Accelerated Piston Problem and High Order Moving Boundary Tracking Method for Compressible Fluid Flows
Accelerated Piston Problem and High Order Moving Boundary Tracking Method for Compressible Fluid Flows
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DOI：
10.1137/19m1266599
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发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
Zhifang Du;Jiequan Li
中科院分区：
文献类型：
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作者：
Zhifang Du;Jiequan Li
运动边界的可靠跟踪对于可压缩流体流动的模拟是非常重要的，在文献中有很多的贡献。我们认识到，从经典的活塞问题，在气体动力学中的一个典型的移动边界问题，加速度是一个关键因素的运动的描述，它应该被纳入到一个移动边界跟踪（MBT）方法的设计。从技术上讲，加速活塞问题的解决归结为一个片面的广义黎曼问题（GRP）求解器，这是作为构建块构造格式在空间和时间上的高阶精度。在本文中，我们考虑到这一点，连同细胞合并的方法，提出了一个新的家庭的高阶精确的移动边界跟踪方法，并验证其性能，通过一维和二维的测试问题，沿着精度分析。
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 the acceleration is a key element in the description of the motion and it should be incorporated into the design of a moving boundary tracking (MBT) method. Technically, the resolution of the accelerated piston problem boils down to a one-sided generalized Riemann problem (GRP) solver, which is taken as the building block to construct schemes with the high order accuracy both in 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.