision.

翻译：动边界和界面的精确建模是计算力学中普遍存在的难题。我们采用极端网格变形方法（X-Mesh），结合有限元法模拟两种不混溶流体间的相互作用，在无需重新网格划分的前提下保持界面的精确锐利描述。该新方法通过局部变形网格使其始终与界面吻合，即便这可能导致单元退化。两流体间的表面张力通过在界面处施加压力跳跃条件来实现，与X-Mesh框架结合后，能获得完全尖锐的界面。若数值方案未能恰当平衡表面张力与压力梯度，将引发称为伪势流或寄生流的数值伪影。本文所提方法具有良好平衡性，能将此类电流降至机器精度量级。