SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page A1558-A1581, January 2020.
Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows, and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas dynamics, that acceleration is a key element in the description of the motion and should be incorporated into the design of a moving boundary tracking method. Technically, the resolution of the accelerated piston problem boils down to a one-sided generalized Riemann problem solver, which is taken as the building block for constructing schemes with high order accuracy in both space and time. In this paper we take this into account, together with the cell-merging approach, to propose a new family of high order accurate moving boundary tracking methods and verify its performance through one- and two-dimensional test problems, along with accuracy analysis.

中文翻译：

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可压缩流体的加速活塞问题和高阶运动边界跟踪方法

SIAM科学计算杂志，第42卷，第3期，第A1558-A1581页，2020年1月。
可靠地跟踪运动边界对于模拟可压缩流体流动很重要，并且在文献中有很多贡献。从经典的活塞问题（气体动力学中的典型运动边界问题）我们认识到，加速度是运动描述中的关键要素，应将其纳入运动边界跟踪方法的设计中。从技术上讲，加速活塞问题的解决归结为一个单侧广义Riemann问题求解器，该求解器被用作构建时空上具有高阶精度的方案的基础。在本文中，我们将其与单元格合并方法一起考虑在内，