We present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

翻译：我们提出了一种用于双材料拉格朗日流体动力学的新型方法，该方法将移位界面法（SIM）与高阶有限元法相结合。该方法基于精确（或尖锐）的材料界面表示，即利用材料界面的精确位置。界面由随材料速度移动的连续高阶有限元函数的零水平集表示。这一策略允许在弯曲单元内演化弯曲材料界面。通过将原始界面问题重构到位于真实界面附近的代理（近似）界面上，SIM避免了切割单元及其相关的实现、数值稳定性和矩阵条件数问题。利用泰勒展开修改原始界面条件以保持精度。我们通过一维、二维和三维的经典数值基准测试验证了所提算法的性能。