极端条件下多介质流体力学的ALE-DG方法研究

多介质流体力学问题的数值模拟一直是计算流体力学中的热门研究领域，开展相关数值模拟方法研究具有重要的理论意义和实际应用价值。高温、高压、高密度比等极端条件下多介质流问题数值模拟的主要难点是：（1）如何精确地追踪物质界面处的流动。（2）高精度数值方法通常难以保物理性质（如保界、保正、无振荡等）。（3）求解单介质问题中获得巨大成功的高精度方法如WENO、DG等，直接应用于求解多介质流问题时存在物质界面分辨率不高的现象。针对这些难点，本项目将结合移动网格方法发展高分辨率ALE-DG方法，通过在物质界面附近加密网格以提高分辨率；设计和发展适用于多介质流问题的高精度、保物理性质限制器，最终获得极端条件下多介质流问题的高精度、高分辨率ALE-DG方法。

Numerical simulations of multi-component flows have been an active research topic in the computational fluid dynamics. It has great theoretical significance and practical application value in development of the related numerical simulation research. There exist three main difficulties in the computation of the multi-component flows under extreme conditions such as high temperature, high pressure, high density ratio and so on. The first one is how to track the material interface exactly. Secondly, it is a challenge to keep the physical properties (such as bound-preserving, positivity-preserving, non-oscillation) for the numerical results of high order methods. Thirdly, the high-order methods such as WENO and DG that have achieved great success in solving single-medium problems have low resolution on the material interface when directly used to solve multi-component flows. Therefore, a high resolution ALE-DG method will be developed in order to improve the resolution of the interface by clustering the mesh at interface in the project. At the same time, a high order limiter that can keep the physical properties will be proposed. Finally, a high order and high resolution ALE-DG method for multi-component flows under the extreme conditions will be developed.